Using the equation [tex]C =a (1 - r)^{t}[/tex] , 179.75 grams will remain after 2 hours
What is Exponential Decay?
Exponential Decay is the process of reducing an amount by a consistent percentage rate over a period of time using the formula [tex]C = a(1-r)^{t}[/tex]
Where a = 480 grams
r = 15.1% = 0.151
t = 2 hours
C = 480(1 - 0.151)^2
C = 480(0.849)^2
C = 346 grams
Therefore, 346 grams will remain after 2 hours
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g questions: if a set of grades for a class has a large range and a small standard deviation, what can you say about the class? include an interpretation that is specific to grades in a class.
If a set of grades have a large range and a small standard deviation, it means that there are few students with high marks and few with low marks. Most students falls in the average region.
Range is the difference between the maximum value and the minimum value. So for the range to be higher, there must be at least one very high grade and at least a very low grade. If the maximum mark scored by the highest scorer is 95 and 10 for the lowest, the range will be 95- 10 = 85.
If one scored 99 and the lowest scorer got 5, then the range is 99-5 = 94. So higher the range means there is great difference between the highest and lowest grade.
Standard deviation means how much the value deviates from average. If it is low, that means most of the students scored near to the average.
So high range and low standard deviation means, there are few high scorers and few low scores. But most students falls in the average category.
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What is the equation of the line that passes through the point (-3,1)(−3,1) and has a slope of \frac{2}{3}
3
2
?
Answer:
y = (2/3)x + 3
Step-by-step explanation:
first we need to find the y-intercept
we can do this by using what is given, the point (-3,1) and the slope (2/3)
using the slope-intercept formula: y = mx + b.
m = slope
b = y intercept
we can plug in the x and y values we were given
so,
1 = (2/3)(-3) + b
we can now easily solve for b
1 = (2/3)(-3) = b
first multiply
1 = -2 + b
then add 2 to both sides, this way we isolate b
3 = b
now that we have the y intercept we can write the equation of the line
y = (2/3)x + 3
if you really wanted to, you can check if this is correct by plugging in the point again and seeing if the equation is true.
1 = (2/3)(-3) + 3
multiply first
1 = -2 + 3
add the like terms
1 = 1
What is the range of function f?
A.{y|4 < y < ∞}
B. {y|-∞}< y < ∞}
C. {yl-∞ < y < 0}
D.{y|-∞< y < 4}
An experiment consists of tossing a coin and casting a die then observing the outcomes. Describe an appropriate sample space for this experiment.
A fair coin and a fair six-sided die, the sample space can be represented as:
{ (H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6) }
where H represents heads and T represents tails for the coin toss, and the numbers 1 through 6 represent the numbers on the die.
The sample space for this experiment can be described as the set of all possible outcomes of the coin toss and die cast. One way to represent the sample space is to use the Cartesian product of the sample space for the coin toss and the sample space for the die cast.
where H represents heads and T represents tails for the coin toss, and the numbers 1 through 6 represent the numbers on the die.
Each element in this sample space represents a possible outcome of the experiment, where the first element represents the outcome of the coin toss and the second element represents the outcome of the die cast. This sample space contains 12 possible outcomes, each with an equal probability of 1/12.
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The prices and weights of three boxes of cereal are shown below.
Brand A: $1.99 for 12 ounces Brand B: $2.29 for 16 ounces Brand C: $2.99 for 18 ounces
If you choose among these three boxes, what is the lowest unit price, in dollars, you can pay? If necessary, round your answer to the nearest cent.
Answer:
Brand b
Step-by-step explanation:
brand a is 0.165 per ounce
brand b is 0.143 per ounce
brand c is 0.166 per ounce
suppose lacrosse balls come in 3 colours: red, yellow, and blue. how many different combinations of colours are possible in a 6-pack of lacrosse balls?
There are 20 different combinations of colors possible in a 6-pack of lacrosse balls.
What is the combination?
A combination is a choice of items from a group of different items where the order of the choices is irrelevant. Either the process of combining or the condition of combining. a combination of several things a mixture of thoughts. something created through fusion: A chord is made up of several notes.
Here, we have
Given: lacrosse balls come in 3 colors: red, yellow, and blue.
We have to find the different combinations of colors that are possible in a 6-pack of lacrosse balls.
We apply here combination formula and we get
= ⁶C₃
= (6×5×4×3!)/(3!×3×2×1)
= 20
Hence, there are 20 different combinations of colors possible in a 6-pack of lacrosse balls.
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Solve using substitution
3x-2y=3
y=6+4x
The system using substitution has its solution to be (-1.8, -1.2)
How to solve the system using substitutionFrom the question, we have the following parameters that can be used in our computation:
3x-2y=3
y=6+4x
By susbstitution, we have the following equation
3x - 12 - 8x = 3
Evaluate the like terms
so, we have the following representation
-5x = 9
Divide by 5
x = -1.8
So, we have
y= 6 + 4 * -1.8
Evaluate
y = -1.2
Hence, the value of y is -1.2
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This circle has a diameter of 40 centimeters. What is the radius?
Answer: 20 centimeters
Step-by-step explanation:
The radius is half the diameter so then the radius is 20 centimeters.
The distance between the center of the circle to its circumference is the radius. The diameter is always double the radius. Hence, the formula is derived by dividing the diameter by 2.
40/2 = 20cm.Marcia's cost, in dollars, to wash her car can be calculated using the expression below,
where m represents the number of minutes the car wash will run.
0.25m +1.50
Evaluate the expression for m = 20, and interpret the meaning of the result.
When m is 20 the value of expression is 6.5. The value 6.5 represent the cost which marcia has to pay for car wash for 20 mins.
What is Expression?An expression is combination of variables, numbers and operators.
Given that Marcia's cost, in dollars, to wash her car can be calculated using the expression
0.25m +1.50
Zero point two five plus one point five.
In the expression m represents the number of minutes the car wash will run.
We need to find the value of expression when m is 20
0.25(20)+1.50
5+1.50
6.5
When m is 20 the value of expression is 6.5. The value 6.5 represent the cost which marcia has to pay for car wash for 20 mins.
Hence, Marcias cost $6.5 to wash her car for 20 minutes.
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These tables represent the relationships between x and y for two different sets of data. Which statements correctly describe the relationships between x and y for each table? Table A represents a multiplicative relationship because y is 2.5 times x, O and Table B represents an additive relationship because y is 2 more than O X. Table A represents an additive relationship because y is 1.5 more Othan x, and Table B represents a multiplicative relationship because y is 3 times x. Both data sets represent multiplicative relationships. In Table A, y is 2.5 times x, and in Table B, y is 3 times X. Both tables represent additive relationships. In Table A, y is 1.5 more than x, and in Table B, y is 2 more than x.
Answer:
Both data sets represent multiplicative relationships. In Table A, y is 2.5 times x, and in Table B, y is 3 times X
Step-by-step explanation:
Self-explanatory
Every value of y in Table A is 2.5 times x value
and
every value of y in table B is 3 times x value
Type the expression that results from the following series of steps: Start with t , add 6, divide by 2, then subtract 5.
Answer:
2(t+6)-5
Step-by-step explanation:
The unknown number is t
=> Adding 6 will make it t+6
=> Multiplying 2 will make it 2(t+6)
=> Subtracting 5 will make it 2(t+6)-5
Answer:
[tex]\frac{t+6}{2}[/tex] - 5
Step-by-step explanation:
[tex]\frac{t+6}{2}[/tex] - 5
What percentage of winners driving a chevrolet won with an average speed of at least miles per hour?
The percentage of winners driving a Chevrolet who won with an average speed of at least miles per hour is fifty percent (50%).
We can infer that for a Chevrolet car,
the percentage of average speed (in miles/hour) for the range of 150-159.9 is 25%,
the percentage of average speed (in miles/hour) for the range of 160-169.9 is 18.75%,
and the percentage of average speed (in miles/hour) for the range of 170-179.9 is 6.25%.
Thereby, the percentage of winners of the race who were driving a Chevrolet and had an average speed of at least 150 miles/hour is,
50%.
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a plane left kennedy airport on tuesday morning for a 595-mile, 5-hour trip. for the first part of the trip, the average speed was 110 mph. for the remainder of the trip, the average speed was 125 mph. how long did the plane fly at each speed? first part of trip h second part of trip h
The plane flew at 110 mph for 4.55 hours and at 125 mph for 0.45 hours.
The first step in solving this problem is to recognize that we can use the formula
=> speed = distance/time
to find the time it took for the plane to travel at each speed. Let's denote the time the plane traveled at the first speed (110 mph) as t1, and the time it traveled at the second speed (125 mph) as t2.
We know that the total distance traveled was 595 miles, and the total time taken was 5 hours. Using the formula for average speed, we can write:
Average speed = total distance / total time
Therefore,
Average speed = 595 / 5 = 119 mph
Now we can use the information about the two speeds to set up a system of equations. The first equation relates the total distance traveled at the first speed to the time it took:
110t₁ = d₁
where d1 is the distance traveled at the first speed. Similarly, the second equation relates the total distance traveled at the second speed to the time it took:
125t₂ = d₂
where d₂ is the distance traveled at the second speed.
The total time taken is the sum of the times taken at each speed:
t₁ + t₂ = 5
We now have three equations and three unknowns (t₁, t₂, and d₂). We can use the first two equations to eliminate d₁ and d₂, and then solve for t₁ and t₂.
Multiplying the first equation by 125/110, we get:
125/110 * 110t₁ = 125/110 * d₁
125t₁/110 = d₂
Substituting d₂ in the third equation, we get:
t₁ + 125t₁/110 = 5
Multiplying both sides by 110, we get:
121t₁ = 550
Solving for t₁, we get:
t₁ = 4.55 hours
Substituting t₁ in the third equation, we get:
t₂ = 0.45 hours
Therefore, the plane flew at 110 mph for 4.55 hours and at 125 mph for 0.45 hours.
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Complete Question:
A plane left Kennedy Airport tuesday morning for a 595−mileˏ 5−hour trip.
For the first part of the tripˏ the average speed was 110 mph.
For the remainder of the tripˏ the average speed was 125 mph. How long did the plane fly at each speed.
a family has two cars. during one particular week, the first car consumed gallons of gas and the second consumed gallons of gas. the two cars drove a combined total of miles, and the sum of their fuel efficiencies was miles per gallon. what were the fuel efficiencies of each of the cars that week?
Quadratic equation gives us the fuel efficiencies of the two cars for the given values of fuel consumption and total distance driven.
Let's denote the fuel efficiency of the first car as x miles per gallon, and the fuel efficiency of the second car as y miles per gallon.
We know that the first car consumed a total of a gallons of gas, and the second car consumed b gallons of gas. If we assume that the fuel efficiencies are constant, then the total distance driven by both cars can be calculated using the formula:
distance = fuel consumed / fuel efficiency
So, the total distance driven by both cars is:
(a/x) + (b/y) = total miles
We also know that the sum of their fuel efficiencies was:
x + y = total miles per gallon
We have two equations and two unknowns, so we can solve for x and y. First, we can solve the second equation for x:
x = total miles per gallon - y
Substituting this expression for x into the first equation, we get:
(a / (total miles per gallon - y)) + (b / y) = total miles
Multiplying both sides by y(total miles per gallon - y) to eliminate the denominators, we get:
ay + b(total miles per gallon - y) = total miles * y(total miles per gallon - y)
Expanding the left side and simplifying, we get a quadratic equation in y:
(total miles^2 - a - b) y^2 + (total miles * a) y - ab = 0
Using the quadratic formula, we can solve for y:
y = [(total miles * a) ± sqrt((total miles * a)^2 + 4ab(total miles^2 - a - b))] / 2(total miles^2 - a - b)
We can then use the equation x = total miles per gallon - y to find the value of x. The gives the fuel consumption of both cars.
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Need this for a math lesson
Answer:
maximum score = 92
Step-by-step explanation:
the maximum score is the largest value in the data set.
maximum score = 92
In order to keep the numbers in the proper place-value column
The order of the place value in increasing order is equal to units , tens , hundreds , thousands , ten-thousand and so on.
The value of every digit present in any number depends on the position of the digit in a number.The place of the digit in the number represents its place value of the digit in a number.Starting position of a digit is ones or units.After unit the place value is tens.In ascending order the place value of all the digit in any given number is represented as units , tens , hundreds , thousands , ten- thousands, so on.Therefore, the order of the place value in ascending order of the place of the digit is given by units , tens , hundreds , thousands , ten-thousand and so on.
The given question is incomplete, I answer the question in general according to my knowledge:
What is the order of the place value ?
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Determine whether f has an inverse function. If it does, find the inverse function and state any restrictions on its domain:
f(x) =[tex]\frac{x - 7}{x + 4}[/tex]
The inverse function of f(x) = [tex]\frac{x-7}{x+4}[/tex] is f⁻¹(x) = [tex]\frac{4x+7}{1-x}[/tex].
What is the inverse function?A function that can reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as "f-1" or "F-1." Here, (-1) should not be confused with an exponent or a reciprocal.
Given that the function is f(x) = [tex]\frac{x-7}{x+4}[/tex]
Change f(x) (or whatever the function name is) to "y". In this case you'd get:
y = [tex]\frac{x-7}{x+4}[/tex]
Now, switch x and y. Wherever you see y, put x. And wherever you see x, put y.
x = [tex]\frac{y-7}{y+4}[/tex]
Solve the new equation for y.
x (y + 4) = y - 7
xy + 4x = y - 7
4x + 7 = y - xy
4x + 7 = y (1 - x)
y = [tex]\frac{4x+7}{1-x}[/tex]
Change y back to function notation. The correct notation for the "inverse of f(x)" is "f⁻¹(x)". So that would give you:
f⁻¹(x) = [tex]\frac{4x+7}{1-x}[/tex]
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Triangle NGM is reflected across the x-axis, and is dilated by a factor of 2
1
2
. The dilation center is the origin.
Dilation Starting with our fundamental equation, x^2+y^2=r^2, we can dilate a circle. The point can be found by multiplying the parameters of the vertices in the bounding box by the scale factor when distorting a figure that is centered at the origin.
What does triangle mean?
A triangle is made up of three vertices, three angles, and three sides. A triangle's internal angles add up to 180 degrees. The triangle's third side is longer than the two sides added together. The base plus the height multiplied by half equals the triangle's area.
What are a few examples of dilation?
Dilation refers to a change in size without a change in shape of an object. Depending on the scale, the object's size could grow or shrink.
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When Jackie woke up, the temperature was 70 °F. For the next 5 hours, the temperature rose by 4 °F each hour. Write an equation in the form y = mx + b that Jackie can use to find the temperature x number of hours after she woke up.
An equation to find the temperature after x number hours of waking up for Jackie is Temperature ( x ) = 4 x + 70
How to find the equation ?The equation which takes the form y = mx + b means that in relation to the temperature when Jackie woke up:
y = current temperature after x hours
x = number of hours after waking up
m = change in temperature per hour
b = starting temperature when Jackie woke up
The equation to find the temperature after x hours is therefore:
Temperature ( x ) = 4 x + 70
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Write a quadratic function in standard form whose graph satisfies the given condition(s). 13. vertex: (-9, -4)
Answer:
Tech 9 rock and no answer
Step-by-step explanation:
f (x) = (x - 6)2(x + 2)2
DONE
The roots of the equation, f (x) = ( x - 6 )²( x + 2 )² are 6 and - 2.
What is the root of function?The root of the function is calculated by setting the function equal to zero.
The given function is f (x) = ( x - 6 )²( x + 2 )²
we will separate the two equation and set them equal to zero.
( x - 6 )² = 0 ---- equation ( 1 )
or
( x + 2 )² = 0 -------- equation ( 2 )
from the first equation, x = 6
from the second equation, x = - 2
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The complete question is below:
Find the roots of f(x) = (x - 6)² (x + 2)²
Tina would like to withdraw an annual salary of $35,756 from an account paying 2.2% compounded annually for 35 years once she retires. Given this information, determine the amount needed in her account in order for her to reach her goal. Round to the nearest cent.
What is 5’7 in cm
Please can I have help
Step-by-step explanation:
Sure, I'd be happy to help!
5 feet 7 inches is equivalent to 170.18 cm.
Triangle ABC has angle measures as noted below. Please note this triangle is not drawn to scale, and the longest leg of the figure may not be the longest leg of the actual triangle.
You will need to use the expressions for the angles given below.
m∠A) 3(x + 5)
m∠B) 5x+15
m∠C) 7x
Identify the angle relationship and setup your equation with the given expressions.
What is the value of x? Show your work.
What is the measure of angle A, B, & C? Show your work and make sure to identify which is which.
GIVING 70 POINTS FOR RIGHT ANSWER NEED ASAP (please and ty)
Answer:
m∠A = 45°;m∠B = 65°;m∠C = 70°.-----------------------------------
Recall triangle angle sum property, the sum of three interior angles is 180°.
Add up the three angle measures, then solve the equation for x:
m∠A + m∠B + m∠C = 1803(x + 5) + 5x + 15 + 7x = 1803x + 15 + 12x + 15 = 18015x + 30 = 18015x = 150x = 10Substitute the value of x and find the value of each angle:
m∠A = 3(10 + 5) = 3(15) = 45m∠B = 5*10 + 15 = 50 + 15 = 65m∠C = 7*10 = 70The number in a bacteria lab can be modeled by the function L(t)= 880(3)^t+2. Write an equivalent function in the form L(t)= ab^t
The equivalent function to the given one is:
L(t) = 7,920*(3)^t
How to rewrite the function?Here we want to rewrite the function:
L(t) = 880*(3)^(t + 2)
Into the form:
L(t) = a*(b)^t
Remember the rule for exponents:
(x^a)*(x^b) = x^(a + b)
Then we can take our function:
L(t) = 880*(3)^(t + 2)
And rewrite this as:
L(t) = 880*(3^t)*(3^2)
L(t) = 9*880*3^t
L(t) = 7,920*(3)^t
That is the equivalent function.
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Find the average value fave of the function f on the given interval. f(x) = 3x2 + 4x, [−1, 2]
The average value of the function f(x) = 3x2 + 4x on the interval [-1, 2] is about 4.67.
To find the average value fave of the function f(x) = 3x2 + 4x on the interval [-1, 2], solve the definite integral of f(x) over the interval and then divide by the interval length.
The definite integral of f(x) over the interval [-1, 2] can be calculated as follows:
[tex]∫[-1,2] (3x^2 + 4x) dx = [x^3 + 2x^2] between x = -1 and x = 2 = (23 + 2(22)) - ((-1)^3 + 2(-1)^2) \s= 14[/tex]
The interval length is 2 - (-1) = 3.
As a result, the average value fave of f(x) on the interval [-1, 2] is as follows:
fave =[tex](1/3) * ∫[-1,2] (3x^2 + 4x) dx \s= (1/3) * 14 \s[/tex]= 4.67 (rounded to two decimal places) (rounded to two decimal places)
As a result, the average value of the function f(x) = 3x2 + 4x on the interval [-1, 2] is about 4.67
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.
Which value of x makes the equation
5(x - 2) - 4 = 6 true?
A. 2
B. 3
C. 4
D. 5
Answer:
Step-by-step explanation:
5x - 10 - 4 = 6
5x - 14 = 6
5x = 20
x = 4
Option C is the solution
Linette and Ruth breed poodles as a hobby. They sold half of the puppies and half a puppy from the latest litter to the local pet shop. Then they sold half of the puppies that were left in the litter and half a puppy to the poodle palace. Then they decided to give the one remaining puppy to their friend Grace. How many puppies were originally in the litter
There were originally 10 puppies in the litter, as of the given condition.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
We can represent the number of original puppies as "x", and the sequence of events can be represented as:
Sold half of the puppies, so they have x/2 left - 1 sold to the local pet shop.
Sold half of the remaining puppies, so they have (x/2 - 1)/2 left sold to poodle palace.
One puppy was given to Grace, so they have ((x/2 - 1)/2- 1 = x - 2 / 4 - 1 remaining.
Since they are left with x - 2 / 4 - 1 puppies in the end, we can set this equal to 1 (the remaining puppy given to Grace), and solve for x:
x - 2 / 4 - 1 = 1
x - 2 = {1 + 1} * 4
x = 8 + 2
x = 10
Therefore, there were originally 10 puppies in the litter.
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In the World of Numbers, there are many number-machines, which work in the following way: the machine adds the two beginning digits of the number and replaces them by their sum. For example, beginning with the number 87312 and using six machines we obtain:
87312-15312-6312-912-102-12-3
How many such machines should be used in order to get to the number 450 from the number 900?
The number of machines used in order to get to the number 450 from the number 900 is 9.
What is an expression?An expression contains more than one term with addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
900 to 450
We need a number of machines such that 450 is the last output starting from 900.
Now,
If we subtract 50 from each consecutive number we get,
900, 850, 800, 750, 700, 650, 600, 550, 500, 450
So,
We use 9 machines to get 450 from 900.
Thus,
9 machines should be used in order to get to the number 450 from the number 900.
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Need answers stat trigonometry
The value of x to the nearest tenth are as follows;
x = 47.0 units.
x = 25.1 units.
x = 23.8 units.
x = 29.7 units.
x = 21.1°.
x = 39.6°.
x = 58.0°.
x = 72.9°.
How to determine the value of x?From the image attached above, we can logically deduce that the triangle is a right-angled triangle with the following side lengths:
Opposite side = x.
Adjacent side = 25.
Therefore, we would determine the value of x by using Tan trigonometric function:
Tanθ = Opposite side/Adjacent side
Tan45 = 25/x
x = 25Tan62
x = 47.0 units.
For right-angled triangle 3, we have:
Sin26 = 11/x
x = 11/0.4384
x = 25.1 units.
For right-angled triangle 4, we have:
Sin48 = x/32
x = 32sin48
x = 23.8 units.
For right-angled triangle 5, we have:
Cos12 = 29/x
x = 29/0.9782
x = 29.7 units.
For right-angled triangle 6, we have:
Cosθ = 14/15
θ = cos⁻¹(0.9333)
θ = 21.1°.
For right-angled triangle 7, we have:
Tanθ = 19/23
θ = tan⁻¹(0.8261)
θ = 39.6°.
For right-angled triangle 8, we have:
Cosθ = 9/17
θ = cos⁻¹(0.5294)
θ = 58.0°.
For right-angled triangle 9, we have:
Sinθ = 43/45
θ = sin⁻¹(0.9556)
θ = 72.9°.
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