[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\dotfill &11\\ P=\textit{initial amount}\dotfill &160\\ t=\textit{elapsed time}\\ h=\textit{half-life}\dotfill &14 \end{cases} \\\\\\ 11=160\left( \frac{1}{2} \right)^{\frac{t}{14}}\implies \cfrac{11}{160}=\left( \cfrac{1}{2} \right)^{\frac{t}{14}}\implies \log\left( \cfrac{11}{160} \right)=\log\left[ \left( \cfrac{1}{2} \right)^{\frac{t}{14}} \right][/tex]
[tex]\log\left( \cfrac{11}{160} \right)=\cfrac{t}{14}\log\left[ \left( \cfrac{1}{2} \right)\right]\implies \cfrac{\log\left( \frac{11}{160} \right)}{\log \left( \frac{1}{2} \right)}=\cfrac{t}{14} \\\\\\ 14\left( \cfrac{\log\left( \frac{11}{160} \right)}{\log \left( \frac{1}{2} \right)} \right)=t\implies {\LARGE \begin{array}{llll} \stackrel{mins}{54.1}\approx t \end{array}}[/tex]
Help please I am struggling no need to graph it though.
Step-by-step explanation:
here are the answers. I hope they're clear.
Solve for c
21 = 5/6c - 9
Answer:
C=36
Step-by-step explanation:
Answer:
c = 36
Step-by-step explanation:
so our equation is 21 = 5/6c - 9
first we need to get rid of the 9. in order to do this, we have to do the opposite of the action shown. so in this case, we would add 9 to both sides. we add it to both sides to keep the equation balanced and equal.
adding 9 to 21 gives us 30. so our equation would then be 30 = 5/6c
now we need to get the c by itself. so we divide by 5/6 because in the original equation the 5/6 and the c are being multiplied to each other.
when we devide 5/6c by 5/6, it cancels out. leaving us with c. 30 divided by 5/6 will in turn gives 36. and there is your answer.
Which expression is equivalent to 2−3?
Answer: 2-3= -1
4-5= -1
Step-by-step explanation:
Answer:3-2
Step-by-step explanation:commutative property
Slope = -1, through point (-3,5)
The equation of the line having slope = -1 and passing through a point (-3, 5) is y = -x + 2 and graph is given below.
The general equation of a line is y = m × x + c, where m is the slope and c is the y-intercept of the line.
Given slope is equal to -1.
Therefore the equation of the required line is y = (-1) × x + c.
Given that this line passes through the point (-3, 5).
Therefore we have 5 = (-1) × (-3) + c
⇒ 5 = 3 + c
⇒ 5 - 3 = c
⇒ 2 = c
⇒ c = 2
Therefore the y-intercept of the required line in cartesian coordinate form is (0, 2).
Therefore the required equation of the line is y = (-1) × x + 2
⇒ y = -x + 2.
Refer to the attached image for the graph of this line.
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Disclaimer: The question is not incomplete.
Assuming the following as the complete question.
Find the equation of the line having slope = -1, through point (-3,5) and also draw the graph of the line.
Suppose that 24 inches of wire costs 72. At the same rate, how much (in cents) will 49 inches of wire cost?
I'm assuming the "costs 72" is referring to 72 cents.
If so, then this is one way to solve:
(24 inches)/(72 cents) = (49 inches)/(x cents)
24/72 = 49/x
24*x = 72*49
x = 72*49/24
x = 147
It costs 147 cents, aka $1.47, to get 49 inches of wire.
A team of explorers on a expedition was interupted by bad weather on 20%, if the weather was bad for 45 days what was the total number of days were on the missoin
The mission was of 225 days.
We are informed from the question the percentage of bad days and number of bad days. So, relating the two parts of question will give the number of days explorers were on mission. Let us assume the total number of days of mission be x.
20% × x = 45
Solving the equation now -
20/100x = 45
Shifting 100 to Right Hand Side of the equation as denominator
20x = 45 × 100
Performing multiplication on Right Hand Side of the equation
20x = 4500
Shifting 20 to denominator on Right Hand Side of the equation
x = 4500 ÷ 20
Performing division on Right Hand Side of the equation
x = 225
Hence, explorers were on mission for 225 days.
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URGENT!!! 100 POINTS
The Thai Pepper has a hotness rating of 7.5 x 10^4 on the Scoville scale.
The Red Savina Habanero has a hotness rating of 4.6 x 10^5 on the Scoville scale.
How many times hotter is the Red Savina Habanero than the Thai Pepper?
The Red Savina Habanero is hotter than the Thai Pepper with a number of 6. 1 times
What is ratio?A ratio can be defined as the comparison of two or more numbers on the basis of their sizes in relation to each other.
It also indicates how many times one number contains another.
Given that;
Hotness rating of Thai Pepper = 7.5 x 10^4 Hotness rating of Red Savina Habanero = 4.6 x 10^5To determine the ratio, we have to divide Red Savina Habanero hotness rating by Thai Pepper hotness rating
= 4.6 x 10^5 / 7.5 x 10^4
= 6. 1 times
Thus, the Red Savina Habanero is hotter than the Thai Pepper with a number of 6. 1 times
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Describe the translation from shape A to
shape B as a vector.
Step-by-step explanation:
Translating it on a vector it will be that
The ______ variable in a study, also known as the response variable, is affected by the ______ variables.
The dependent variable in a study, also known as the response variable, is affected by the independent variables.
What is a variable?
A variable is a sign and placeholder for any mathematical object (from the Latin variabilis, "changeable") in mathematics. A variable can, for example, represent a number, a vector, a matrix, a function, the argument of a function, a set, or a set's component.
Numerous issues are resolved in a single computation by using variables in algebraic calculations as if they were explicit integers. For instance, by exchanging the variables that represent them in the quadratic formula with the numerical values of the coefficients in any given quadratic equation, the quadratic formula may solve any quadratic equation. A variable in mathematical logic is either a symbol for an undefined term in the theory or an undefined phrase itself (a meta-variable).
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The Reunion Tower in Dallas, Texas, is topped by a spherical dome that has a surface area of approximately 13,924 \pi square feet. What is the volume of the dome? Round to the nearest tenth.
The volume of the spherical dome will be 12.9π cubic feet when the surface area of the dome is 13.924π.
What is the volume of the sphere?The volume of the cone is the amount of quantity, which is obtained in the 3-dimensional space. The dome is the shape of a semi-sphere the volume of the dome will be half of the volume of the sphere.
Given that the Reunion Tower in Dallas, Texas, is topped by a spherical dome that has a surface area of approximately 13,924π square feet.
The volume of the dome will be calculated as below:-
SA = 13.924π
2πr² = 13.92π
r = √6.96
r = 2.63 feet
Volume = 2 / 3 πr³
Volume = ( 2 / 3 ) π ( 2.63)³
Volume = 12.24π cubic feet
Therefore, the volume of the spherical dome will be 12.9π cubic feet.
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A square rug has an area 38 ft2. Write the side length as a square root. Then decide if the side length is a rational number.
Then the rug has side length
Is the side length a rational number?
The side length of rug is 6.16 ft which is not a rational number.
A rational number, in arithmetic, a number that can be expressed as the quotient p/q of two integers such that q ≠ 0.In addition to all fractions, the set of rational numbers also includes all integers. Each of these can be expressed as a quotient with an integer in the numerator and 1 in the denominator.
Area of square rug = 38 ft square
Area of square = side * side
area of square = area of square rug
side*side=38
(side)^2= 38
side=√38
side=6.16
Hence, The side length of rug is 6.16 ft which is not a rational number.
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Graph the equation. Plot at least five points on the graph and label them with their
coordinates.
3. y = x - 1
4. y = 2|x|
S -6
6
4
4
-8-1
x
S -6
4
3
41
6
x
Answer: answer is si - 90w 8y 28y xis 4
Step-by-step explanation:
Please help me please help me
Answer: FINAL IMAGE OF L IS 6 AND 7
Step-by-step explanation:
Answer:(1,-2)
Step-by-step explanation:
HELP!!!!
Bone-shaped treats are 5 for $3.50 at Shelley’s store and Sarah wants to buy 12. She set up and solved this proportion to find how much they would cost. Describe her error and find the correct solution.
5
3.5
=
12
x
3.5x = 60
x = $17.14
Answer:
3.5/5x12=8.4
Step-by-step explanation:
Olivia's Cupcake Shoppe sells small and large cupcakes in three flavors.
Niamh paid $3 for a cupcake with buttercream icing.
Bethany bought a small vanilla cupcake.
Mateo paid $3.50 for a cupcake with strawberry icing
and a chocolate cupcake.
Use the axioms to make two conclusions about the
cakes that were purchased
Answer:
Step-by-step explanation:
Answer:
Small
Small
Vanilla
Strawberry
Step-by-step explanation:
Gracie has two identical fidget cubes shown below. The edge length of the fidget cubes is 4 centimeters. What is the combined volume of the two fidget cubes in cubic centimeters?
Answer:
24
Step-by-step explanation:
so edge length means you count how many cubic units you can see when looking from length width and height
since the edge length is four, you multiply that by 3 (length width and height are all 4) and that would be 12
since there are two you do two times 12= 24 (im not 100% sure cuz I haven't learned this yet)
Simplify 57 over 85 hurry
Answer:
Step-by-step explanation:
since no numbers can go into 57 over 85 except one your answer would be 57/85
Answer: 57/85
Step-by-step explanation:
57/85
is already in the simplest form. It can be written as 0.670588 in decimal form (rounded to 6 decimal places).
Find the GCD (or HCF) of the numerator and denominator
GCD of 57 and 85 are 1
Divide both the numerator and denominator by the GCD
57 ÷ 1
85 ÷ 1
Reduced fraction:
57
85
Therefore, 57/85 simplified to the lowest terms is 57/85.
hope this helps u ; )
10 times as much as 2,000 is 1/10 of what number?
When a new charter school opened in 2005, there were 350 students enrolled. Since then, the student population has
decreased by 100 students every two years.
Choose the formula below which gives the function N(t) representing the number of students attending the charter school
t years after 2005.
Select the correct answer below:
ON(t) = 100t + 350
ON(t)=-100t + 350
ON(t) = 50t + 350
ON(t) = -50t + 350
ON(t) = 350t + 100
ON(t) = -350t + 100
The number of students attending the charter school t years after 2005 is given by -50t + 350
What is an equation?An equation is used to show the relationship between numbers and variables. An equation can be linear, quadratic depending on the degree.
Let N(t) represent the number of students after t years, hence:
Since the population has decreased by 100 students every two years:
N(t) = -(100)/2 * t + 350 = -50t + 350
The number of students attending the charter school t years after 2005 is given by -50t + 350
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2(s+t) 3 power - 6 when s=3 t=2.
We'll observe that the evaluated expression equals 244 in the next step.
How is an expression evaluated?To evaluate an expression, we only need to swap out the variables with the desired values.
What does evaluating expressions look like in practice?When x = 5 x = 5 x=5, you can be asked to "Evaluate 3 x 3x 3x." In the formula 3 x 3x 3x, take note of the proximity of the number 3 to the variable x. This denotes "x times three."
Here, we must assess:
2(s+t)³-6
By substituting them in the formula for t = 2 and s = 3, we obtain:
2(3+2)³- 6
= 2*(5) (5)³ - 6
= 2*125 - 6
= 244
Consequently, the evaluated expression equals 244.
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a bus picks up a group of tourists at a hotel. the sightseeing bus travels 2 blocks north, 2 blocks east, 1 block south, 2 blocks east, and 1 block south. where is the bus in relation to the hotel?
The bus is 4 blocks east of the hotel.
For given question
A sightseeing bus picks up a group of tourists at a hotel. It then travels 2 blocks north, 2 blocks east, 1 block south, 2 blocks east, and 1 block south, to determine where the bus is in relation to the hotel, the following calculation must be carried out:
North and South are antagonistic, the same as East and West
2 N + 2 E - 1S + 2E - 1S
2 N - 2S = 0
2E + 2 E = 4E
Therefore, the bus is 4 blocks east of the hotel.
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Find a value for x that will make each of the following equations true. x+8=21 b. 8-32=55 c. 3x=54 d. x/5=10
Answer:
a) X= 13
b) already answered
c) 18
d) 2
what is the slope of the line that passes through the points (-5, 7) and( -2, 4)? Write your answer in simplest form
[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{(-5)}}} \implies \cfrac{4 -7}{-2 +5}\implies \cfrac{-3}{3}\implies \text{\LARGE -1}[/tex]
14
Digital Genius manufactures a cell phone charging pad that can fully charge any cell phone that is placed on it in 15 minutes.
The analytics department determined that at a price of $103.00 each, the demand would be 6 thousand pads, and at $53.00
each, the demand would be 16 thousand pads. Based on the assumption that a linear relationship exists between price and
demand, the price-demand equation is given by
p(x) = 5x + 133,
OA $23.80
OB. $70.00
OC. $63.00
OD. $26.60
where x is the number of thousands of pads in demand. At what price point should they sell the pads to have a demand of
14 thousand pads?
-
Reset
Submit
Answer:
digital genious manufacture a cell phone charging pad that can fully charge any cell phone that is placed on it in 15 min
Step-by-step explanation:
Answer:
Step-by-step explanation:
the following data represent the pulse rates (beats per minute) of nine students enrolled in a statistics course. treat the nine students as a population. complete parts (a) to (c). student perpectual bempah megan brooks jeff honeycutt clarice jefferson crystal kurtenbach janette lantka kevin mccarthy tammy ohm kathy wojdya . . . question content area right part 1 (a) determine the population mean pulse. the population mean pulse is approximately enter your response here beats per minute. (type an integer or decimal rounded to the nearest tenth as needed.)
The population mean pulse is approximately 70.44 beats per minute. The mean pulse of sample 1 is approximately 65 beats per minute.
The mean pulse of sample 2, is approximately 73.67 beats per minute.
How to solve for the mean pulsea. mean = ∑x/n
= 634 / 9
= 70.44
b. The mean of sample 1
= 64 + 65 + 66 / 3
= 195 / 3
= 65
c. the mean of sample 2
= 81 + 67 + 73 / 3
= 221 / 3
= 73.67
In summary, The population mean pulse is approximately 70.44 beats per minute. The mean pulse of sample 1 is approximately 65 beats per minute. The mean pulse of sample 2, is approximately 73.67 beats per minute.
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Complete question
Student
Pulse
Perpectual Bempah
64
Megan Brooks
81
Jeff Honeycutt
67
Clarice Jefferson
68
Crystal Kurtenbach
80
Janette Lantka
70
Kevin McCarthy
73
Tammy Ohm
65
Kathy Wojdya
66
(a) Determine the population mean pulse is approximately ____?__beats per minute.
(Type an integer or decimal rounded to the nearest tenth as needed.)
(b) Determine the sample mean pulse of the following two simple random samples of size 3.
Sample 1: {Perpectual, Tammy Kathy}
Sample 2: {Jeff, Megan, Kevin}
The mean pulse of sample 1 is approximately ___?___ beats per minute.
(Round to the nearest tenth as needed.)
The mean pulse of sample 2, is approximately ____?__ beats per minute.
(Round to the nearest tenth as needed.)
Find the quotient of the quantity 21 times ten raised to the negative twenty first power end quantity divided by the quantity 7 times ten raised to the negative twenty first power end quantity.. write the final answer in scientific notation. 3 x 10−42 3 x 100 3 x 1021 3 x 1042
Answer:3x10^0 or 3x10 to the power of 0
Step-by-step explanation:
I did the same exact one with my teacher i hope this helps you
Question 1 (Multiple Choice Worth 1 points)
(02.01 MC)
Is the following relation a function? Justify your answer.
6
-2
4
-1
Yes bara
utout un
-2
Lessons
-2
Assessments
Gradebook.
i need the points. qnuddwdtg6tfr5v
Rewrite the product in exponential form.
(u-v) (u-v) 8-8 (u-v)
Answer:
[tex]8\left(u-v\right)^2-8\left(u-v\right)[/tex]
Step-by-step explanation:
[tex]\left(u-v\right)\left(u-v\right)=\left(u-v\right)^2\\\left(u-v\right)^2\cdot \:8-8\left(u-v\right)\\=8\left(u-v\right)^2-8\left(u-v\right)[/tex]
➲ Hope this helps.
➲ Notify me of any concerns.
Help I'm Stressed my Maths Homework is due in 2 days so I need answers asap
Please the image attached below to find the image by pure translation of the figure seen in the picture set aside.
How to translate a shape by using rigid transformations
In this problem we find a figure formed by eight vertices: (1, 3), (1, 4), (4, 4), (4, 3), (2, 3), (3, 3), (2, 1), (3, 1), each of which has to be modified by applying the translation vector (4, 5). Now we proceed to find the resulting coordinates:
(1, 3) + (4, 5) = (5, 8)
(1, 4) + (4, 5) = (5, 9)
(4, 4) + (4, 5) = (8, 9)
(4, 3) + (4, 5) = (8, 8)
(2, 3) + (4, 5) = (6, 8)
(3, 3) + (4, 5) = (7, 8)
(2, 1) + (4, 5) = (6, 6)
(3, 1) + (4, 5) = (7, 6)
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A speed skater moving across frictionless ice at 12 m/s hits a 7.0 m wide patch of rough ice. she slows steadily, then continues on at 6.0 m/s. what is her acceleration on the rough ice?
As per kinematic theory, when any object is moving on a rough surface, the friction force will act on the surface. And the friction force is in the opposite direction to the motion of the object.
Using kinematic formulas, the acceleration speed can be calculated:
[tex]v^{2} = u^{2} +2as[/tex]
As per the given data,
The initial speed of the skater [tex](u) = 12m/s[/tex]
The width of the pitch on the rough ice [tex](s) = 7.0 mt[/tex]
The final speed of the skater [tex](v) = 6.0m/s[/tex]
Substituting these values in the kinematic formula, we get
[tex]a = \frac{v^{2}-u^{2} }{2s}[/tex]
[tex]a = \frac{6^{2}-12^{2} }{14}[/tex]
[tex]a=- 7.71 m/s[/tex]
Therefore the calculated acceleration on the rough ice is [tex]-7.71m/s[/tex]
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