The daily rate of decay is approximately equal to 0.0347 days⁻¹.
What is the rate of decay of a substance?
According to the statement, we find that a substance is under a decay process, whose differential equation is introduced below:
dm(t) / dt = - k · m(t) (1)
Where:
m(t) - Current mass of a substance, in miligrams.k - Rate of decay, in 1 / day.The half-life of the substance is the time needed for a substance to decrease its mass by half. The rate of decay can be found in terms of half-life:
k = (㏑ 2) / t' (2)
Then, the daily rate of decay of the substance is:
k = (㏑ 2) / (20 days)
k ≈ 0.0347 day⁻¹
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Mr. K needed to rent a moving van; U-Haul charges $90 per hour plus a $50 truck fee. Enterprise
charges $70 per hour plus a $90 truck fee. For what number of hours of rental is the cost for the two
companies the same?
Here is three different real world examples of slope as a unit rate. Please read the graphs below and fill in the blanks for each one for slope. (PLEASE HELP!!)
10
40
15
PLEASE CORRECT ME IF I AM WRONG, AND TELL ME IF I AM RIGHT.
A solid cylinder has a diameter of 8.4 cm and a height of 12.0 CM. Calculate the volume of a cylinder.
Answer:
Volume = 665 cm³
Step-by-step explanation:
We can calculate the volume of a cylinder using the following formula:
[tex]\boxed{\mathrm{Volume = \pi r^2 h}}[/tex],
where:
• r = radius of cylinder
• h = height of the cylinder
In the question, we are told that the diameter of the cylinder is 8.4 cm. Since the diameter is twice of radius:
[tex]\mathrm{radius = 8.4 \div 2}[/tex]
[tex]= \bf 4.2 \: cm}[/tex]
We are also told that the height of the cylinder is 12.0 cm. Therefore, using this information, as well as the formula above, we can find the volume of the cylinder:
[tex]{\mathrm{Volume = \pi \times (4.2 \mathrm{\: cm})^2 \times 12.0 \mathrm{\: cm}}}[/tex]
[tex]= \pi \times 17.64 \mathrm{\: cm^} \times 12.0 \mathrm{\: cm}[/tex]
[tex]\approx \bf 665 \: cm^3[/tex]
Therefore the volume of the cube is 665 cm³.
need help. every rectangle is a whole.
The best product of the model is 3 * 5/6
How to determine the best product of the model?On the grid, we have the following parameters
Three big rectangles5 shaded sections on each6 total sectionsThe best product of the model is then represented as
Number of big rectangles * Shaded Sections/Total sections
So, we have
3 * 5/6
Hence, the best product of the model is 3 * 5/6
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What is the formula for the volume of a cylinder, V= πr²h , solved for h ?
(F) h= r²πV (G) h= πV/r² (H) h= V/πr² (I) h= πr²/V
h= V/πr² is the formula for the volume of a cylinder, V= πr²h , solved for h.
⇒ V= πr²h
⇒ V/πr² = h
⇒ h= V/πr²
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every Linear equation can be solved easily.
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Caylie's coin bank contains only dimes and nickels. The bank contains 46 coins. If 5 dimes and 2
nickels were removed, the total value of the coins would be $3.40. Find the number of nickels and the
number of dimes in the bank.
There were 29 nickels and 10 dimes in the bank.
We know that:
1 dime = 5 cents
1 nickel = 10 cents.
Also, $ 3.40 = 340 cents
Let the number of nickels be n and the number of dimes be d.
Now, we are given that:
5 dimes and 2 nickels were taken away.
So, total coins = 46 - 2 - 5 = 46 - 7
Total coins = 39
We get the equation:
n + d = 39
d = 39 - n
Now, we also know that:
5 d + 10 n = 340
d + 2 n = 68
Put the value of d, we get that:
39 - n + 2 n = 68
n = 68 - 39
n = 29
d = 39 - n
d = 39 - 29
d = 10
Therefore, we get that, there were 29 nickels and 10 dimes in the bank.
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Divide.
−0.0468÷0.002
What is the quotient?
Enter your answer in the box.
Answer:
-23.4
Step-by-step explanation:
-0.0468 ÷ 0.002 = -23.4 (A negative divided by a negative is a positive!)
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
Two angles form a linear pair. The measure of one angle is 1/3 the measure of the other angle. Find the measure of each angle.
Step-by-step explanation:
MARK ME AS A BRAINLIST. OK
Need help asap please
Answer:
2) y= 4x+17
Step-by-step explanation:
y- y1 = m(x- x1)
y- 5 = 4 (x - (-3))
y-5= 4( x+ 3)
y-5= 4x+ 12
y= 4x+17
On Monday, a bookstore sold 57 books. On Tuesday, the store sold 64 books. Let p represent the percent increase in the sale of books from Monday to Tuesday. Drag the tiles to fill in all the boxes and complete a proportion that can be used to find the value of p.
The value of the percent increase "p" is 12.28%.
Percent Increase can be calculated using the formula
Percent increase = (Amount increased/original amount) x 100
In the given question
Number of books sold on Monday = 57 books
Number of books sold on Tuesday = 64 books
Increase in number of books = books sold on Monday - books sold on Tuesday.
Substituting the values we get
Increase in number of books = 64-57 = 7
the percent increase = (7/57)x100
= 0.1228 x 100
= 12.28
Therefore , the value of the percent increase "p" is 12.28%.
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round 2,874.2878 to two decimal places
Answer: If your rounding to the second spot after the decimal it would be in the hundredths place so in case it would be 2874.29 Although I'm not sure if that's how you wanted it to be done.
Round the number 2,874.2878 to two decimal places will be 2,874.29.
What is the rounding of a number?The action of forming anything into a circle. Mathematics. the act of substituting a number with one that is roughly equivalent in value but has fewer digits: To the closest dollar, rounding $27.68 results in $28. a comparable procedure that identifies one of several rules.
The decimal number is given below.
⇒ 2,874.2878
Round 2,874.2878 to two decimal places.
If the third place after the decimal is more than 5, then the second place after the decimal will be increased by one.
In the third place after the decimal is 7, then the number 8 is increased by one that is 9.
Round the number 2,874.2878 to two decimal places will be 2,874.29.
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Please help
let f(x)=-4x^3+9x^2-5x+132
Is x-1 a factor of f(x)
Is x+1 a factor of f(x)
Is x-4 a factor of f(x)
Answer:
x-4 IS a factor
Step-by-step explanation:
IF x-1 is a factor then putting x = 1 into the equation will make it = zero...... it does not
IF x+1 is a factor then putting x = -1 into the equation will result in = 0
it does not
IF x -4 is a factor , then puting in x =4 into tthe equation will = 0 it DOES !
Jim says,
"When you subtract a number from 10, the answer will always be less than 10" Is Jim correct?
David requires at least $250 to hold his birthday party. If David can save $43 a month, how many months will he need to save to be able to afford his birthday party?
a. Write an inequality that describes this situation.
b. Solve the inequality. Show all your work.
c. Write your answer in a complete sentence.
Answer:
b. Solve the inequality. Show all your work.
Step-by-step explanation:
What is the geometric mean of 8 and 18 ?
A 9
B 10
C 11
D 12
The geometric mean of a and b [tex]=\sqrt{a*b}[/tex] then the geometric mean of 8 and 18 is 12.
What is geometric mean?In Mathematics, the Geometric Mean (GM) is the average value or mean which signifies the central tendency of the set of numbers by finding the product of their values. Basically, we multiply the numbers altogether and take the nth root of the multiplied numbers, where n is the total number of data values.
The geometric mean is used in finance to calculate average growth rates and is referred to as the compounded annual growth rate.
To calculate the geometric mean of two numbers, you would multiply the numbers together and take the square root of the result.
Geometric mean of a and b [tex]=\sqrt{a*b}[/tex]
Geometric mean of 8 and 18 [tex]$=\sqrt{8*18}[/tex]
a = 8 , b = 18
= √144
= 12
The geometric mean of 8 and 18 is 12.
Therefore, the correct answer is option D. 12.
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PLEASE HELP 25 pointss
The difference of the polynomials, (p² + p - 8) - (-4p² - p + 3), is: D. 5p² + 2p - 11.
How to Find the Difference of Two Polynomials?To find the difference of two polynomials, group like terms together after opening up the parentheses, then combine the like terms together.
Given the polynomials:
(p² + p - 8) - (-4p² - p + 3)
Apply the distributive property to eliminate the parentheses
p² + p - 8 -1(-4p²) -1(-p) -1(3)
p² + p - 8 + 4p² + p - 3
Group like terms
p² + 4p² + p + p - 8 - 3
Combine like terms
5p² + 2p - 11
Thus, the difference of the polynomials, (p² + p - 8) - (-4p² - p + 3), is: D. 5p² + 2p - 11.
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Shannon will be assigned at random to 1 of 6 P.E. classes throughout the day and 1 of 3 lunch times. What is the probability that she will be in the second P.E. class and the first lunch?
A. 1/18
B. 1/9
C. 1/6
D. 1/2
The correct option is A. 1/18. Shannon has a 1/18 chance of being in the second P.E. class along with the first lunch.
What are defined as independent events?Two events are considered independent if the happening of the one doesn't affect the likelihood of the happening of the other.
The mathematical model of event independence A and B is the probability of both A and B occurring becoming equal to the product of a probabilities of A & B.
Now, for the stated question;
Let the probability that the Shannon will get second P.E class is P(A) = 1/6.
Now, Let the probability that the Shannon will get first lunch is P(B) = 1/3.
Ad, both events are independent.
Thus, the intersection will be -
P (A∩B) = P(A).P(B)
P (A∩B) = 1/6×1/3
P (A∩B) = 1/18.
Therefore, the probability that Sharron will be in the second P.E. class and the first lunch is 1/18.
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Suppose m = 25-0.15 n describes the amount of money remaining on a 25 phone card m , as a function of the number of minutes of calls you make n . What are a reasonable domain and range?
A function's domain is the set of values that can be put into the function. This set is the x-value of a function like f(x). In its simplest form, the domain includes all values entering the function, and the range includes all values output.
A function's range is the set of values it takes on. This set is the values that the function executes after inserting the x values. Those are the y-values.
The amount of money remaining is 25 on the phone card, and the value of m given is
M=25-0.15
25>=M>=0 (it is a 25 Dollar Phone Card)
25-0.15n>=0
N=<500/3
N>= 0
Their range and domain are
Range: 0=<N=<500/3
Domain: 0=<M=<25
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A landscaper is forming an isosceles triangle in a flowerbed using chrysanthemums. She wants m∠A to be three times the measure of ∠B and ∠ C . What should the measure of each angle be?
The measurement of each angle is : m∠A = 108° , m∠B = 36° , m∠C = 36°.
What is an isosceles triangle ?In mathematics, an isosceles triangle is a triangle in which any of the two sides are equal. Or we can say that if a triangle has at least two sides of equal length then it is known as isosceles triangle. In geometry, isosceles triangle follow the property of congruency of triangles. That means in an isosceles triangle the two angles of equal sides are congruent to each other.
In the given question,
Let m∠B = m∠C = x , where m denotes measure of angle
therefore, m∠A = 3x
According to Triangle Angle-Sum Theorem,
m∠A + m∠B + m∠C = 180
thus,
3x + x + x = 180
5x = 180
x = 36
Hence,
m∠A = 3x = 180
m∠B = 36°
m∠C = 36°
Therefore, the measure of each angle A , B and C is 180°, 36° and 36° respectively.
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Evaluate each finite geometric series. 1/5 + 1/10 + 1/20 + 1/40 + 1/80
Evaluate each finite geometric series.
1/5 + 1/10 + 1/20 + 1/40 + 1/80=0.3875
What is the sum of a finite geometric series?
Given:
a=1/5
r=5/10 = 1/2
n=5
[tex]S_n=\frac{a(1-r^{n} )}{1-r} \\\\S_5=\frac{\frac{1}{5}(1-(\frac{1}{2}))^{5} }{1-\frac{1}{2} } \\\\S_5=\frac{1}{5} (\frac{31}{32} *\frac{2}{1}) \\\\S_5=\frac{1}{5} (\frac{31}{16} )\\\\S_5=0.3875[/tex]
What is a finite geometric series?
A geometric series is a series with a geometrically connected progression. A geometric series is a list of numbers where each number, or term, is found by multiplying the preceding term by a common ratio r. Because there are only a finite number of terms, we refer to this geometric series as a finite geometric series (an infinite geometric series continues on forever.)To learn more about finite geometric series, refer:
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How to construct a Right-Angled Triangle if I'm given two angles (excluding the 90° angle) and one side length?
Step-by-step explanation:
there are many construction vids if you need a visual, but first off you need to a ruler, compass and protractor. draw a straight line horizontally, leave enough space above to add the length given as vertical side.
on the straight line choose a point preferably near centre and. place compass on the point and open to any distance, on the pencil side, draw a semi circle cutting the horizontal line at two points.
label the two points a and b
place compass on point and draw a smaller curve from that point above the center then do the same on other side
remember do not change the Size the compass was opened at for drawing the curves
the two new curves you drew should intersect, using ruler, draw a straight line vertically through intersection and center point
this line can be the required length given
you will notice an inverted T shape
the angle will be 90deg on either side, measure to ensure
form a smimulatenous equation for : a cyclist completes a journey of 500 m in 22 seconds, part of the way at 10m/s and the remainder at 50m/s. How far does she travel at each speed?
The distance traveled in each section will be 150 meters and 350 meters.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
From a simultaneous equation for: A cyclist completes a journey of 500 m in 22 seconds, part of the way at 10m/s and the remainder at 50m/s.
Let x distance be covered with velocity 10 m/s in time t₁ and the remaining distance (500 - x) covered with velocity 50 m/s in time t₂. Then the equation will be
t₁ + t₂ = 22 ....1
Then the time t₁ will be
10 = x / t₁
t₁ = x / 10
Then the time t₂ will be
t₂ = (500 - x) / 50
Put the time in equation 1, then we have
x / 10 + (500 - x) / 50 = 22
5x + 500 - x = 1100
4x = 600
x = 150 meters
And the remaining distance will be
500 - x = 500 - 150
500 - x = 350 meters
The distance traveled in each section will be 150 meters and 350 meters.
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EASY POINTS WILL GIVE BRIANLIST TO BEST ANSWER
Slove then equation below and give the reasons for each step:
View photo
Use the Distance Formula to find the distance between the pair of points.
R(-2,3), S(3,15)
Using the distance formula, the distance between the pair of points R(-2,3) and S(3,15) is 13 units
Given,
The points = R(-2,3) and S(3,15)
We know the distance formula = [tex]\sqrt{(x_{2}-x_{1})^{2}-(y_{2} -y_{1})^{2} }[/tex]
Substitute the values in the equation
The distance = [tex]\sqrt{(3--2)^{2}+(15-3)^{2} }[/tex]
[tex]=\sqrt{5^{2}+12^{2} }\\ =\sqrt{25+144}\\ =\sqrt{169}[/tex]
=13 units
Hence, using the distance formula, the distance between the pair of points R(-2,3) and S(3,15) is 13 units
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give the geometrical representation of y=3 as an equation in
a) one variable
b) in two variables.
The geometrical representation of y=3 as an equation in
a) one variable is y = 3
b) in two variables is 0x + y = 3.
How to illustrate the information?Based on the information illustrated, the geometrical representation of y=3 as an equation in one variable is y = 3.
Also, the geometrical representation of y=3 as an equation in two variables is:
y = 3.
0x + y = 3
0x + y - 3 = 0
Therefore, y = 3.
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61-60÷2[35-3{-12÷6-4(15÷3-8)}]
Answer:
1/2(35-3(2-4)(5-8)
1/2(32(-2(-3))
1/2(32(-6))
1/2(192)
1into192/2
=96
Step-by-step explanation:
Write the equation in slope-intercept form. What are the slope and y -intercept?
a. 3 x+2 y=18
The equation in slope-intercept form is y = -3/2x + 9. Slope of the equation is - 3/2 and y - intercept is 9.
How do we find slope-intercept form?Calculate the slope (m).
Keep in mind that the slope is determined by dividing the change in y by the change in x. (rise over run).
Find the y-value of the y-intercept by solving (b).
In the formula y=mx+b, swap out m and b with their respective values.
The given equation is -
3x + 2y = 18
divide the equation by 2
3/2x + y = 9
Rearranging the equation -
y = -3/2x + 9
Comparing it with y = mx + c
so slope m = -3/2
and y - intercept = 9
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A company rents accessible bikes for people with physical disabilities. The scatter plot shows the relationship between the number of hours an accessible bike rented and the total amount paid at rental locations in different cities. Is the line y = 10x a good fit for the data? Use the drop -down menus to explain.
The Proportional relationship y = 10x is a good fit for the data.
What is a proportional relationship?
A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality,
i.e., y = kx
In which k is the constant of proportionality.
For this problem, foe each value of x, the output is 10 times that, hence the constant is k = 10 and the proportional relationship y = 10x is a good fit for the data.
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Answer:
The Proportional relationship y = 10x is a good fit for the data.
2. Use Structure Why do you multiply by a power
of 10 when writing a repeating decimal as a
rational number?
Answer:The idea is to multiply by some number (10, 100, 1000, etc.) so that when we subtract the original number from the multiple, the repeating part cancels out. If we multiply by 10, we get 10x = 2
Step-by-step explanation: sorry if its wrong thats all i remember
The formal for the valume v of a cylinder v=nr^(2)h,where is r is the radius of the base and h is height of the cylinder. solve the formal for h. then find the height of a cylinder with a valume of 36n cm^(2) and base with radius of 3 cm
The formula for the height of a cylinder is h = V / (π.r²) and the height of a cylinder with a volume of 36 cm³ and a radius of 3 cm is 4/π cm
Given a cylinder with a radius r and height h, then its volume is given by the formula:
V = π.r².h
Where:
V = volume
r = radius
h = height
To find the formula for the height, divide both sides by π.r²
V : π.r² = π.r².h : π.r²
or,
h = V / (π.r²)
The given parameters are:
V = 36 cm³
r = 3 cm
Substitute those parameters into the formula:
h = 36 / (π.3²)
h = 36 / (9π)
h = 4/π cm
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