Using the properties of half-life we calculate that approximately 22.33 grams of radium will be present after 720 years.
The half-life of radioactive element radium = 1690 years.
Time = 720 years
the formula for calculating half life is given by:
[tex]N(t)&=N_{0}\left({\frac {1}{2}}\right)^{\frac {t}{t_{1/2}}[/tex]
Now we substitute the values to find the N(t) which is the amount of radium left after 720 years.
t = 720
half life = 1690
N₀ (initial mass) = 30gm
[tex]N(t)&=30\left({\frac {1}{2}}\right)^{\frac {720}{1690}[/tex]
N(t) = 22.329 gm
N(t) ≈ 22.33 gm
The half-life of a substance is the amount of time required for it to reach that point. The phrase is widely used in nuclear physics to describe how quickly unstable atoms decay radioactively or how long stable atoms remain.
Additionally, a broader definition of the term is used to characterize any exponential decay (or, very infrequently, nonexponential decay). For instance, a term used in the medical sciences is the biological half-life of drugs and other compounds in the human body.
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Solve the linear programming problem
After solving the linear programming problem, we get the answer as 250.
What is linear programming?
When a linear function is exposed to multiple restrictions, linear programming maximizes or minimizes the function. This method determines the best way to use the resources that are currently available and aids managers in using the process to make decisions about the most efficient use of scarce resources, such as money, time, materials, and machinery. Linear programming has been useful for guiding quantitative decisions in business planning, industrial engineering, and—to a lesser extent—in the social and physical sciences.
Solution explained:
[tex]\left \{ {{2x + y = 12} \atop {x + y = 7}} \right.[/tex] x=3, y=4 P(3,4) Coordinates of the solution point
[tex]\left \{ {{x + y = 7} \atop {x + 2y = 10}} \right.[/tex] x=4, y=3 Q(4,3)
Coordinates of the simultaneous eqs.
[tex]\left \{ {{2x + y = 12} \atop {x + 2y = 10}} \right.[/tex] x=14/3, y=8/3
Putting the values of x and y in the equation P = 30x + 40y and calculating we get
P(P) = 250, P(Q) = 240, P(R) = 246.67
So, the answer is 250
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c. Write two different expressions you could use to represent the
combined area of the Description and Small Diagram sections.
What information about the combined area does each
expression show
500
Step-by-step explanation:
research
P(H)=
P(T)=
let me know if you know how to do this
Answer:
Step-by-step explanation:
they are asking for probability
so they want to know, what's the probability of getting a "heads" on a coin toss. What do you think it is? You probably know this intuitively.
P(H) = ?
P(T) = ?
They are asking for fractions, so just say what you already know to be how often you'll get a "heads" in words, then just make that a fraction. :)
Find three even numbers less than 400, each of which can be expressed as a sum of consecutive positive odd numbers in at least six different ways.
Answer:
394, 396 and 398
Step-by-step explanation:
Which inequality is represented by the graph?
Answer:
x<1
Step-by-step explanation:
since the circle is not filled it will not be equal to one but either grater or equal to it
Since the arrow is pointing left than x is less than 1
x<1
hopes this helps please mark brainliest
Please show your work:
-5/2(8a - 2b) =
[tex]-\frac{5}{2} (8a - 2b) = ...[/tex] the answer for this question is zero (0)
How can the answer is zero?
The first thing that we should do is simplify questions.
[tex]-\frac{5}{2} (8a - 2b) \\= -\frac{5}{2} (8a) + -\frac{5}{2} (- 2b)\\= - 20a + 5b[/tex]
After that, we will search for "a" and "b" to solve the question. For me, i will search for "b" first.
[tex]- 20a + 5b \\5b = 20a\\b = \frac{20}{5} a\\b = 4a[/tex]
Next step is find the "a" by enter the "b" into the same question.
[tex]- 20a + 5b =\\20a = 5b\\20a = 5 (4a)\\20a = 20a\\a = 1[/tex]
After we find the "a" and "b", the next step is to enter it into the main question to find the right answer.
[tex]-\frac{5}{2} (8a - 2b) \\= -\frac{5}{2} (8a - 2[4a]) \\= -\frac{5}{2} (8a) + -\frac{5}{2} (-8a)\\= - 4a + 4a\\= -4 (1) + 4 (1)\\= -4 + 4\\= 0[/tex]
So, the answer is zero (0).
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Answer:
[tex] - 20a + 5b[/tex]
Step-by-step explanation:
[tex] - \frac{5}{2} (8a - 2b)[/tex]
[tex] - \frac{5}{2} (8a) - \frac{5}{2} ( - 2b)[/tex]
[tex] - 20a + 5b[/tex]
Please HELP..
Our class is studying the effects of mindfulness on mental health. To help with data collection, we will have the support of ten grade 9, eleven grade 10, twelve grade 11 and thirteen grade 12 students. Showing your calculations,how many different groups of 12 volunteers can we make if:
a) the group must have the same number of students from each grade?
b) the group must have at least two grade 9 students? [2A]
c) the group must have James and Lucy (both grade 11 students) in it? [2A]
The number of groups, using the combination formula, for each case, is given as follows:
a) Same number of students from each grade: 1,245,816,000
b) At least two grade nine students: 31,650,886,995.
c) James and Lucy are in it: 2,481,256,778.
How to obtain the number of groups?The number of groups is obtained for the three cases using the combination formula, as the order in which the students are chosen is not important.
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, obtained by the following formula, involving factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
For item a, the same number of students is taken from each class, hence 3 students are taken from each class, as 12 students are taken from 4 classes, hence 12/4 = 3.
Hence the number of groups, considering the number of students in each class, is of:
[tex]C_{10,3}C_{11,3}C_{12,3}C_{13,3} = \frac{10!}{7!3!} \times \frac{11!}{8!3!} \times \frac{12!}{9!3!} \times \frac{13!}{10!3!} = 120 \times 165 \times 220 \times 286 = 1,245,816,000[/tex]
For item b, we use complementary events, first obtaining the total number of students that can be taken, and then removing the combinations that do not have at least two grade nine students.
The total number of groups is obtained as follows:
[tex]C_{46,12} = \frac{46!}{12!34!} = 38,910,617,655[/tex]
(as there are 10 + 11 + 12 + 13 = 46 students, and 12 are taken).
The number of groups with none students from grade 9 is:
[tex]C_{36,12} = \frac{36!}{12!24!} = 1,251,677,700[/tex]
(removing the 10 students from grade 9).
The number of groups with one student from grade 9 is:
[tex]C_{10,1}C_{36,11} = 10 \times \frac{36!}{11!25!} = 6,008,052,960[/tex]
(one from grade 10 and the remaining from the other classes).
This the number of groups with at least two grade 9 students is calculated as follows:
38,910,617,655 - (1,251,677,700 + 6,008,052,960) = 31,650,886,995.
For item c, considering Jamie and Lucy in it, the remaining 10 students are taken from a set containing the 44 remaining students, hence:
[tex]C_{44,10} = \frac{44!}{10!34!} = 2,481,256,778[/tex]
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3 years is to 4 , , ,
Solve for x
-21 = -7x
Simplify your answer as much as possible.
Answer:
Step-by-step explanation:
-21 = -7x
-21 divided by -7 = -7 divided by -7
3=x
The temperature gauge in your car records the temperature to be 27°C. What is that temperature to the nearest degree Fahrenheit?
===============================================
Work Shown:
F = (9/5)*C + 32
F = (9/5)*27 + 32
F = 80.6
F = 81
Side note: 9/5 = 1.8
Answer:
81 degrees Fahrenheit.
Step-by-step explanation:
Using the standard Fahrenheit-Celsius conversion formula.
27 * 9/5 = 48.6.
48.6 + 32 = 80.6.
Rounded to 81.
Therefore 81 degrees Fahrenheit.
or Each morning, Sleepwell Hotel offers its guests a free continental breakfast with pastries and orange juice. Last year, the hotel served a total of 490 gallons of orange juice to its guests. This year, the hotel served 931 gallons of orange juice. What is the percent of increase in the amount of orange juice served yearly?
Answer:
90% increase
Step-by-step explanation:
490-931=-441
931-490=441
931/490=1.9
therefore, 190% of 441=931
Answer:90% increase
A survey of 780 was conducted while visiting Sonoma county on vacation. Each person was asked if they drank wine on their trip. 532 people responded "Yes".
What proportion of people did NOT drink wine in the survey? Round your answer to two decimal places.
Answer:
0.32
Step-by-step explanation:
[tex]\frac{780-532}{780}[/tex] = [tex]\frac{248}{780}[/tex] = 0.32 Rounded.
A five-gallon tank full of water starts draining at t = 0 at a rate of 1/(1 + t) gallons per hour. How long until the tank is empty?
1. It will take 5 hours for the five-gallon tank full of water to become empty at the drainage rate of 1/(1 + t) gallons per hour.
2. A correct setup of the equation problem above in terms of function is D. None of these will give the correct solution.
What is an equation?An equation is a mathematical statement that shows that two or more mathematical expressions share equality or are equivalent.
Functions, which are mathematical expressions involving one or more variables known as domain (or the independent variable) and range (or the dependent variable), using the equation symbol to show that two expressions are equal.
Drainage rate per hour = 1/(1 + t) gallons
t = 0
The capacity of the tank = 5 gallons
1/(1 + t) gallons
= 1/(1 + 0) gallons
= 1/1 gallons
= 1 gallon per hour
Since the tank is 5 gallons, it will take = 5 hours (5/1)
Thus, based on the drainage equation rate, the five-gallon tank will empty in 5 hours.
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4.8 is what percent of 12
Answer:
40%
Step-by-step explanation:
4.8 * 100 = 480
480 / 12 = 40
= 40%
I hope this helps.
Carter shared his post with 10 friends, who each share with only 2 people each day. Carter shared his post with 10 friends, who each share with only 2 people each day.
write an exponential function to represent the spread of carters social media post.
The exponential function will be equal to y = 20ˣ.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Carter shared his post with 10 friends, who each share with only 2 people each day.
The exponential function will be written as,
y = abˣ
y = 10(2)ˣ
y = 20ˣ
Therefore, the exponential function will be equal to y = 20ˣ.
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Answer:
f(x) = 10(2)^x
Step-by-step explanation:
Rule for solving: The first number is the first part of the equation, and the second number is in parenthesis.
Which of the following is an example of the identity property of 1?
1.11(0)=0
0+2 4/5=2 4/5
11/15(1)=11/15
3-2=1
Answer:
i think third answer is write
A group of 15 athletes participated in a golf competition. Their scores are below:
Score (points) 1 2 3 4 5
Number of Athletes 1 2 3 4 5
Would a line plot or a histogram best represent the data presented here? Why?
Histogram, because a large number of scores are reported as ranges
Histogram, because a small number of scores are reported individually
Line plot, because a large number of scores are reported as ranges
Line plot, because a small number of scores are reported individually
The solution is Option D.
Line plot , because a small number of scores are reported individually
What is a line plot?
A line plot is a graph that shows data as points or check marks above a number line, indicating the frequency of each value.
If we need to compare two different groups , a line chart does have one advantage for visualizing frequency distributions
Given data ,
Total number of athletes = 15
The score points of athletes = { 1 , 2 , 3 , 4 , 5 }
The number of athletes = { 1 , 2 , 3 , 4 , 5 }
The best option to plot the line plot because of the data set
The line plot , a data visualization chart that more accurately represents the small data set, is chosen.
And , to begin, unlike a line plot , a histogram involves data ranges or intervals. A line plot uses a dot to represent each observation, whereas a histogram divides the data into intervals, masking the identity of each observation
Furthermore, because line plots are one of the simplest statistical plots, they are better suited to small to moderate-sized data sets. They are more effective than histograms at highlighting clusters and gaps
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Answer:D
Step-by-step explanation:
Apply the distributive property to the following expression: 2n (5m -1)
I need HELP!! ASAP!!
By using the distributive property, we will rewrite the expression as:
2n*(5m -1) = 10*n*m - 2n
How to apply the distributive property?
The distributive property of the multiplication says that the product:
A*(B + C)
Can be rewritten as:
A*(B + C) = A*B + A*C
So we are "distributing" the product.
In this case, we have the expression:
2n*(5m - 1)
If we apply the distributive property, then we will get:
2n*(5m - 1) = (2n)*(5m) + (2n)*(-1)
Now we can simplify this expression to get:
(2n)*(5m) + (2n)*(-1) = 10*n*m - 2n
That is what we wanted to get.
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How far up the wall does the ladder reach (round your answer to the nearest tenth) enter only the numerical answer no label
Answer: 8.7m
Step-by-step explanation:
We can use the Pythagorean theorem to solve this,
[tex]a^2+b^2 = c^2[/tex]
We have a (5m) and c (10m) so we're looking for b.
We can rearrange the equation to find b into,
[tex]b^2 = c^2-a^2[/tex]
[tex]b^2=10^2-5^2[/tex]
[tex]b^2 = 100-25[/tex]
[tex]b^2=75[/tex]
[tex]b=8.66025404[/tex]
Rounded to the nearest tenth is 8.7m.
For a pole-vaulter in training, the height the athelete will be able to pole-vault after t months of training is given by
H(t) = 17-11e^-0.02t
After how many months will she be able to vault 11 ft?
The number of months after which she will be able to vault 11 feet is 30 months.
For a pole-vaulter in training, the height the athlete will be able to pole-vault after t months of training is given by a mathematical formula. The formula is given below.
H(t) = 17 - 11e^(-0.02t)
We need to find the number of months after which she will be able to vault a height equal to 11 feet. We will substitute the value of height in the given equation.
11 = 17 - 11e^(-0.02t)
11e^(-0.02t) = 17 - 11
11e^(-0.02t) = 6
e^(-0.02t) = 6/11
Now, we will take the natural logarithm on both sides of the equation.
-0.02t = -0.606
t = 0.606/0.02
t = 30.3
Thus, she will be able to vault 11 feet in approximately 30 months.
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See picture-multiple choice.
From the given graph the correct statement is option (B) " As x approaches - ∞, f(x) approaches - ∞ and x approaches + ∞, f(x) approaches - ∞
From the given graph
The x axis represents the values of x, and the y axis represents the value of y
From the graph,
When the value of x moves from 0 to - ∞, then the value of f(x) is moves from 0 to - ∞
Similarly, when the value of x moves from 0 to ∞, the the value of f(x) is increased to positive values and then decreased to - ∞.
Hence, from the given graph the correct statement is option (B) " As x approaches - ∞, f(x) approaches - ∞ and x approaches + ∞, f(x) approaches - ∞
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The height of a triangle is 8 centimeters greater than the base. The area of the triangle is 356.5 square centimeters. Find the length of the base and the height of the triangle.
The lengths of the base of the triangle are 31cm while the height of the triangle is 39cm
A triangle is a polygon that has 3 sides, three angles and three vertices whose sum of angles equal to 180 degrees.
How to find the lengths and height of a triangle?
from the statement,
h=b+8Area = 256.5 square centimetersA=1/2bh
A=1/2 xbx(8+b)
cross multiplying,
713 = 8b+b²
rearrange the function
b²+8b-713=0
Simplyfying the equation,
(b²+23b)-(31b-713)=0
b(b+23)-31(b+23)=0
b-31=0 or b+23 =0
b=31 or b=-23
length cannot be negative. therefore base = 31cm
Recall the h= b+8
this implies that h=8+31
h=39cm
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In QRS, RS QR and m/Q = 46°. Find m/S.
In triangle QRS, ∠S=67⁰ if ∠R =∠S and ∠Q=46⁰
What is meant by an angle?An angle is a figure in Euclidean geometry made up of two rays that share a vertex, or common endpoint, and are referred to as the sides of the angle. Two planes intersecting at an angle also produces an angle.
A measure of an angle or of a rotation is also referred to as an angle. The ratio of a circular arc's length to radius is known as this quantity. When it comes to a geometric angle, the arc's vertex serves as its center and its sides as its boundaries. When there is a rotation, the arc is defined by the rotation's image and any other point other than the rotation's center.
In triangle QRS,
And from the figure,
∠R=∠S
Therefore,
∠R+∠S+∠Q=180⁰
2∠S+46⁰=180⁰
2∠S=134⁰
∠S=67⁰
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A shelf and bracket are shown below. The shelf is
perpendicular to the wall.
Note: The figures is not drawn to scale
What angle (x), in degrees, does the bracket make with the wall?
60 degrees is he angles which are made by bracket with the wall
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The shelf is perpendicular to the wall.
The shelf makes an angle of 90 degree to the wall because when the shelf is perpendicular then the wall and shelf should be ninety degrees.
From the shelf edge to wall there creates an angle x.
We need to find the angle x.
As it forms a right angle triangle one angle is 90 degrees and the other angles should be 60 degrees and 60 degrees.
Hence 60 degrees is the angles which are made by bracket with the wall
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a polytunnel for growing plants has a semi circular opening. the diameter of the opening is 14 feet and the length is 10 feet. the air inside the polytunnel needs to be heated to grow the plants. what is the volume of air inside the polytunnel in cubic feet.
anyone know the answer please it's for a level 2 booklet
Answer:140
Step-by-step explanation:
14 x 10=
Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 33 miles. If the two airplanes are 55 miles apart, how far has the eastbound airplane traveled?
The eastbound airplane traveled 44 miles far.
Given:
Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 33 miles. If the two airplanes are 55 miles apart.
Let x be the eastbound airplane traveled.
we know that,
north and east direction are perpendicular and with hypotenuse 55 miles it forms a right angle triangle with side = 33 miles.
According to pythagorean theorem:
[tex]33^2+x^2=55^2[/tex]
[tex]x^{2} =55^2-33^2[/tex]
= 3025 - 1089
x = [tex]\sqrt{1936}[/tex]
= 44 miles.
Therefore The eastbound airplane traveled 44 miles far.
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solve the equation for y
5x+7y=35
Answer:
[tex]y=-\frac{5}{7}+5[/tex]
Step-by-step explanation:
the goal is to isolate y on one side
5x+7y=35
-5x. -5x
7y=35-5x
/7. /7. /7
y=-5/7x+5
Hopes this helps please mark brainliest
Stefanie bought a package of pencils for \$ 1.75$1.75 and some erasers that cost \$ 0.25\$0.25 each. She paid a total of \$ 4.25$4.25 for these items, before tax
Exactly how many erasers did Stefanie buy?
The number of eraser Stefanie bought is 10.
How to find the number of eraser she bought?Stefanie bought a package of pencils for $1.75 and some erasers that cost $0.25 each. She paid a total of $4.25 for these items, before tax.
Therefore, the number of eraser Stefanie bought can be calculated as follows;
let
x = number of eraser bought
Therefore,
4.25 = 1.75 + 0.25x
subtract 1,75 from both sides of the equation
4.25 - 1.75 = 1.75 - 1.75 + 0.25x
2.5 = 0.25x
divide both sides by 0.25
x = 2.5 / 0.25
x = 10
Therefore,
number of eraser = 10
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onsider the following equation:
3|x+3|−12=0
Step 1 of 4: Rewrite the equation above in standard form and determine if there is a solution.
The value of x in the following equation: 3|x+3|−12=0 is -7 and 1
The equation is 3|x+3|−12=0
We need to rewite the equation above in standard form
The modulus function can be positive and negative
Considering it to be negative,
the equation is
3((-1)(x + 3) - 12
3(-x - 3) - 12
-3x - 9 - 12 = 0
3x + 21 = 0
3x = -21
x = -7
3(x + 3) - 12
3x + 9 - 12
3x - 3 = 0
3x = 3
x = 1
Therefore, the value of x in the following equation: 3|x+3|−12=0 is -7 and 1
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will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest
Answer:should be 40 because WxL=area soooo try 40
Step-by-step explanation:
Answer:
Area = width x height
Area = 4cm x 10cm
Area = 40 cm²