What does the constant 0.9955 reveal about the rate of change of the quantity?
Answers
The model given is:
[tex]f(t)=290(0.9955)^{60t}[/tex]The term in the parentheses represents the change of rate of the model. If the number is the parentheses is less than 1, we call it exponential decay.
If the number in parentheses is bigger than 1, we call it exponential growth.
In this case, the correct option is "decaying"
The number in parentheses let's call it R, is:
[tex]R=1-r[/tex]Where r is the rate of change. To find it:
[tex]\begin{gathered} 0.9955=1-r \\ . \\ r=1-0.9955=0.0045 \end{gathered}[/tex]To convert to percentage, we convert by multiplying by 100::
[tex]0.0045\cdot100=0.45\%[/tex]The second answer is 0.45%
And since t is the time passed in hours, and has a "60" multiplying it, the last answer is: Every 60 hours
The final answer is:
The function is exponentially decaying at a rate of 0.45% evary 60 hours.
Related Questions
Is the following statement true or false? The cube root of zero is zero.
Answers
The statement that The cube root of zero is zero is true .
What is cube root ?The number that results in the original number after being multiplied three times is known as the cube root of a number.[tex]\sqrt[3]{}[/tex] The sign is used to represent a number's cube root in radical form.
The cube root of 0 will be calculated and explained here. First, observe that the mathematical symbol for the cube root of O is as follows:
[tex]\sqrt[3]{0}[/tex]
The number (n), which you can multiply twice by itself to get the number zero, is the cube root of zero. Alternatively, n×n×n should equal 0. Consequently, the following equation can be used to address the issue:
[tex]n^{3}[/tex] = 0
The answer to the cube root of 0 is as follows when the aforementioned equation is solved:
[tex]\sqrt[3]{0}[/tex]= 0
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3 1/8 times 3 1/2 times 4/5
Answers
Answer: 8.75
Step-by-step explanation:
3 1/8 into a decimal is 3.125
3 1/2 into a decimal in 3.5 or 3.50
4/5 into a decimal is 0.8 or .8
Then just multiply 3.125 and 3.5 and you get 10.9375
Next, multiply 10.9375 by 0.8 and you get 8.75
Therefore your answer is 8.75
let x denote the number of times harry potter manages to irritate professor snape in one day. let y denote the number of times ron weasley manages to irritate professor snape in one day. and let the joint probability mass function for (x, y) be given as
Answers
the probability that Ron will get in trouble with Professor Snape at least two times in one day is 0.7
We are given
X 0 1 2 3 4
P(X) 0.15 0.20 0.20 0.30 0.15
we want Ron Weasley to get in trouble at least two time in one day
that mean X 2
P(X 2) = P(X=2) + P(X=3) + P(X=4)
= 0.20+0.30+0.15
= 0.65= 0.7 (rounded to nearest tenth)
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If BC= 6x+6 , AB= 8x+9 , and AC=142 find BC
Answers
The value of BC is 60.6.
What exactly is the segment addition property?According to the segment addition postulate, if we have two locations on a line segment, A and C, a third point B lies on the line segment AC if and only if the lengths between the points match the requirements of the equation AB + BC = AC.
Given:
BC = 6x+6
AB = 8x+9
AC = 142
We need to find BC.
As AB and BC combine to form AC, we add them together and equate them with the value of AC to determine the value of x.
Using the property of segment addition,
AB + BC = AC
8x + 9 + 6x + 6 = 142
Combine the variable terms and constants together,
14x + 15 = 142
14x = 142 - 15 (Subtracting both sides by 15)
14x = 127
x = 9.1
Hence the value of BC is,
BC = 6x + 6 = 6(9.1) + 6 = 60.6
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PLEASEEEE HELPPP!!!!
Answers
Height=4
Área=25
2. x=35
Hypotenuse= 39
Area=296
Hope this helps!
I keep getting the wring answer. I don’t know what I’m doing wrong.
Answers
we have the expression
[tex]y=x^2+x-4[/tex]Remember that
[tex]i^2=-1[/tex]Evaluate
For x=2i
substitute
[tex]y=(2i)^2+2i-4[/tex][tex]y=4i^2+2i-4[/tex][tex]\begin{gathered} y=4(-1)+2i-4_{} \\ y=-4+2i-4 \\ y=-8+2i \end{gathered}[/tex]Evaluate.
15÷(3+13)^2
Responses:
1 7/20
1 7/9
4 1/2
5 1/9
PLEASE HELP
Answers
Answer:
explain 15/256
find the length of the arc shown in red. Leave your answer in terms of pie
Answers
EXPLANATION
Given the circle, we can see the following facts:
Diameter= 24 ft ----> radius= 12 ft
Total arc length = 360°
The arc of a semi-circle is equal to 360/2 = 180 degrees
The red labeled arc is given by the difference between 360, the other 60 degrees and the semi-circle,
360° - 180° - 60° = 120°
So, representing this as a radian form:
[tex]\text{arc length = 2}\cdot\pi\cdot r\cdot(\frac{\theta}{360})[/tex][tex]\text{arc length = 2}\cdot\pi\cdot12\cdot(\frac{120}{360})[/tex]Multiplying terms:
[tex]\text{arc length = 24}\cdot\pi\cdot\frac{1}{3}[/tex]Simplifying:
[tex]\text{arc length= 8}\cdot\pi[/tex]So, the answer is 8π ft
6+3x^4+7x^5+7x^2 it’s polynomials
Answers
The given polynomial 6+3x⁴ +7x⁵ +7x² is a quadrinomial.
What is Quadronomial?An expression that consists of variables, constants, and exponents and is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).One-term polynomials are referred to as monomials, two-term polynomials as binomials, and three-term polynomials as trinomials depending on the number of terms with nonzero coefficients. A four-term polynomial is occasionally referred to as a "quadrinomial."So, 6+3x⁴ +7x⁵ +7x²:
We can observe that the given polynomials have 4 terms, and a polynomial with 4 terms is known as a quadrinomial.Hence, the given expression is quadrinomial.Therefore, the given polynomial 6+3x⁴ +7x⁵ +7x² is a quadrinomial.
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On a cold January day, Klara noticed that the temperature dropped 21 degrees over the course of the day to –9°C. Write and solve an equation to determine what the temperature was at the beginning of the day.
Answers
x = 12
The temperature at the beginning of the day was 12* C
A cyclists speed is 1.5 times faster than a walkers speed. they simultaneously start moving in the same direction from the same point and, after 1.5 hours, the distance between them is 12.5 miles. what are their speeds?
Answers
Answer:
The biker's pace is 25 miles per hour and the walker's speed is 50/3 miles per hour.
Answer:The speed of the walker is 16.67 miles per hour.
The speed of the cyclist is 25 miles per hour.
How to calculate the value?
Let the speed of a walker = x
Biker's speed = 1.5x
Their relative speed will be:
= 1.5x - x = 0.5x
Distance between them = 12.5 miles
Time taken = 1.5 hours.
It should be noted that distance will be:
= Speed × Time
12.5 = 1.5 × 0.5x
Divide through to get x
12.5 = 0.75x
x = 16.67 miles per hour.
Speed of cyclist = 16.67 × 1.5 = 25 miles per hour.
The nurse is assessing a client’s lymphatic system. For which enlarged node should the nurse suspect that the client has a blockage within the right lymphatic duct?.
Answers
The enlarged node that the nurse should suspect that the client has a blockage within the right lymphatic duct is the right cervical node
What is the lymphatic system?A network of tissues, blood arteries, and organs called the lymphatic system collaborates to transport lymph, a colorless, watery fluid, back into your circulatory system. Every day, your body's arteries, smaller arteriole blood vessels, and capillaries circulate about 20 liters of plasma.
The right lymphatic duct receives drainage from the right cervical node. The thoracic duct receives drainage from the superficial popliteal, superficial inguinal, and lumbar nodes. The sides and back of the neck include the cervical lymph nodes.
Typically, these glands are incredibly tiny. A lymph node, however, is swollen if its diameter is higher than 1 centimeter. Deep inside the neck, the cervical lymph nodes are located.
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:: 3x + 3 = 2(x + 7)
Answers
Answer: x= 11
Step-by-step explanation:
Answer:
x=11
Step-by-step explanation:
im assuming u r trying to find x
you need to solve the bracket first (2×x =2x , 7×2= 14)
After that move numbers with x to ur left, to make life easier
3x-2x= x
14-3 = 11
x=11
Write a two-column proof
Answers
The angles ∠4 and ∠6 are found to be supplement angles.
What are termed as the supplement angles?Supplementary angles are the ones that total 180 degrees. Angles 130° and 50°, for example, are supplementary angles since the sum of 130° and 50° equals 180°. Complementary angles, on the other hand, add up to 90 degrees. When the 2 supplementary angles are joined together, they create both a straight line and an angle.It should be noted, however, that the two supplementary angles are not required to be adjacent to each other. As a result, any two angles could be supplementary if their total amount is equal to 180°.For the given question;
∠5 ≅ ∠6 ( both are congruent means equal)
As, ∠4 and ∠5 are forming on the straight line. Thus,
∠4 + ∠5 = 180 (linear pair)
But, ∠5 ≅ ∠6 , replacing ∠5 with ∠6 .
∠4 + ∠6 = 180 supplement angles.
Thus, ∠4 and ∠6 are found to be supplement angles.
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what is an equation of the line that passes through the points (-4, 5) and (-4, -2)
Answers
Answer: no equation can pass through those points
Step-by-step explanation:
the x value -4 has two y values, 5 and -2. a function needs at most 1 y value to be considered a function.
2/5 y 6/15 son equivalentes?
Answers
To know if 2/5 and 6/15 are equivalent, we do a multiplication, then,
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{2}{3}=\frac{2\times2}{5\times2}=\frac{4}{10} \ \ \longmapsto \ Not \ the \ result } \end{gathered}$} }[/tex]
Since if we try it with number 1, the result would be the same, then we continue with 2 being closer, then we continue with number 3, successively, until we reach the expected answer.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{2}{3}=\frac{2\times3}{5\times3}=\frac{6}{15} } \end{gathered}$} }[/tex]
2/5 and 6/15 are equivalent?, The two fractions are equivalent, (True).Terms from two sequences are given in tables below. Which of the following statements are true? Select all that apply.
Answers
As per the terms from the two sequences given in tables as attachment hereby along with the question statement, the following statements from the provided options are true.
(i) [(a₁) > (g₂)]
(iv) Initially (aₙ) is greater than (gₙ), and as "n" gets larger, (gₙ) is greater than (aₙ).
As per the question statement and the reference tables attached thereby along with the question, we are provided with terms from the two sequences in table format, and five statements based on the sequences.
We are required to determine which statements among the five, are true.
To solve this question, we will use the trial-and-error method, where we will consider individual statement and assess it's honesty.
First statement is [(a₁) > (g₂)], which is true. As we can see from the table, that, [(a₁) = 10] and [(g₂) = 4], i.e., (10 > 4), or, [(a₁) > (g₂)].
Second statement is that, "The constant difference for (aₙ) is 10" which is False. We can clearly see from the table that, (a₁ = 10), (a₂ = 15), (a₃ = 20), (a₄ = 25) and so on, and [(25 - 20) = (20 - 15) = (15 - 10) = 5], i.e.,
[(a₄ - a₃) = (a₃ - a₂) = (a₂ - a₁) = 5]. Hence, the common difference for (aₙ) is 5, and not 10.
Third statement is that, "(aₙ) can be modelled by a linear function, and (gₙ) can be modelled by an exponential function" which is true for the first part, but false for the second, making the complete statement false as whole.
From the left hand side table, we can see that, (a₂ = 15) and (a₁ = 10),
Or, [a₂ = (10 + 5)]
Or, [a₂ = (a₁ + 5)]
Similarly, (a₃ = 20),
Or, [a₃ = (15 + 5)]
Or, [a₃ = (a₂ + 5)]
That is, we can generalise (aₙ) as
[aₙ = {(aₙ₋₁) + 5}] where, (n = 2, 3, 4, 5...) and (a₁ = 10).
Hence, (aₙ) can be modelled by a linear function.
But from the right hand side table, we can see that, (g₂ = 4) and (g₁ = 2),
Or, [g₂ = (2 * 2)]
Or, [g₂ = 2g₁]
Similarly, (g₃ = 8),
Or, [g3 = (2 * 4)]
Or, [g₃ = 2g₂], it goes on for (gₙ).
Therefore, we can generalise (gₙ) as
[gₙ = 2*(gₙ₋₁)] where, (n = 2, 3, 4, 5...) and (g₁ = 2).
Here, (gₙ) can also modelled as a linear function and not as a exponential function (which goes in the form of "xⁿ").
Coming to the fourth statement, "Initially (aₙ) is greater than (gₙ), and as "n" gets larger, (gₙ) is greater than (aₙ)" is true, as from both the tables,
For (n = 5), [aₙ = a₅ = (a₄ + 5) = (25 + 5) = 30],
And [gₙ = g₅ = (2 * g₄) = (2 * 16) = 32], which is greater than 30,
Or, [(g₅) > (a₅)].
Similarly, for (n = 6), (a₆ = 35) while (g₆ = 64), i.e., [(g₆) > (a₆)], and it continues for greater values of "n".
Coming to the last statement, that [a₁₀ > g₆], is false. As we can observe from the both the tables and their sequence,
For (n = 5), (aₙ = 50), for (n = 6), (aₙ = 35), for (n = 7), (aₙ = 40), for (n = 8), (aₙ = 45), for (n = 9), (aₙ = 50) and for (n = 10), (aₙ = 55),
While on the other hand, for (n = 5), (gₙ = 32) and for (n = 6), (gₙ = 64).
Since (64 > 55), therefore, [(g₆) > (a₁₀)].
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in a rectangle, one side is 3 times as long as the other. Now the longest side is extended by 4m. Then the area will be 96 square meters larger. How long were the original sides?
Answers
The length of the original sides of the rectangle are 72m and 24m.
What is Area of a Rectangle?The area of a rectangle formula is used to calculate the area occupied by the rectangle within its boundaries. A rectangle's area is calculated by multiplying its length and breadth.
Given:
One side is 3 times as long as the other in a rectangle.
Let the length of the rectangle be 3x and the breadth of the rectangle be x.
Area of original rectangle = length × breadth
= 3x² m²
Now, the longest side is extended by 4m.
Length of rectangle = 3x + 4
Area of rectangle = length × breadth
= x(3x + 4) m²
It is given that this area will be 96 square meters larger than the former.
So, x(3x + 4) - 3x² = 96
⇒ 3x² + 4x - 3x² = 96
⇒ 4x = 96
⇒ x = 24 m
Original length of the rectangle = 3x = 3×24 = 72m
Therefore, the original length of the rectangle is 72m and the original breadth of the rectangle is 24m.
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What are the sum of all the factors of 50 which are between 1 and 50. A. 42B. 2550C. 92D. 15
Answers
Factors of 50 are the numbers which on dividing 50 leave no remainder. 50 is a composite number, therefore, it has more than 2 factors.
We can get the factors of 50 by Prime Factorization. We can draw a factor tree to get the prime factors of 50 as shown below:
Therefore, the prime factors are:
[tex]2,5,5[/tex]Hence, the other factors are:
[tex]\begin{gathered} 2\times5=10 \\ 5\times5=25 \end{gathered}[/tex]Therefore, the factors of 50, including 1 and 50, are:
[tex]1,2,5,10,25,50[/tex]The question asks to sum all the factors between 1 and 50. This means that 1 and 50 are not included in the sum.
Therefore, the sum will be:
[tex]\Rightarrow2+5+10+25=42[/tex]The correct option is OPTION A.
Change 36 inches into feet given the fact that 1 foot = 12 inches.
Answers
===============================================
Work Shown:
1 foot = 12 inches
3*1 foot = 3*12 inches
3 feet = 36 inches
I multiplied both sides by 3 so that the "12" turns into "36".
Answer:3 feet
36/12=3
3x12=36
so 36 inches= 3 feet
hope it helps
can you help me with this? i got it wrong
Answers
1) Let's sketch this out so that we can better understand it
2) Reminding ourselves of the metric relations of a right triangle we can write out the following:
[tex]\begin{gathered} h^2=m\cdot n \\ YO^2=26\cdot12 \\ YO=\sqrt[]{312} \\ OZ=\sqrt[]{26.12} \\ OZ=\sqrt[]{312} \\ YZ=\sqrt[]{312}+\sqrt[]{312} \\ YZ=2\sqrt[]{312} \\ YZ=35.3 \end{gathered}[/tex]Note that the radius intersects that chord with a 90º angle so it bisects that chord.
“If the sum of two angles is 180 then the angles are supplementary
Answers
If the sum of two angles is 180 then the angles are supplementary.This is true.
What are supplementary angles?Supplementary angles are those that total 180 degrees. Angles 130° and 50°, for example, are supplementary angles since the sum of 130° and 50° equals 180°.
If the total of two angles is 180 degrees, they are considered to be supplementary angles since they form a linear angle when combined. If the total of two angles is 90 degrees, they are considered to be complimentary angles since they produce a right angle when combined.
If two angles add up to 180 degrees, they are considered to be supplementary angles in geometry. For example, if A + B = 180°, A and B are referred to as supplementary angles. When supplementary angles are combined, they always yield a straight angle (180 degrees).
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Trina wants to hang-glide at the same number of meters above sea level as she scuba-dived below sea level. Will she fly higher than Jessie did? Explain
Answers
Trina is closer to the surface of the ocean. She will not fly higher than Jessie did.
Consider the provided information.
The distance is the absolute value of a number.
Part (A) : It is given that Trina went scuba diving and reached an elevation of -85.5 meters, which is below sea level.
That means the distance she covers is: |-85.5| = 85.5 meters
Thus Trina covers 85.5 meters.
Jessie went hang gliding and reached 87.9 meters which is above sea level.
That means the distance she covers is: |87.9| = 87.9 meters
We know that 85.5 < 87.9
So, we can say that Trina is closer to the surface of the ocean as she covers less distance.
Part (B) : Trina wants to hang glide at the same number of meters above sea level as she scuba dived below sea level.
That means she will hang the glide at a height of 85.5 meters.
As we know 85.5 < 87.9
Thus, she will not fly higher than Jessie.
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line L passes through (3,5) and is parallel to y = 6x-2. Find the equation of line L
Answers
Answer:
y = 6m - 13
Step-by-step explanation:
Parallel lines have the same slope. The slope in the equation y = 6x -2 is 6.
To write an equation in the slope intercept form, we need a slope and a y-intercept. We have the slope, we need to find the y-intercept.
To find the y intercept, we need a slope, and x on the line and a y on the line. The point (3,5) gives us the x and the y.
slope = 6
x = 3
y = 5
y = mx + b plug in what we know and solve for b
5 = 6(3) + b
5 = 18 + b Subtract 18 from both sides of the equation
-13 = b
y = mx + b
y = 6m - 13
a length of black steel pipe is 21'-0" long. how much if the length remains of two pieces 7'-9 5/8" are cut from the length?
Answers
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 9 5/8, where 9 is the quotient and 5 is the remainder.
Remain length = 13.2' = 13' 2 2/5 ".
What is a mixed fraction?The quotient and remainder of a fraction are used to represent it, making it a mixed fraction. For instance, 2 1/3, where 2 is the quotient and 1 is the remainder, is a mixed fraction. A mixed fraction is a combination of a whole number and a recognized fraction.Subtract the denominator from the numerator. The quotient's whole number component should be written down. Write the leftover amount on top of the original denominator.A mixed number is said to be in its simplest form if its fractional part's highest common factor, or HCF, is 1. When mixed numbers are simplified, the fraction's value doesn't change. We can assert that the actual mixed number and the simplified mixed number are fractions of the same size.Length of black steel pipe is 21'-0".
7' 9 5/8" =7.8 '
Remain length = 13.2' = 13' 2 2/5 ".
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SSS stands for ___ Congruence Postulate ( will mark Brainliest )
Answers
Answer:
I believe it stands for Side, Side, Side
Step-by-step explanation:
When two triangles with all three sides are equal they're SSS
A car park charges £1.20 to each car entering.
The payment station only accepts £1 coins and 20p coins.
Here are the coins collected from the payment station on a particular day:
Number of £1 coins
176
Number of 20p coins
320
Assuming each driver paid the exact amount due on that day, work out the
percentage of drivers that paid with six 20p coins.
Optional working
+
Answer:
Answers
Answer: 12%
Step-by-step explanation:
12%
Explanation:
If has 176 £1 coins then 176 drivers paid £1 and 20 p coins.
The rest of the driver paid with 20 p coins.
So the number of 20 p coins is:
320 - 176 = 144
Since £1 and 20 p need 6 coins of 20 p, the number of drivers who paid only for 20 p coins is:
144 / 6 = 24
The total number of drivers is:
176 + 24 = 200
The percentage of drivers who paid only with coins id 20 p is:
24 / 200 • 100% =
0.12 • 100% = 12%
4. last year nina invested $6,000. she put some of it in a cd the paid 4% simple interest, and she put the rest of it in a savings account that earned 2.5% simple interest. at the end of the year she earned a total of $204 interest. how much did she invest in each account? assume there were no other deposits or withdrawals.
Answers
She invested $2,400 in the 2.5% account and $3,600 in the 4% simple interest account
Here, we want to know the amount of money invested in each account
Let the amount invested in the 4% simple interest account be $x ----> (a)
While the amount invested in the 2.5% account be $y -------->(b)
So mathematically;
Both the interests are added to get total interest
x + y = 6,000 ••••••(i)
Let’s now evaluate the interest
for the 4% account , interest = 4/100 * x = 4x/100
For the 2.5% account, interest = 2.5/100 * y= 2.5y/100
The addition of both interests gives the total simple interest;
4x/100 + 2.5y/100 = 204
Multiply through by 100
4x + 2.5y = 20,400 •••••••(ii)
From i, x = 6,000 - y
Putting this into equation ii
4(6,000-y) + 2.5y = 20,400
24,000 - 4y + 2.5y = 20,400
24,000-20,400 = 4y - 2.5y
1.5y = 3,600
y = 3,600/1.5
y = $2,400
Recalling it again,
x = 6000 - y
x = 6,000 - 2,400
x = $3,600
Therefore, Nina invested $2,400 in the 2.5% account and $3,600 in the 4% simple interest account
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Andre wants to make an open-top box by cutting out corners of a 22 inch by 28 inch piece
of poster board and then folding up the sides. The volume V(x) in cubic inches of the
open-top box is a function of the side length x in inches of the square cutouts.
Write an expression for V(x).
what is the volume of the box when x=6
Answers
The expression for volume is (28-2x)(22-2x)x and when x=6, the volume is 840 inch^3.
What is volume?
A 3D object's volume is the amount of actual space it occupies. It is a 2D shape's 3D equivalent of area. It is quantified in cubic units like cm3. It means that the amount of space a closed form can occupy in three dimensions depends on its volume. Volume is a gauge of a thing's potential. For instance, a cup is said to have a 100 ml capacity if the brim can hold 100 ml of water. Another way to measure volume is the amount of space a three-dimensional item takes up.
According to question,
Let x be the height of the cubic box
Length = (28-2x)
Breadth = (22-2x)
Volume = x(28-x)(22-x)
When x =6
Volume = 6(28-6×2)(22-6×2)
=6(10)(14)
=840 inch^3
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Please help , I need help thanks
these are the questions there are five , I need this today
I will give out brainlist
Answers
The solution to the inequality problem is represent by the graph attached below.
Graph of InequalitiesTo solve this problem we simply need to use a graphing a calculator to plot the graph of the two inequalities. The points of intersection represents the solution of the graph.
The broken purple line represents the first inequality and the second straight line represents the second inequality.
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