Finding the final amount in a word problem on continuous exponential growth or decay
Answers
Given:
The mass of radioactive follows an exponential decay model
The initial mass = 418 kg
Decreases at a rate = r = 4% per day
So, the general formula for the mass will be:
[tex]m=418\cdot(1-0.04)^d[/tex]where: (m) is the mass after (d) days
So, to find the mass after 2 days, we will substitute with d = 2
so,
[tex]m=418\cdot(1-0.04)^2=418\cdot0.96^2=385.2288[/tex]rounding to the nearest tenth
so, the answer will be mass after 2 days = 385.2 kg
Related Questions
A circle has a circumference of 43.96 inches. What is the area?
Answers
Solution:
Given that the circumference of the circle is
[tex]C=43.96in[/tex]Step 1:
Calculate the radius of the circle
To calculate the radius of the circle, we will use the formula below
[tex]\begin{gathered} C=2\pi r \\ \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} C=2\pi r \\ 43.96=2\times\pi\times r \\ 43.96=6.28r \\ \text{divide both sides by 6.28} \\ \frac{6.28r}{6.28}=\frac{43.96}{6.28} \\ r=7in \end{gathered}[/tex]Step 2:
Calculate the area of the circle using the formula below
[tex]\begin{gathered} A=\pi r^2 \\ \text{Where,} \\ \pi \\ r=7in \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} A=\pi r^2 \\ A=\pi\times7^2 \\ A=\pi\times49 \\ A=153.94in^2 \end{gathered}[/tex]Hence,
The Area of the circle is = 153.94 in²
A machine worked for 4hours and used 6kilowatts of electricity.What is the rate ofenergy consumed inkilowatts per hour?*Enter your answer as a decimal
Answers
4 hours ---> 6 kilowatts
1 hour -----> x kilowatts
[tex]\begin{gathered} 4\times x=1\times6 \\ 4x=6 \\ \frac{4x}{4}=\frac{6}{4} \\ x=\frac{3}{2}=1.5 \end{gathered}[/tex]answer:
1.5 kilowatts per hour
Graph the function and state the domain and range.g(x)=x^2-2x-15Domain-Range-Graphed function-
Answers
The domain: -∞ < x < ∞
The range: g(x) ≥ -16
Explanation:The given function is:
[tex]g(x)\text{ = x}^2\text{-2x-15}[/tex]The domain is a set of all the valid inputs that can make the function real
All real values of x will make the function g(x) to be valid
The domain: -∞ < x < ∞
The range is the set of all valid outputs
From the function g(x):
a = 1, b = -2
[tex]\begin{gathered} \frac{b}{2a}=\frac{-2}{2(1)}=-1 \\ g(-1)=(-1)^2-2(-1)-15 \\ g(-1)=1-2-15 \\ g(-1)=-16 \end{gathered}[/tex]Since a is positive, the graph will open upwards
Therefore, the range of the function g(x) is: g(x) ≥ -16
The graph of the function g(x) = x^2 - 2x - 15 is plotted below
5.) y = -5/4 x + 10 (Use Slope Int. Method Make apparent your Int. Point AND the point from your slope = RISE/RUN)
Answers
write a ratio that is equivalent to the ratio 25:10
Answers
25:10 can be writen as
[tex]\frac{25}{10}[/tex]Since the numerator and the denominator are divisible by 5, then we have
[tex]\frac{25}{10}=\frac{5\times5}{5\times2}=\frac{5}{2}[/tex]Then, an equivalent ratio of 25:10 is 5:2
Which equation could result from
performing the distributive property
to
8.53 – 2 (2x + 8) =?
-
A
О
4.52 + 16 = 11.5
B
O
4.5x + 27 = -9
С
O
4.5x - 16 = 11
D
-4.52 +27 = 45
Answers
C
1) The distributive property allows us to rewrite some product in factors.
2) Let's then examine that equation:
[tex]\begin{gathered} 8.5x-2(2x+8)=\text{?} \\ 8.5x-4x-16= \\ 4.5x-16 \end{gathered}[/tex]3) Then examining the options, the only option that displays the correct application of the Distributive Property on the left side is: C
"Solve for x. Enter as a decimal not as a fraction. Round to the nearest hundredth if necessary."
Answers
Answer:
x =
5
Explanation
From the given diagram, it can be infered that WY = 2QR
From the diagram
WY = x+9
QR = 2x-3
substitute into the expression
x+9 = 2(2x-3)
x+9 = 4x - 6
Collect the like terms
x-4x = -6-9
-3x = -15
x = -15/-3
x = 5
Hence the value of x is 5
Brady needs to fill his daughter's sandbox that is 5 feet by 7 feet. He wants to buy sand bags to fill the sand 2 feet deep. He compares the prices found for sand at two different stores.PART AWhat is the unit rate that store X is selling for? ____ lbs/dollarPART BWhich store is offering the better price?____PART CBrady finds online that it takes 100 pounds of sand to fill 1 cubic foot. Using the better priced store, compute how much it will cost him to purchase enough sand to fill the sandbox. Use the volume formula, V = I × w × h, to determine your answer.$____from____
Answers
The sand box is rectangular with
Wide= 5feet
Length= 7feet
He wants to fill the box with a depth of 2 feet
Solve for the remaining angles and side of the one triangle that can be created. Round to the nearest hundredth:A = 100"a = 3.5, b = 3
Answers
Given:
• A = 100 degrees
,• a = 3.5
,• b = 3
Let's solve for the remaining angles and side of the triangle.
Here, we are given one angle and two sides.
To solve, apply the Law of Sines:
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]• To solve for measure of angle B, we have:
[tex]\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b} \\ \\ \frac{\sin100}{3.5}=\frac{\sin B}{3} \\ \\ \sin B=\frac{3\sin 100}{3.5} \\ \\ \sin B=\frac{2.954}{3.5} \\ \\ \sin B=0.844 \end{gathered}[/tex]Take the sine inverse of both sides:
[tex]\begin{gathered} B=\sin ^{-1}(0.844) \\ \\ B=57.58^0 \end{gathered}[/tex]Therefore, the measue of angle B is = 57.58 degrees.
• To solve for angle C, apply the Triangle Angle Sum Theorem.
m∠A + m∠B + m∠C = 180
m∠C = 180 - m∠A - m∠B
m∠C = 180 - 100 - 57.68
m∠C = 22.32
The measure of angle C is 22.32 degrees.
• To find the length of c, apply the Law of Sines:
[tex]\begin{gathered} \frac{\sin A}{a}=\frac{\sin C}{c} \\ \\ \frac{\sin100}{3.5}=\frac{\sin 22.32}{c} \\ \\ c=\frac{3.5\sin 22.32}{\sin 100}\tan ^{-1}\tan ^{-1} \\ \\ c=\frac{1.329}{0.9848} \\ \\ c=1.35 \end{gathered}[/tex]The length of side c is 1.35 units.
ANSWER:
• B = 57.58,°
,• C = 22.32,°
,• c = 1.35
A study determined that 9% of children under 18 years of age live with their father only. Find the probability that at most 2 persons selected at random from 12 children under18 years of age lived with their father onlyThe probability that at most 2 children live with their father only is(Do not round until the final answer. Then round to the nearest thousandth as needed)
Answers
Step 1: Write out the formula for binomial distribution
[tex]P(x)=^nC_x\times p^x\times q^{n-x}[/tex]Where
[tex]\begin{gathered} p\Rightarrow\text{probability of success} \\ q\Rightarrow\text{probability of failure} \\ n\Rightarrow\text{ number of trails } \\ x\Rightarrow\text{ number of success required} \end{gathered}[/tex]Step 2: State out the parameters needed in the formula to find the probabilty
[tex]\begin{gathered} p=9\text{ \%=}\frac{9}{100}=0.09 \\ q=1-p=1-0.09=0.91 \\ n=12 \\ x\Rightarrow\le2\Rightarrow0,1,2 \end{gathered}[/tex]Step 3: The probability that at most 2 children live with their father only can be described as;
[tex]P(x\le2)=P(0)+P(1)+P(2)[/tex]Step 4: Find the probability of each number of successes required
[tex]\begin{gathered} P(0)=^{12}C_0\times(0.09)^0\times(0.91)^{12-0} \\ P(0)=1\times1\times0.322475487=0.322475487 \end{gathered}[/tex][tex]\begin{gathered} P(1)=^{12}C_1\times(0.09)^1\times(0.91)^{12-1} \\ =^{12}C_1\times(0.09)^1\times(0.91)^{11} \\ =12\times0.09\times0.354368667=0.38271816 \end{gathered}[/tex][tex]\begin{gathered} P(2)=^{12}C_2\times(0.09)^2\times(0.91)^{12-2} \\ =^{12}C_2\times(0.09)^2\times(0.91)^{10} \\ =66\times0.0081\times0.389416118=0.208181856 \end{gathered}[/tex]Step 5: Add all the number of successess required
[tex]\begin{gathered} P(x\le2)=0.322475487+0.38271816+0.208181856 \\ =0.913375503 \\ \approx0.913 \end{gathered}[/tex]Hence, the probability that at most 2 children live with their father only is 0.913
convert the equation of a parabola to vertex formy^2+4x-14y+57=0
Answers
first we need to solve X
[tex]\begin{gathered} -y^2+14y-57=4x \\ x=-\frac{1}{4}y^2+\frac{7}{2}y-\frac{57}{4} \\ \end{gathered}[/tex]we need to write the equation on this form
[tex]x=a(y-h)^2+k[/tex]where h=-(b/2a) and k=c- a (b/2a)2
we obtain a,b and c from the equation to solve x
so a=-1/4, b=7/2 and c=-57/4
now lets find h and k
[tex]\begin{gathered} h=-(\frac{b}{2a}) \\ h=-(\frac{\frac{7}{2}}{2\cdot-\frac{1}{4}}) \\ \\ h=-(\frac{\frac{7}{2}}{\frac{-1}{2}}) \\ \\ h=-(-7) \\ h=7 \end{gathered}[/tex][tex]\begin{gathered} k=c-a(\frac{b}{2a})^2 \\ \\ k=-\frac{57}{4}-(-\frac{1}{4})(\frac{\frac{7}{2}}{2\cdot-\frac{1}{4}})^2 \\ \\ k=-\frac{57}{4}+\frac{1}{4}(-7)^2 \\ \\ k=-\frac{57}{4}+\frac{1}{4}(49) \\ \\ k=-\frac{8}{4} \\ k=-2 \end{gathered}[/tex]now replace a, h and k on the equation
[tex]\begin{gathered} x=a(y-h)^2+k \\ \\ x=-\frac{1}{4}(y-7)^2-2 \end{gathered}[/tex]the evrtex is (h,k)=(7,-2)
It is question 16 pls help
Answers
Answer: yes it is 16 i did my work let me know if you want me to show my work
Step-by-step explanation:
How much higher is the summit of Mt. McKinley than the summit of Mt. Kosciuszko?
Answers
Based on the heights of the summits of Mt. McKinley and Mt. Kosciuszko, we find that Mt. McKinley is higher than Mt. Kosciuszko by 13,000 ft
What are the heights of Mt. Kosciuszko and Mt. McKinley?Mt. McKinley is reputed to be the tallest mountain in the North American continent which makes sense considering it has a summit with the height of 20,310 feet.
Mt. Kosciuszko on the other hand, is not that tall and stands at a height of 7,310 ft and is located in Australia.
The difference between both summits is:
= 20,310 - 7,310
= 13,000 ft
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Which mapping diagram is NOT a function?
Answers
Answer:
D is not a function--an x-value cannot correspond to more than one y-value.
Count the unit squares, and Ind the surface area of the shape represented byeach net. One cube = 1 ft^2
Answers
The surface area of the figure is the sum of the area of the squares. Since they're all equal, is the amount of squares times the area of one square. We have a total of six squares, with a side length equal to 4 units. The area of a square is given by the product of its side length by itself, therefore, the total surface area of this figure is
[tex]6\cdot(4^2)=6(16)=96[/tex]The area of this figure is 96 ft².
Answer: 72 Square Meters sorry super late
Step-by-step explanation:
Simplify 3√12 +8✓12 - √6 how
Answers
In order to simplify this equation, we are going to start by simplifying the radicals.
[tex]\sqrt[]{12}=\sqrt[]{2^2\cdot3}=\text{2}\sqrt[]{3}[/tex]Now we have the radicals simplified and we are going to replace them on the equation that we already have.
[tex]\begin{gathered} 3\cdot(2\sqrt[]{3})+8\cdot(2\sqrt[]{3})-\sqrt[]{6} \\ 6\sqrt[]{3}+16\sqrt[]{3}-\sqrt[]{6} \\ 22\sqrt[]{3}-\sqrt[]{6} \end{gathered}[/tex]what is the equation of the line passing through (-4,0) and (01)
Answers
The from y=mx passes through the points (2, - 15) and (6, - 45)
Answers
y = -7.5x
Explanation:The given points: (2, -15) and (6, -45)
The equation of the proportional relationship given:
y = mx
m = slope
We apply slope formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} x_1=2,y_1=-15,x_2=6,y_2\text{ = }-45 \\ m\text{ = }\frac{-45\text{ - (-15)}}{6\text{ - 2}} \\ m\text{ = }\frac{-45+15}{4} \end{gathered}[/tex][tex]\begin{gathered} m\text{ = }\frac{-30}{4} \\ m\text{ = -15/2} \\ m\text{ = -7.5} \end{gathered}[/tex]The relationship of the equation becomes:
y = -7.5x
Pedro can't decide which size pizza to order. The 10-inch cheese and sausage pizza is $4.99, while the 12-inch deluxe is $5.99. If he gets the 10-inch pizza, the total price will be divided among 3people. If he chooses the 12-inch pizza, then the total price will be divided among 4 people. Which is the better buy? How much will each person pay? (Use 3.14 for r.)A. 10-inch pizza; $1.50B. 12-inch pizza; $1.50C. 10-inch pizza; $1.66 D. 12-inch pizza; $1.66
Answers
Answer: The better buy is the the 12-inch deluxe for $5.99.
B. 12-inch pizza; $1.50
Explanation:
From the information given, the 10-inch cheese and sausage pizza is $4.99, while the 12-inch deluxe is $5.99. If he gets the 10-inch pizza. We would calculate the area of both pizzas by applying the formula for calculating the area of a circle which is expressed as
Area = πr^2
where
π = 3.14
r is the radius of the circle
For the 10-inch cheese and sausage pizza,
diameter = 10
r = 10/2 = 5
Area = 3.14 x 5^2 = 78.5
If it is divided among 3 people,
each person gets 78.5/3 = 26.2 in^2
Amount that each person pays = 4.99/3 = $1.66
This means that each person pays $1.66 for 26.2 in^2
For the 12-inch cheese and sausage pizza,
diameter = 12
r = 12/2 = 6
Area = 3.14 x 6^2 = 113.04
If it is divided among 4 people,
each person gets 113.04/4 = 28.26 in^2
Amount that each person pays = 5.99/4 = $1.5
This means that each person pays $1.5 for 28.26 in^2
Thus, the better buy is the the 12-inch deluxe for $5.99.
The amount that each person pays is
B. 12-inch pizza; $1.50
Which x-value is in the domain of the function? Thank you!
Answers
Solution:
Given the function;
[tex]f(x)=4\cot(2x)+3[/tex]The graph of the function is;
ANSWER:
[tex]\frac{\pi}{3}[/tex]i inserted a picture of the question state whether it’s a b c or d please don’t ask tons of questions yes i’m following
Answers
The possible values for any probability are between zero and one. With this in mind we conclude that A, B, C and E are allowed probabilities
i am stuck and need help ASAP with itfind the area
Answers
Given:
Required:
We want to find the area of given
Explanation:
As we can see that measurement of given figure is 5 by 5 so it is square and the area of square is
[tex]5*5=25\text{ unit}^2[/tex]Final answer:
25 sq unit
An auto mechanic recommends that 3 ounces of isopropyl alcohol be mixed with a tankful of gas (14 gallons ) to increase the octane of the gasoline for better engine performance. At this rate, how many gallons of gas can be treated with a 16-ounce bottle of alcohol (You don’t need to translate or understand just solve the word problem please )
Answers
Let be "x" the number of gallons of gas that can be treated with a 16-ounce bottle of alcohol.
According to the information given in the exercise, 3 ounces of isopropyl alcohol should be mixed with 14 gallons of gas.
Then, you can set up the following proportion:
[tex]\frac{14}{3}=\frac{x}{16}[/tex]Now you have to solve for "x":
[tex]\begin{gathered} (16)(\frac{14}{3})=x \\ \\ \frac{224}{3}=x \\ \\ x\approx74.67 \end{gathered}[/tex]Therefore, the answer is:
[tex]\approx74.67\text{ }gallons[/tex]How do you slove this promblem 207.4÷61
Answers
we have
207.4÷61
[tex]207.4\div61=\frac{207.4}{61}=\frac{2,074}{610}=\frac{1,830}{610}+\frac{244}{610}=3+\frac{244}{610}=3\frac{244}{610}[/tex]simplify
244/610=122/305=4/10=2/5
therefore
the answer is 3 2/5A grocery store sells bags of oranges in two different sizes.The 3-pound bags of oranges cost $4. The 8-pound bags of oranges cost $9. Which oranges cost less per pound? Explain your reasoning
Answers
The per pound cost of the bag of oranges which price is $9 for 8-pounds is less .
In the question ,
it is given that a grocery store sells bags of oranges in two different sizes .
in first bag where 3 pound bags of oranges cost $4 .
So, 1 pound bag of orange will cost = 4/3 = $1.333 .
in the second bag where 8 pounds bags of oranges cost $9 .
So, 1 pound bag of orange will cost 9/8 = $1.125 .
we can see that $1.125 < $1.333 .
hence , the second bag of oranges costs less .
Therefore , the per pound cost of the bag of oranges which price is $9 for 8-pounds is less .
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A landscape supply business charges $35 to deliver mulch. The cost of the mulch is
$29 per cubic yard. Write a linear equation to find the cost of having x cubic yards of
mulch delivered to a site.
Answers
The linear function to represent the number of mulch delivered to a site is y = 29x + 35
What is a linear function?In mathematics, the term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.
For this question, we can represent the cost of having x cubic yards of mulch delivered to a site. For a standard linear function, it can be represented as y = mx + c
m = slope
c = intercept
We can use this concept to write a linear function to represent this problem:
y = mx + c
y = 29x + 35
In this case, the slope is 29 and the intercept is 35. The slope in this situation is the cost of the mulch and the amount charged by the business is the intercept.
The equation representing this problem is y = 29x + 35
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What is the x-intercept of the line y=-2x+6? (3,0) -6,0) (0,3) (-3,3)
Answers
The given equation is expressed as
y = - 2x + 6
The x intercept of a line is the point at which y = 0
By applying this concept, it means that
0 = - 2x + 6
Adding 2x to both sides of the equation, it becomes
0 + 2x = - 2x + 2x + 6
2x = 6
Dividing both sides by 2, it becomes
2x/2 = 6/2
x = 3
Therefore, the correct option is (3, 0)
can somone hep me please
Answers
Hi
a) = (8x2) x (10 ‐³ x10 ‐⁴)
= 8 x 2 you get 16 then 10‐³-⁴
16 x 10 ‐⁷
= 1.6 x 10¹ x 10 ‐⁷
= 1.6 x 10 ‐⁶
final answer
1.6 x 10 ‐⁶
Which of the following is NOT a factor of x3 + x2 - 4x - 4?x + 1x + 2x - 1x - 2
Answers
Answer: (x - 1)
Explanation
Given:
[tex]x^3+x^2-4x-4[/tex]To factor a third-degree polynomial, we can do it by grouping:
[tex]=(x^3+x^2)+(-4x-4)[/tex]Then, we have to find the common factor between groups:
[tex]=x^2(x+1)-4(x+1)[/tex]Now, we can get the common factor of (x+1):
[tex]=(x^2-4)(x+1)[/tex]Finally, the differences of squares equal the following:
[tex](x^2-a^2)=(x-a)(x+a)[/tex]Then, applying this rule to our factor we get:
[tex]=(x+2)(x-2)(x+1)[/tex]Thus, the only factor that is not correct is (x - 1)
Solve. Your answer should be in simplest form. (2 1/6)(1 1/3) HELP!!!!
Answers
The simplified form of the expression (2 1/6 ) × (1 1/3) is 26/9.
What is the simplified form of the given expression?Given the expression in the question;
(2 1/6 ) × (1 1/3)
To simplify, first convert from mixed to improper fraction.
(2 1/6 ) × (1 1/3)
( (2×6 + 1)/6 ) × (1 1/3)
( (12 + 1)/6 ) × (1 1/3)
( 13/6 ) × (1 1/3)
( 13/6 ) × (1×3 + 1/3)
( 13/6 ) × (3 + 1/3)
( 13/6 ) × (4/3)
Now, cancel the common factor 2.
13/6 × 4/3
13/3 × 2/3
( 13 × 2 ) / ( 3 × 3 )
( 26 ) / ( 9 )
26/9
Therefore, the simplified form is 26/9.
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