It would be 13.3 years till the mass of the sample reached 24 grams.
What is exponential decay of a substance?'A quantity is subject to exponentially decay if it decreases at a rate proportional to its current value.'
According to the given problem,
Let x be the number of years spent,
Initial mass = 40 grams
Final mass = 24 grams
Half-life = 18 years
⇒ 24 = 40 × [tex]0.5^{\frac{x}{18} }[/tex]
⇒ 24/40 = 0.5^[tex]\frac{x}{18}[/tex]
⇒ 3/5 = 0.5^[tex]\frac{x}{18}[/tex]
Taking ln on both sides,
⇒ ln (3/5) = [tex]\frac{x}{18}[/tex] ln 0.5
⇒ ln (3/5) / ln (0.5) = x/18
⇒ x = ( 18 × ln (3/5) ) / ln (0.5)
⇒ x = 13.3 years
Hence, we can conclude that the sample need s 13.3 years to decrease its mass from 40 grams to 24 grams.
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PLEASE HELP ME QUICKKK, FIRST CORRECT PERSON GETS BRAINLIEST
PLEASE HELP I HAVE TO SUBMIT IT TODAY
Answer: 17,160 feet
Step-by-step explanation:
Because I mile = 5280 feet, 3 and 1/4 miles = 3.25 x 5280 = 17160 feet
Brainliest if correct
Answer:
x=29
Step-by-step explanation:
Just as simple as substitution:
We will substitute in 16 for y
So the equation will look like 16=x-13
Isolate x:
Add 13 to both sides isolate the variable
-13+13=0
16+13=29
The new equation:
29=x
29-13 is 16.
Identification of materials
It is used to analyze and verify materials for quality assurance.PMI is used to prevent potential product failure in manfunctioning.
Sheila lives in a $95,000 brick home in the country with contents valued at
$15,000. Use the table below to calculate her monthly property insurance
premium.
Annual Premium per $100 of coverage
Brick
Steel
Mixed
Wood
Area
Building Contents Building Contents Building Contents Building Contents
rating
City 0.39 0.43 0.5 0.54 0.55 0 65 0.66 0.76
Suburb 0.45 0.52 0.56 0.63 0.72 0.74 0.83
0.85
Rural 0.6 0.69 0.71 0.8 0.89 0.91 1
1.02
A. $95.00
B. $56.13
C. $173.50
D. $78.65
Her annual property insurance premium is $673.50.
Option A is the correct answer.
What is insurance?Insurance is a means of protection from financial loss in which, in exchange for a fee, a party agrees to compensate another party in the event of a certain loss, damage, or injury. It is a form of risk management, primarily used to hedge against the risk of a contingent or uncertain loss.
here,
We have,
To calculate Sheila annual property insurance premium, we need to determine the appropriate rating based on the type of house and the area where it is located. Aida's house is a brick house in the country,
So we need to use the "Brick" and "Rural" ratings from the table.
The rating for the building is 0.6 per $100 of coverage, so for a value of $95,000, the premium for the building is:
0.6 x $950 = $570
The rating for the contents is 0.69 per $100 of coverage, so for a value of $15,000, the premium for the contents is:
0.69 x $150 = $103.50
The total annual premium is:
$570 + $103.50 = $673.50
Thus,
Her annual property insurance premium is $673.50.
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helpp pleass love you if you answer meeee
Answer:
C. No solution.
Step-by-step explanation:
Due to the y-intercepts (When the equation is in slope-intercept form: 1.5, and 3.5) we can identify that the equations are parallel from each other.
The slopes are the same, but the y-intercepts are different, the equations will be 2 (y) apart since each will intersect at different values. This means that both equations can't intersect with each other, making it impossible to find a solution.
In a bag, there are a total of 50 dimes and quarters. 40% of the coins are quarters and 35% of the quarters are on heads. How many of the quarters are on tails?
Answer:
13 quarters must be tails.
Step-by-step explanation:
Number of quarters = 40% of 50 coins
Number of quarters = 40/100 * 50 = 20 coins which are quarters.
35% of these 20 quarters on heads. We can proceed in 2 ways from here.
We can actually find the number of quarters that are on heads.
35/100 * 20 = 7 quarters are showing heads.
Since the other quarters must be tails 20 - 7 = 13 quarters must be tails.
The other way to do it is to realize that if 35% of the coins are heads, 65% of the coins must be tails 20 * 65/100 = 13 which is a bit more direct.
Which inequality represents all values of x for which the product below is
defined?
A. x2-2
B. X20
c. xs-2
D. x >0
Answer:
B
Step-by-step explanation:
First you put that then multiply inside of that then you cross over percent than boom there's your awnser your welcome
The inequality that represents all values of x for which the product is defined is x ≥ 0
What is an inequality?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
Given is an expression, we need to determine the all values of x for which the product is defined,
The product is √4x · √x+2
We must meet both conditions:
(4x) ≥ 0 and (x+2) ≥ 0
So, 4x ≥ 0
x ≥ 0
And, x ≥ -2 [subtract 2 from both sides.]
So, we can say the condition should be x ≥ 0
Hence, the inequality that represents all values of x for which the product is defined is x ≥ 0
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Pls, look at the picture for the question.
Answer:
It would be m = -2
Step-by-step explanation:
For this line slope would be negative because it is going down. It is going 2 down 1 across. Since it is rise over run it would be -2/1.
A cook has 5 and 5/8 cups of flour he uses 2/3 on Saturday morning how much flour does he use in saturday morning
Answer:
2/3
this question doesn't make sense
X - 4y = -4
5x - 4y = 12
Answer:
Nothing further can be done with this topic. Please check the expression entered or try another topic.
x−4y=−45x−4y=12x-4y=-45x-4y=12
You have to give more than 5 gifts to friends this Christmas. You decide to give everyone scented candles. The candles in plain jars cost $3.79 each, and the ones in decorated jars cost $8.99 each. If you have at most $50 to spend, what is a possible solution to the problem? Let the number of candles in plain jars and the number of candles in decorated jars - y
2 candles in plain jars and 2 candles in decorated jars
6 candles in plain jars and 4 candles in decorated jars
8 candles in plain jars and 2 candles in decorated jars
14 candles in plain jars and 2 candles in decorated jars=y
Answer:
8 candles in plain jars and 2 candles in decorated jars
Step-by-step explanation:
Answer: 8 candles in plain jars and 2 candles in decorated jars
Step-by-step explanation:
Has to buy MORE than 5 and spend LESS than $50.00
8(3.79) = 30.32
2(8.99) = 17.98
30.32 + 17.98 =48.30
therefore she can buy 10 candles at $48.30
8 candles in plain jars and 2 candles in decorated jars
felipe deposits $500 into a bank account that pays simple interest at a rate of 2% per year how much interest will be be paid in the first 4 years
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ t=years\dotfill &4 \end{cases} \\\\\\ I=(500)(0.02)(4)\implies I=40[/tex]
MATH
Devon is making table runners for his niece's wedding. The short tables are 6 feet
(ft) long, and the long tables are 10 ft long. Each runner will overhang its table by 8
inches (in.) on each end. Devon was told there will be 12 small tables and twice that
number of long tables. How many total yards (yd) of fabric will he need to make the
table runners, assuming no waste? (Note: 12 in. = 1 ft and 3 ft = 1 yd.)
The sum of the lengths of the tables and the total length of overhang
give the length of fabric that Devon needs.
Response:
The total yards of fabric needed to make the table runners is 12 yd.How can the given dimensions be added to obtain the length of fabric needed?The given parameters are;
Length of the small tables = 6 feet
Length of the long tables = 10 feet
Length of overhang on each end = 8 inches
Number of small tables = 12
Number of long tables = 2 × 12 = 24
Required:
The yards of fabric needed to make the table runners.
Solution;
The total number of tables = 12 + 24 = 36
Length of overhang for each table = 8 inches + 8 inches = 16 inches
Sum of the length of the overhang = 36 × 16 inches = 576 inches
From the given unit conversion factors, we have;
Sum of the length of overhang = 576 inches ÷ 12 inch/feet = 48 feet
Length of the tables = 12 × 6 feet + 24 × 10 feet = 312 feet
Total length of table runner = 312 feet + 48 feet = 360 feet
Length of table runner needed = 360 feet ÷ 3 feet/yd = 120 yd.
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what is the remainder when you divide 2x^3+4x^2 - x +3 by x+2
Answer: The required remainder is 5.
Step-by-step explanation: We are given to find the remainder when we divide the following cubic polynomial by (x+2 :
3 f(x)=2x^ 3 +4x^ 2 - 6^ 2 -x+
(i)
We have the following theorem:
Remainder theorem: If a polynomial p(x) is divided by the factor (x-a), then the remainder is p(a).
So, for the given linear factor, we have
x + 2 = 0
Rightarrow x=-2
Substituting x = - 2 in equation (i), we get
f(- 2)
=2(-2)^ 3 +4(-2)^ 2 -(-2)+3
=-16+16+2+3
=5 .
Thus, the required remainder is 5.
Consider the following quadratic equation.
(x + 3)2 = 43
When taking the square root of both sides of this equation, how many solutions will the equation
have? How do you know?
Answer choices ⬇️
Answer:
(x+3)
2
=43
BY TAKING SQUARE ROOT ON BOTH SIDES
x + 3 = \sqrt{43}x+3=
43
OR
x + 3 = - \sqrt{43}x+3=−
43
THUS
x = \sqrt{43} - 3x=
43
−3
OR
x = - \sqrt{43} - 3x=−
43
−3
THIS QUADRATIC EQUATION HAS 2 SOLUTIONS SINCE √43 CAN BE A POSITIVE OR A NEGATIVE INTEGER. FOR EXAMPLE, 2^2=4
BUT, (-2)^2=4 Thus. √4=2 or (-2)
After this. Simply shifting the 3 on the LHS to keep 'x' on one side to find its value.
Taking the square root of both sides of the equation (x + 3)² = 43 will result in two solutions for x.
The correct option is C.
What is a quadratic equation?A basic quadratic equation, or a second-order polynomial equation with a single variable, is represented by the equation x : ax² + bx + c = 0, where a≠0 for the variable x. As it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution.
When taking the square root of both sides of the equation (x + 3)² = 43, we get:
x + 3 = ±√43
To solve for x, we can subtract 3 from both sides:
x = -3 ±√43
So there are two solutions for x:
x = -3 + √43
x = -3 - √43
Therefore, the solutions are x = -3 + √43 and x = -3 - √43.
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Algebra A
dations and inequantes
2. Which of the following graphs would represent the solution to y + 2 > 5?
-2 -1 0 1
2 3 4 5 6 7 8 9 10
+++
-109-8-7-6-5-4-3-2-101234 5 6 7 8 910
-2 -1 0 1 2 3 4 5 6 7 8 9 10
-2 -1 0 1 2 3 4 5 6 7 8 9 10
H4
[tex]\\ \tt\longrightarrow y+2>5[/tex]
[tex]\\ \tt\longrightarrow y>5-2[/tex]
[tex]\\ \tt\longrightarrow y>3[/tex]
[tex]\\ \tt\longrightarrow y\in (3,\infty)[/tex]
Graph attached
Answer:
see attached diagram
Step-by-step explanation:
y + 2 > 5
Subtract 2 from both sides:
⇒ y > 3
Graphing inequalities
< or > : dashed line to show that the line is not included in the region.
≤ or ≥ : solid line to show that the line is included in the region.
Draw a horizontal dashed line at y = 3 and shade above the line.
Number line
≤ or ≥ : closed circle
< or > : open circle
Draw an open circle at 3 and shade to the right.
Which best represents the approximate height of a coffee cup?
A) 10 centimeters
B) 10 kilometers
C) 10 millimeters
D) 10 meters
Answer:
10 centimeters, I think.
Step-by-step explanation:
NEED HELP ASAP!
Jennifer works in a music store and earns 15.4% commission on each sale. If Jennifer sells a piano and earns $48.00, what is the price of the piano? Round your answer to the nearest cent.
Answer:
The price of the piano is $311.69
Write 1.52888… as a mixed number in simplest form
Answer:
1 6611/12500
Step-by-step explanation:
1 is the whole number and 6611/12500 is in simplest form :)
Does the 90% confidence interval for the reduction in crime in the preschool group include zero? A. No, the 90% confidence interval for the population proportion is 1.70 1.70 to 4.10 4.10. (Round to two decimal places as needed.) Your answer is not correct.B. Yes, the 90% confidence interval for the population proportion is enter your response here to enter your response here . (Round to two decimal places as needed.) Part 3 Is this important? A. Yes, if zero is included in the confidence interval, then it is possible that there is a difference between the preschool programs. B. No, this is not important because confidence intervals always contain zero. C. No, this is not important because confidence intervals never contain zero. D. Yes, if zero is included in the confidence interval, then it is possible that there is no difference between the preschool progra
Help asap
Arian wants to save 20% of his paycheck is an a savings account .
A. Write an equation to represent the amount Arian should save , s, from a paycheck in the amount of p dollars .
B. Create a table of value with five different paycheck amounts.
Paycheck amount (p)
saving amount (s)
C. Plot the values in the coordinate plane to show the relationship between the amount Arian saves and the amount Arian earns.
D. Explain how you could use your graph to find how much of a $60 paycheck Arian should put into his savings account.
The equation that represents the amount that Arian should save is S = P x 20 / 100, and she should save $12 in case of earning a $60 paycheck.
EquationsGiven that Arian wants to save 20% of his paycheck is an a savings account, to determine A) an equation to represent the amount Arian should save, S, from a paycheck in the amount of P dollars; B) create a table of value with five different paycheck amounts; and D) find how much of a $60 paycheck Arian should put into his savings account; the following calculations must be made:
A) S = P x 20 / 100B) S = 500 x 20 / 100 = 100S = 1000 x 20 / 100 = 200S = 100 x 20 / 100 = 20S = 50 x 20 / 100 = 10S = 250 x 20 / 100 = 50D) S = 60 x 20 / 100 = 1200 / 100 = 12Therefore, the equation that represents the amount that Arian should save is S = P x 20 / 100, and she should save $12 in case of earning a $60 paycheck.
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Radhika’s mother gave her some money to buy Papaya from the market at
the rate of p(x) = x² – 12x – 220 per kg.
(i) Find the factors of the given polynomial.
(ii) if she purchase 5kg papaya, what money she have to pay?
Answer:
p ( x ) = ( x- 6 ) ² - 256
Step-by-step explanation:
1- Add the same value to both sides
2- Add 36 to the expression
3- Add 36 to the left-hand side
4- Factor the expression
5- Move the constant to the right
6- Calculate
The factors of the given polynomial is (x-10) (x+22) and the price of 5 kg papaya is 5x²-60x-1100.
What is Polynomial?An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.
Given:
p(x) = x² – 12x – 220
i) These two terms are 22x and -11x.
p(x) = x²-12x-220
p(x) = x²+22x-10x-220
Taking x common from the first two terms and -10 from the last two terms,
x(x+22)-10(x+22)
(x-10) (x+22)
ii) We are given that the rate of papaya per kg is p(x) = x²-12x-220.
1 kg = x²-12x-220
5 kg = 5(x²-12x-220)
5 kg = 5x²-60x-1100
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I need help with this question.
Answer:
The rate of change is 1 for both functions A and B
Step-by-step explanation:
Hope this helps!
Pls give brainliest :)
Help me with this please !! , the struggle is reall. :/
Answer: The slope would be 2/3. The parallel slope would be 2/3. the parallel intercept is -4
Step-by-step explanation: I how this helps!
find the volume and round to the nearest whole number
Answer:
527 cubic meters
Step-by-step explanation:
The area of the cube would be 7.5^3 and the area of the rectangular prism would be 3.75*3.75*7.5. Then it would be 421.9 + 105.5 and rounded to the whole number the answer would be 527
Solve the equation
2x + 5 -12
2. The result of multiplying a number by another number is called the
a. Quotient
b. Product
c. Sum
d. Difference
The answer is the product
100 points!!!
“The revenue equation for a certain brand of toothpaste is y=2.6x, where X is the number of toothpaste sold and y is the income for selling X tubes. Cost equation is y=X+2000, where X is the number of tubes of toothpaste manufactured and y is the cost of producing X tubes. The following set of axis shows the graph of the cost and revenue equations. For what X-values will the company make a profit”
The company will make a profit for X-values: (greater than, less than, or equal to) ____?
Answer:
The revenue equation is y=2.6x,
cost equation is y=x+2000
When the company makes profit only when revenue > cost
Lets frame inequality using revenue > cost
Replace the revenue equation and cost equation
Now solve the inequality for x
Subtract 1x from both sides
Divide both sides by 1.6
The company makes profit when x is greater than 1250
Step-by-step explanation:
Answer:
Greater than 1250
x > 1250
Step-by-step explanation:
Base on the revenue equation and cost equation , we can infer that the company make a profit when x > 1250
Important Given Information:
The revenue equation is [tex]y=2.6x[/tex]
Cost equation is [tex]y = x+2000[/tex]
When the company makes profit only when: [tex]revenue > cost[/tex]
Let's frame inequality using: [tex]revenue > cost[/tex]
Replace the revenue equation and cost equation
[tex]Revenue > Cost: 2.6x > + 2000[/tex]
Now Let's solve the inequality for x
[tex]2.6x > 1x + 2000[/tex]
[tex]2.6x - 1x > 2000[/tex] [tex][2.6x-1x=1.6x][/tex]
[tex]1.6x > 2000[/tex]
Divide both sides by 1.6 ( what you do on one side do to the other)
[tex]\frac{1.6x}{1.6}=\frac{2000}{1.6}[/tex]
[tex]x >1250[/tex]
Hence, the company makes profit when x is greater than 1250
[RevyBreeze]
the dimensjlns of regulation tennis courts are 27 feety by 78 feet.
Answer:
26 in. x 9 in.
Step-by-step explanation:
27 / 9 =
3
78 / 3 =
26
9 inches by 26 inches