A 1200 gram sample of radioactive matter will completely decay (be undetectable) in 10 hours. There exists a set of ordered pairs (t. m), where t is the amount of time in hours that the substance has been decaying, and m is the mass in grams that has decayed.
If t≥ 0, what is the range of m?
Answers
Using it's concept, the range of the function is given as follows:
0 ≤ m ≤ 1200.
What is the range of a function?The range of a function is the set that contains all possible output values for the function.
For this problem, we have to consider these two bullet points next, considering the mass is the output value of the function.
The smallest possible mass for the substance is of 0 grams, as after the substance decays to 0 grams, it will not assume a negative value, it will just disappear.The greatest possible mass for the substance is the initial mass of 1200 grams, as the substance does not adquire mass with time, it just loses it.Considering these masses, the range of the function is given as follows:
0 ≤ m ≤ 1200.
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Related Questions
I need this answered please
Answers
Answer: 1. x-8
2. x/8
3. x squared
4. 4x
When they say "a number" that just means "x".
9)
Find the length of
the hypotenuse of
the right triangle.
6 ft
6 ft
Answers
The hypotenuse of the right triangle is found to be 6√2 ft.
What is defined as the Pythagorean theorem?A right triangle contains a single 90 angle within it, which is known as a right angle.The hypotenuse is really the side straight from the right angle in a right triangle. It is the only side of a triangle that does not form a right angle.The Pythagorean Theorem describes the relationship between the sides of a right triangle, where c represents the hypotenuse and a and b represent the sides that form the right angle.The formula is as follows:
H² = B² + P²
where, H is the hypotenuse.
B is the base
P is the perpendicular.
In the given question, hypotenuse is to be calculated.
Lets, base B = 6 ft and
Perpendicular P = 6 ft.
Thus, put the values in the formula;
H² = 6² + 6²
H² = 2×6²
Taking square root on both sides.
H = 6√2
Thus, the value of the hypotenuse if the right angled triangle is found as 6√2 ft.
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ojos del salado is the highest mountain in chile, with a peak at about 6900 meters above sea level. The atacama trench, just off th coast of peru and chile,is about 8100 meters below sea level (at its lowest point.) What is the difference in elevations between Mount Ojos del salado and the atacama trench.
Answers
The difference in elevations between Mount Ojos del salado and the atacama trench is 15000 meters
From the question, we are to calculate the difference in elevations between Mount Ojos del salado and the atacama trench
From the given information,
"Ojos del salado is the highest mountain in Chile, with a peak at about 6900 meters above sea level"
and
"The atacama trench, just off the coast of Peru and Chile, is about 8100 meters below sea level"
Thus,
With respect to the sea level,
The elevation of Mount Ojos del salado is 6900 meters
and
The elevation of the atacama trench is -8100 meters
Then,
The difference in elevation between Mount Ojos del salado and the atacama trench is 6900 - (-8100) meters
6900 - (-8100)
= 6900 + 8100
= 15000 meters
Hence, the difference in elevations between Mount Ojos del salado and the atacama trench is 15000 meters
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Forty two billion, three hundred and seven million, one hundred and Two thousand, three hundred and fourteen in number. Please help me
Answers
Answer:
42,307,0102,014 is the number form
Simplify each radical expression. Use absolute value symbols when needed. 4√16 x¹²
Answers
The simplified value of radical expression 4√16 x¹² is 2x^3.
By considering the given expression
4√16 x¹²
=(16x^12)^1/4
=(2^4)^1/4( x^12)^1/4
=2x^3.
An expression with a square root is referred to as a radical expression. Radicand: A value or phrase contained within the radical symbol. Equation with radical expressions and variables as radicands is referred to as a radical equation.
The 'V'-shaped portion of the radical symbol will have a superscript number when it is used to represent any root other than a square root. For instance, the expression 3(8) denotes the cube root of 8.
The radical symbol, which resembles a check mark, the index, a small number written outside the radical symbol, and the radicand, a quantity written beneath the horizontal bar of the radical symbol, are the three main components of the radical expression ab.
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Scarlett made a scaled copy of the following quadrilateral. She used a scale factor greater than 1.
A
B
C
D
What could be the length of the side that corresponds with AD on the scaled copy of the
quadrilateral?
Answers
Answer:
Step-by-step explanation:
First of all AD is 9 units long. Anything less than or equal to 9 is not an answer because the scale factor is greater than 1. That means that anything over 9 will work.
So the answer must be 12 or 15 from those answers given.
I would really appreciate some help. I am confused with this problem..it says Solve for
Answers
3q + 15q + 18 = 180
Simplify
18q + 18 = 180
Subtract 18 from both sides
18q = 162
Divide by 18
q = 9
Plug 9 in for q in the equation “15q + 18”
Then your answer should be 144.
Steve is going to prom with a group of friends. steve's group of friends decide to rent a limo. a local company is willing to rent a limo for $130 an hour. the limo can hold up to six people. steve and his five friends decide to split the cost of the limo evenly. if they rent the limo for four hours, how much will steve and his friends expect to pay? (round up to the nearest dollar amount)
Answers
$ 86.67 , Steve and his five friends has to pay $86.67 each to rent limo for four hours.
According to the question,
rent of limo for five hours = $130
now by multiplication ,
rent of limo for four hours = $130 * 4
= $520
now we know that there are six people including Steve hence we divide this $520 by 6 to get the share of each individual,
by division ,
hence the amount for each = $520 / 6
= 86.666666
amount round up to the nearest dollar is $86.67
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The vertices of a quadrilateral are A(−5, 3), B(2, 2), C(4,−3), and D(−2,−2). Find the slope of each side.
Answers
The sole of AB = 1/7, BC = -5/2, CD= -1/6, DA= -5/3
Here we have to find the slope of the side of the quadrilateral
The formula of the slope between A(x1, y1), B (x2, y2)
slope = (y2 - y1)/( x2- x1)
Slope of AB , where A = (-5, 3), B = (2,2)
AB = (2-3)/ ( 3- (-5))
= 1/ 8
Slope of BC, where B= (2,2 ), C = (4, -3)
BC = (-3 -2)/ (4-2)
= -5/2
Slope of CD, where C= (4,-3), D=(-2,-2)
CD = (-2-(-3))/ (-2-4)
= 1/ (-6)
=-1/6
Slope of DA , where D=(-2,-2), A=(-5,3)
DA= (3-(-2))/(-5-(-2))
= (3+2)/(-5+2)
= 5/-3
=-5/3
Therefore the slope of AB, BC, CD, DA = 1/7, -5/2, -1/6, -5/3 respectively.
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Find the midpoint of the segment with the following endpoints.
(9, 6) and (5, 2)
Answers
The midpoint of the segment is (7, 4).
According to the section formula-
If a point (x , y) divides a line in the ratio of m : n, where the two endpoints of the line are (x1, y1) and (x2, y2), then-
x = (nx1 + mx2)/ (m + n)
and y = (ny1 + my2)/ (m + n)
Here, we are given two points- (9, 6) and (5, 2)
Therefore,
x1 = 9, y1 = 6
x2 = 5, y2 = 2
Since, midpoint divides a line segment into two equal halves, m : n = 1 : 1
Now, substituting the values in the section formula we get-
x = (9 + 5)/2
x = 14/2
x = 7
and y = (6 + 2)/2
y = 8/2
y = 4
Thus, the midpoint of the segment is (7, 4).
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Find the inverse of each function.
y=log (x-6)
Answers
The inverse of the function y = log(x ₋ 6) is y = 10ˣ + 6.
Given the function is :y = log₁₀ (x ₋ 6)
we are asked to find the inverse of the function.
steps to find inverse function are:
Change f(x) to y to get y = ax + b for the provided function f(x) = ax + b.To get x = ay + b from the equation y = ax + b, replace x with y and y with x.
Here, find y and solve for x = ay + b.
Then we get :
y = (x - b/a).
Finally, we can substitute y = f⁻¹(x) with f⁻¹(x) = (x - b)/a.
now interchange the positions of x and y in the function.x = log₁₀(y ₋ 6)
the next step is to isolate the dependent variables.
y = 10ˣ + 6
hence we get the inverse of the function y = log₁₀ (x ₋ 6) as y = 10ˣ + 6.
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i need help with this
Answers
Answer:of not
Step-by-step explanation: ops
A recipe requires 3/4 cups if milk.Paula is making 1/2 of the recipe .How many cups of Milk will Paula use?
Answers
The answer to this question is:
No. of cups of milk will Paula use = 3/8
Given that recipe requires 3/4 cups of milk.
Paula is making half (1/2) of the recipe.
And we are asked to find that No. of cups of milk will Paula use.
To solve this question, we have to multiply the quantity of milk required by the quantity she is going to make.
The quantity of milk required * the quantity she is going to make
= 3/4 * 1/2
= 3/8
Therefore, No. of cups of milk will Paula use = 3/8
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Duo makes 65 percent of his dumplings with vegetarian fillings.
What fraction of Duo's dumplings have vegetarian fillings?
Answers
The fraction 13/20 of Duo's dumplings have vegetarian fillings.
What is fraction?
A fraction having whole numbers for the numerator and denominator. A fraction is a number of the form: ab where a and b are integers and b≠0. It represents the division of two numbers.
Given:
Duo makes 65 percent of his dumplings with vegetarian fillings.
According to given question we have
A percentage is a number or ratio expressed as a fraction of 100.
65 percent
=65 %
=65/100
Simplify fraction into simpler fraction,
⇒13/20
Therefore, the fraction 13/20 of Duo's dumplings have vegetarian fillings.
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i need help on this 4−d<4+d
Answers
For all the values of 'd' the expression 4-d will be less than 4+d.
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
Given that 4−d < 4+d. The inequality expression will be solved as:-
4−d < 4+d
4 - 1 < 4 + 1
3 < 5
4 - 2 < 4 + 2
2 < 6
It is concluded that for all the values of d in the given expression the portion 4 - d will be less than 4 + d.
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Alice, Billy, and Anna are spending the weekend baking cookies for
winter holiday gifts. For each batch of cookies, they’ll need 21
/2 cups of
flour and 11
/4 cups of butter. Each person contributed supplies from
their mothers’ kitchens and met at Anna’s house.
Answers
The fraction that Alice, Billy, and Anna should bring when they are spending the weekend baking cookies for winter holiday is 11/12 cups.
How to calculate the value?It should be noted that based on the information, for each batch of cookies, they’ll need 2 1/2 cups of flour and 1 1/4 cups of butter.
In this case, it should be noted that there are 3 people.
The fraction will be:
= (2 1/2 + 1 1/4) / 3
= 3 3/4 ÷ 3
= 11/12
Therefore, the fraction will be 11/12 cups for each person.
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Alice, Billy, and Anna are spending the weekend baking cookies for.winter holiday gifts. For each batch of cookies, they’ll need 2 1/2 cups of flour and 1 1/4 cups of butter. Each person contributed supplies from their mothers’ kitchens and met at Anna’s house. What fraction should each person bring?
Christopher is the oldest of three siblings whose ages are consecutive odd integers. If the sum of their ages is 6363, find Christopher's age.
Answers
Christopher's age given the sum of the ages of the three siblings is 23.
What is Christopher's age?An odd number is a number that is not perfectly divisible by 2. An odd number can be a positive number or a negative number. An example of an odd number is 3 and 7.
Consecutive odd integers are odd integers that follow each other on the number line. Consecutive odd integers increase by a value of (x + 2). Examples of consecutive odd integers are 11, 13, 15.
Let x represent the youngest sibling's age
Second sibling's age : x + 2
Christopher's age : x + 4
x + x + 2 + x + 4 = 63
3x + 6 = 63
3x = 63 - 6
3x = 57
x = 57 / 3
x = 19
Christopher's age : x + 4 : 19 + 4 = 23
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an oil tank is being filled at a constant rate of .2 feet per minute. After 15 minutes the tank is 6 feet deep. Write an equation that can be used to determine the amount of oil in the tank at any time.
Answers
The equation that represent amount of oil in the tank at x minutes is
6- 0.2t
What is an equation?A mathematical statement that shows that two mathematical expressions are equal.
Given:
rate of filling the tank = 0.2 feet/ minute
After 15 minutes,
height = 6 feet
let the time take be x minutes
So, the equation that represent amount of oil in the tank at x minutes.
=6- 0.2t
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Factor each expression.
x²+x-6
Answers
After solving, the factors of equation x²+x-6 are:
(x-2) and (x+3)What is an equation, clearly?A mathematical statement made up of two characterizations joined by an equal sign is known as an equation.3x - 5 = 16 is an example of an equation.We get the value for the variable x as x = 7 after solving this equation.So,
Given the equation: x²+x-6
Then,
x²+x-6x²+x( - )-6x²+x(3-2)-6x²+3x-2x-6x(x+3)-2(x+3)Factors are: (x+3) and (x-2)
Therefore, after solving, the factors of equation x²+x-6 are:
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Solve each equation for θ with 0 ≤ θ <2 π.
cotθ=-10
Answers
Answer:
0 with 0 2 pi cot0=-10 am not sure what It is
Find the average rate of change for the following functions over the interval.
Answers
Given the function and interval, the average rate of change of the function over the given interval is 1.
What is the average rate of change of the function over the given interval?The average rate of change of a function is calculated by dividing the change in y-values over the change in x-values of the two point.
r = ( f(1) - f(0) / ( (1) - (0) )
Given the data in the question;
f(x) = 2x² - x - 2
Intervals: [0, 1]
Plug the given values into the average rate of change formula and simplify.
r = ( f(1) - f(0) / ( (1) - (0) )
r = ( (2(1)² - (1) - 2) - ( 2(0)² - (0) - 2 )) / ( (1) - (0) )
r = ( (2 - 1 - 2) - ( 0 - 0 - 2 )) / 1 -0
r = ( (-1) - (-2 )) / 1r = ( -1 - (-2 ) / 1
r = ( -1 + 2 ) / 1
r = 1/1
r = 1
Therefore, the average rate of change of the function over the given interval is 1.
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The average rate of change of the function f(x) = 2x² - x - 2 over the intervals of 0 to 1 is 1.
What is the average rate of change of the function over the given interval?The average rate of change of a function is calculated by dividing the change in y-values over the change in x-values of the two point.
AVR = ( f(1) - f(0) / ( (1) - (0) )
Given the data in the question;
f(x) = 2x² - x - 2Intervals: [0, 1]Plug the given values into the average rate of change formula and simplify.
r = ( f(1) - f(0) / ( (1) - (0) )
r = ( (2(1)² - (1) - 2) - ( 2(0)² - (0) - 2 )) / ( (1) - (0) )
r = ( (2 - 1 - 2) - ( 0 - 0 - 2 )) / 1 -0
r = ( (-1) - (-2 )) / 1
r = ( -1 - (-2 ) / 1
r = ( -1 + 2 ) / 1
r = 1/1
r = 1
The average rate of change of the function f(x) = 2x² - x - 2 over the intervals of 0 to 1 is 1.
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What is the value of x+26
Answers
The value of x can not be told as there is no answer to the question "x+26".
Hence, can not be solved and it is left as 'x+26'
Please help with problem 8
Answers
Answer:
The correct answer is A.
diary entry on 180 word about a sick friend 3 entrys
Answers
Given the expression -7x -1/6y +2z - xy+28 answer the questions below
A. how many terms are there? How did u find them
B. how many different variables are there list all of them.
C. what is the coefficient of the 4th term.
Answers
Answer:
A. 5 || how? uh counting; -7x -1/6y +2z -xy +28
B. 3 (2;x | 2;y | 1;z)
C. 28
Hope this helps!
--Blu
Translate each of the following verbal descriptions into an algebraic rule.The total cost of the order, t, is 11 dollars multiplied by the number of pizzas ordered, p.
Answers
The algebraic expression which correctly represents the verbal description; The total cost of the order, t, is 11 dollars multiplied by the number of pizzas ordered, p is; t = 11p.
Which algebraic expression correctly represents the verbal description as in the task content?It follows from the task content that the expression which correctly represents the verbal description be determined.
On this note, since total cost is; t and the number of pizzas ordered is; p.
The required expression is therefore;
t = 11 × p
t = 11p.
Ultimately, the verbal representation of the algebraic expression where total cost of the order, t, is 11 dollars and number of pizzas ordered, is p is given by t = 11p.
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Solve each equation.
ln (x+2)- ln 4=3
Answers
After solving the given equation ln(x+2)-ln4=3, the value of [tex]x=e^{4 \ln +3}-2[/tex].
What exactly is an equation?An equation is a mathematical statement made up of two expressions joined by an equal sign.An example of an equation is 3x - 5 = 16.After solving this equation, we obtain the value of the variable x as x = 7.So,
Given equation: ln(x+2)-ln4=3Then,
ln(x+2)-ln4 = 3log(e)(x+2)-In4 = 3log(e)(x+2)-4In = 3[tex]x=e^{4 \ln +3}-2[/tex]Therefore, after solving the given equation ln(x+2)-ln4=3, the value of [tex]x=e^{4 \ln +3}-2[/tex].
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2x² + 5x-11
+3x² -11x +2
please solve thankyou!!
Answers
Answer:
5x^2 - 6x -9
Step-by-step explanation:
(-3 1/3 n +1/6) + (1 3/6n - 3/12 )
- 2/6n-1/12
-29/6 n + 1/12
-11/6n - 1/12
- 11/6n+5/12
(-3 1/4d +3/5) -2 7/8 d +7 /10
Answers
Answer:
[tex]\frac{4080n+1585d-188}{240}[/tex]
Step-by-step explanation:
I simplified it to the best possible state
Find all solutions to 8x³-10x² - 21x + 18 = 0 if x= 2 is one solution.
Answers
According to the given cubic equation 8x³-10x² - 21x + 18 = 0 the other value of x will be 4.
How does one solve a three-degree equation?Traditionally, a cubic problem can be solved by converting it to a quadratic equation and then solving it using factoring or the quadratic formula. A cubic equation, like a quadratic equation, has three roots.
What is the simplest method for solving a cubic equation?The typical strategy for solving a cubic problem is to convert it to a quadratic equation and then solve the quadratic using the standard methods, either factoring or using the formula. All of them are cubic equations. A cubic equation, like a quadratic equation, may have two or three real roots.
According to the given data:8x³-10x² - 21x + 18 = 0
x= 2
substituting the value in the equation we get:
8x³-10x² - 21x + 18 = 0
8(2)³-10(2)² - 21(2) + 18 = 0
68 - 40 - 42 + 18 = 0
4 = 0
According to the given equation 8x³-10x² - 21x + 18 = 0 the other value of x will be 4.
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