A) The exponential function that models the mass show many grams remain from a 480-gram sample after t minutes is G(t) = 22(1/2)^(t/5.5)
B) The grams that remain after 2 hours is 51.42 grams.
What is the definition of half life?A substance's half-life is the amount of time needed for half of a radioactive substance to decay. It is a word that is used in nuclear chemistry to describe how quickly unstable atoms undergo radioactive decay into other nuclear species by emitting particles or the amount of time needed for the rate of disintegrations per second of radioactive material in order to reduce by half of its initial value.
Given:
The half-life of goo is 22 minutes/4 = 33.75 minutes
b) A formula for the amount remaining could be ...
G(t) = 22(1/2)^(t/5.5)
c) After 2 hours, the amount remaining is ...
G(120) = 135(1/2)^(47/33.75) ≈ 51.42 . . . grams
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A). After t minutes, the exponential function used to describe the mass remaining from a 480-gram sample is [tex]G(t) = 22(\frac{1}{2} )^{(t/5.5)}[/tex]
B). 51.42 grammes are still there after two hours.
What is the definition of half life?The amount of time required for a radioactive substance to decay by half is known as its half-life. It is a term used in nuclear chemistry to describe how quickly unstable atoms transform into different nuclear species by emitting particles or how long it takes for the rate of radioactive material's disintegrations per second to fall by half of its initial value.
Given:
The half-life of goo is 22 minutes/4 = 33.75 minutes
b) The amount left could be calculated using the method...
[tex]G(t) = 22(\frac{1}{2} )^{(t/5.5)}[/tex]
c) The amount left after two hours is...
[tex]G(120)=135(\frac{1}{2} )^{(\frac{47}{33.5} )}[/tex] ≈ 51.42 . . . grams
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On average, for every 100 customers at a coffee shop, 25 customers, or 25%of the customers come in after 5:00 pm. Last Tuesday, a coffee shop had a total of 84 customers. How many customers would you expect came I. after 5:00pm.
If 25% of customers come in after 5:00 pm, then we can expect that 0.25 times the total number of customers come in after 5:00 pm.
Let's use this to find how many customers we expect to come in after 5:00 pm on last Tuesday:
Number of customers who came in after 5:00 pm = 0.25 * 84 = 21
Therefore, we would expect that 21 customers came in after 5:00 pm on last Tuesday.
Graph the following equation on the coordinate plane.
y = -3x + 8
Answer:
See the picture below
Step-by-step explanation:
To graph this linear function, you need two things: slope and y-intercept.
y-intercept:
This is where the line crosses the x axis. It will cross when x = 0. (0,b). The b is the y-intercept. You see this in the equation at the end. In this case the y-intercept it 8.
Slope:
This is the change in y over the change in x. On the graph I highlighted two points (0,8) and (1,5). If you start at (0,8) and go to (1,5), you go straight down 3 units and 1 unit right. This is your slope. Going down is a negative direction and going right is a positive direction. The slope would be the change in y over the change in x. [tex]\frac{-3}{1}[/tex] which simplified would be -3. The slope is -3.
Helping in the name of Jesus.
From midnight to 2:00 am, the temperature rose 1.55°C each hour. If the temperature at midnight was −7°C, what was the temperature at 2:00 am?
Please help!!!!!!!!!!!!!!!!!!!!!!!!!
It will cost $1200 to cover both sides of the green roof with plants at a cost of $0.75 per square foot.
To calculate the cost of covering both sides of the green roof, we first need to find the area of the roof. We can use the formula for the area of a rectangle:
area = length x width
Since the roof is 40 feet long, we need to find the width to calculate the area. We can estimate the width from the picture, but it's not given explicitly. So, we can make a reasonable assumption that the width is the same as the length of the shorter side of the roof, which appears to be about 20 feet.
Using this assumption, we can calculate the area of one side of the roof:
area = length x width = 40 ft x 20 ft = 800 sq ft
Since there are two sides to the roof, the total area is twice this amount:
total area = 2 x 800 sq ft = 1600 sq ft
To find the total cost of covering both sides of the roof, we can multiply the area by the cost per square foot of plants:
total cost = area x cost per sq ft
= 1600 sq ft x $0.75/sq ft
= $1200
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the area of this parallelogram is 51.5 cm2. work out the value of x
Answer:
The formula for area of a parallelogram is A=bh
x=10.3
Step-by-step explanation:
We don't have the base but we have the height.
the base is x and the height is 5
if the area is 51.5
we should divide the height to find the base.
51.5÷5=10.3
so the base is 10.3
Check if answer is correct:
b=10.3
h=5
a= 51.5
10.3(5)=51.5
a= 51.5cm²
I hope this helps as long as you know the formula it's easy :D
Justine just ran her first race. Her distance from the finish line decreased as she ran.
This situation can be modeled as a linear relationship.
What does the y-intercept of the line tell you about the situation?
The y-intercept of a linear equation represents the value of the dependent variable when the independent variable is equal to zero.
What is linear equation?
A linear equation is a mathematical equation of the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept.
What is y-intercept?
In a linear equation of the form y = mx + b, the y-intercept (b) is the point where the line intersects the y-axis.
According to given information:The y-intercept of a linear equation represents the value of the dependent variable when the independent variable is equal to zero. In the context of Justine's race, the y-intercept would represent her starting distance from the finish line.
It would be the distance from the finish line when she began the race, or the distance she would have to run to reach the finish line if she started at the beginning. The slope of the line would tell you how much the distance decreases as she runs.
Together, the y-intercept and slope of the line can provide useful information for understanding and analyzing Justine's race.
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The answer of the given question based on the linear relationship is , the y-intercept gives information about Justine's initial position or starting point before she started running the race.
What is Linear relationship?A linear relationship is a type of relationship between two variables where their relationship can be described by a straight line. In other words, the change in one variable is directly proportional to the change in the other variable. This means that as one variable increases or decreases, the other variable also changes in a consistent and predictable way. Linear relationships are commonly studied in mathematics, statistics, and other fields as they provide a useful framework for understanding the relationship between two variables and making predictions based on that relationship.
In the context of this linear relationship, the y-intercept represents the starting point of Justine's race. It is the point where her distance from the finish line is zero, which is the beginning of the race. Therefore, the y-intercept gives information about Justine's initial position or starting point before she started running the race.
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Pls help , my geometry teacher can't teach
A carnival charges $3 for kids and $10 for adults. On Saturday, there were 500 visitors, and the total amount taken at the gate was $3,600. The
equation representing the number of visitors is k + a = 500, where k represents the number kids and a represents the number of adults. The
equation representing the amount of money collected is 3k + 10a = 3,600. How many kids and adults visited the carnival?
Keisaun was covering a square bulletin board with paper. One side of the bulletin board measure 3 feet. How much paper did he need?
-------------------------------------------------------------------------------------------------------------
Answer: 9 square feet
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Keisaun needs to cover a square. One side is 3 feet}[/tex]
Find: [tex]\textsf{We need to find how much paper he needs}[/tex]
Solution: Using the information that was given to us we know that we need to determine the area of the square that Keisaun needs to cover. We know that the area formula for a square is side * side. We are also given the information that a single side of the board is measured to be 3 feet. Therefore, using that information we can plug the value into the square area formula and solve.
[tex]\textsf{Area of a square = side * side}[/tex][tex]\textsf{Area of a square = 3 feet * 3 feet}[/tex][tex]\textsf{Area of a square = 9 feet}^2[/tex]Therefore, the answer to the question would be that Keisaun would need 9 square feet of paper to cover the square bulletin board.
Gabriel goes out to lunch. The bill, before tax and tip, was $9.50. A sales tax of 7.5% was added on. Gabriel tipped 15% on the amount after the sales tax was added. How much tip did he leave? Round to the nearest cent.
Answer:
Gabriel left $1.53 in tips.
Step-by-step explanation:
Sales tax: 9.50*0.075=0.7125
9.50+0.71=10.21
Total with Sales Tax: $10.21
Tip: 10.21*0.15=1.5315
What is the
measure of x and why?
100°
Answer:
alternate exterior angles
Step-by-step explanation:
Both x and 100° are alternate exterior angles. Therefore, by definition, x = 100°.
imagine that these cards are face down, and you pick at random.
A A A B B C
Answer:
1:A
2:B
3:A
that's the answer I think
Finding equations of exponential function
The exponential function are y = 10(2)^x, y = 1.270(1.389)^x, y = 5.656(0.957)^x and y = 6.567(0.870)^x.
What is the equation of the exponential function1. (a) To find the equation of the exponential function that passes through the points (0,10) and (3,80), we can use the formula:
y = a(b)^x
where a and b are constants that we need to find.
First, we can use the point (0,10) to solve for a:
10 = a(b)^0
10 = a
Next, we can use the point (3,80) to solve for b:
80 = 10(b)^3
8 = b^3
b = 2
Therefore, the equation of the exponential function is:
y = 10(2)^x
(b) To find the equation of the exponential function that passes through the points (0.18, 2.8) and (2, 8), we can use the same formula:
y = a(b)^x
First, we can use the point (0.18, 2.8) to solve for a:
2.8 = a(b)^0.18
Next, we can use the point (2, 8) to solve for b:
8 = a(b)^2
Dividing the second equation by the first, we get:
2.857 = (b)^1.82
b = 1.389
Substituting this value of b back into one of the equations to solve for a, we get:
2.8 = a(1.389)^0.18
a = 1.270
Therefore, the equation of the exponential function is:
y = 1.270(1.389)^x
2. (a) To find the equation of the exponential function that passes through the points (2, 5.12288) and (1.92, 2.192), we can again use the formula:
y = a(b)^x
First, we can use the point (2,5.12288) to solve for a:
5.12288 = a(b)^2
Next, we can use the point (1.92,2.192) to solve for b:
2.192 = a(b)^1.92
Dividing the second equation by the first, we get:
0.427 = (b)^(0.08)
b = 0.957
Substituting this value of b back into one of the equations to solve for a, we get:
5.12288 = a(0.957)^2
a = 5.656
Therefore, the equation of the exponential function is:
y = 5.656(0.957)^x
(b) To find the equation of the exponential function that passes through the points (1.192,5) and (5,0.75), we can use the same formula:
y = a(b)^x
First, we can use the point (1.192,5) to solve for a:
5 = a(b)^1.192
Next, we can use the point (5,0.75) to solve for b:
0.75 = a(b)^5
Dividing the second equation by the first, we get:
0.149 = (b)^3.808
b = 0.870
Substituting this value of b back into one of the equations to solve for a, we get:
5 = a(0.870)^1.192
a = 6.567
Therefore, the equation of the exponential function is:
y = 6.567(0.870)^x
3. To find the equation of the exponential function that passes through the points (2.14,7) and (7,205), we can use the same formula as before:
y = a(b)^x
First, we can use the point (2.14,7) to solve for a:
7 = a(b)^2.14
Next, we can use the point (7,205) to solve for b:
205 = a(b)^7
Dividing the second equation by the first, we get:
29.285 = (b)^(4.86)
b = 5.474
Substituting this value of b back into one of the equations to solve for a, we get:
7 = a(5.474)^2.14
a = 0.00061
Therefore, the equation of the exponential function is:
y = 0.00061(5.474)^x
Rounding a and b to the nearest hundred, we get:
a = 0.0006
b = 5.47
So, the final equation of the exponential function is:
y = 0.0006(5.47)^x
We can check if the points (2.14,7) and (7,205) fall on the curve by plugging them into the equation:
y = 0.0006(5.47)^x
When x = 2.14:
y = 0.0006(5.47)^2.14 ≈ 7
When x = 7:
y = 0.0006(5.47)^7 ≈ 205
So, the points do fall on the curve, which means that the equation we found is correct.
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Pleaseee help for robust
The answer for B is: 5÷4 cups of fruit drink are made with 1 cup of apple juice.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.
For A:
We want to find the ratio of carrot juice to apple juice when 1 cup of apple juice is used. Let's represent the amount of carrot juice with "x".
So, we have the ratio:
x : 1 cup
which is equivalent to:
1÷5 cup : 3÷5 cup
To solve for x, we can set up a proportion:
1÷5 cup ÷ 3÷5 cup = x ÷ 1 cup
Simplifying the left side:
(1÷5 cup) ÷ (3÷5 cup) = (1÷5 cup) x (5÷3) = 1÷3 cup
So, the ratio of carrot juice to apple juice when 1 cup of apple juice is used is:
1÷3 cup : 1 cup
Therefore, the answer for A is: 1/3 cup of carrot juice is used for 1 cup of apple juice.
For B:
We want to find how many cups of fruit drink are made with 1 cup of apple juice. Let's represent the amount of fruit drink with "y".
So, we have the ratio:
1 cup : y
which is equivalent to:
3÷5 cup : (1÷5 cup + 3÷5 cup) = 4÷5 cup
To solve for y, we can set up a proportion:
1 cup ÷ 4÷5 cup = y ÷ 1
Simplifying the left side:
(1 cup) ÷ (4÷5 cup) = (1 cup) x (5÷4) = 5÷4 cup
So, 5/4 cups of fruit drink are made with 1 cup of apple juice.
Therefore, the answer for B is: 5÷4 cups of fruit drink are made with 1 cup of apple juice.
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What is the equation of the line that passes through the point
(
5
,
0
)
(5,0) and has a slope of
6
5
5
6
The equation of the line that passes through the point (5, 0) and has a slope of 6/5 is:
y = (6/5)x - 6To find the equation of the line that passes through the point (5, 0) and has a slope of 6/5,
we will use the point-slope form of the equation of a line, which is given by:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Step 1: Plug in the given point (5, 0) as (x1, y1) and the slope (6/5) as m.
y - 0 = (6/5)(x - 5)
Step 2: Simplify the equation.
y = (6/5)(x - 5)
Step 3: Distribute the slope (6/5) on the right side.
y = (6/5)x - 6
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Apply the distributive property to factor out the greatest common factor. 24a−18b
Step-by-step explanation:
The GCF of 24 and 18 is '6'...factor that out to get
6 ( 4a-3b) that is all you can do....
Can someone help me ASAP it’s due tomorrow. I will give brainliest if it’s all done correctly.
Answer part a, b, and c for brainliest!!
The sample space when 2 lollipops are randomly selected with replacement is S_with_replacement = {(Grape, Grape), (Grape, Cherry), (Grape, Lemon), (Cherry, Grape), (Cherry, Cherry), (Cherry, Lemon), (Lemon, Grape), (Lemon, Cherry), (Lemon, Lemon)}
The sample space when lollipops are selected without replacement is S_without_replacement = {(Grape, Grape), (Grape, Cherry), (Grape, Lemon), (Cherry, Grape), (Cherry, Cherry), (Cherry, Lemon), (Lemon, Grape), (Lemon, Cherry), (Lemon, Lemon)}.
The experiment with replacement (Part A) shows independent events because the probability of each lollipop being chosen is the same for both selections.
How to find the sample space ?When selecting 2 lollipops with replacement, we put the first lollipop back into the bag before choosing the second one. When selecting 2 lollipops without replacement, we do not put the first lollipop back into the bag before choosing the second one.
The outcome of the first event does not affect the probability of the second event.
The experiment without replacement (Part B) shows dependent events because the probability of the second lollipop being chosen is affected by the outcome of the first event. When one lollipop is removed from the bag, there are fewer options available for the second selection, and the probabilities of the remaining lollipops change.
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A meter reader determines that a business has used 3550 kW•h of energy in two months. If electricity costs 10 cents per kW•h, calculate the bill.
Answer:
The first step is to calculate the total cost of energy used in two months. To do that, we need to multiply the amount of energy used by the cost per kilowatt-hour:
3550 kW•h x $0.10/kW•h = $355.00
So the total cost of energy used in two months is $355.00. This is the amount of the bill that the business will receive for its electricity usage.
Step-by-step explanation:
Answer:
To calculate the bill, we need to multiply the amount of energy used (3550 kW•h) by the cost per kW•h (10 cents).
3550 kW•h x 10 cents/kW•h = $355.00
Therefore, the bill for the business is $355.00.
Step-by-step explanation:
please pa brainliest po thanks.
if you have 220 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose?
Answer:
6050 square meters
Step-by-step explanation:
You want to know the largest rectangular area that can be enclosed using 220 meters of fencing for 3 sides.
DimensionsFor enclosure length x, the width of the enclosure is half the remaining fence: (220 -x)/2. The area is the product of length and width.
A = (x)(220 -x)/2
This is the equation of a parabola that opens downward. Its vertex (maximum) is halfway between the zeros, which are x=0 and x=220. This means the area is maximized when x=110 and the width is (220-110)/2 = 55.
The maximum area is (110 m)(55 m) = 6050 m².
__
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The answer is 2025 sq. meter.
If you have 220 meters of fencing and want to enclose a rectangular area up against a long, straight wall, the largest area you can enclose is 4840 square meters. Explanation: To determine the largest possible area, we have to find out how to divide the 220 meters of fencing so that we can maximize the space enclosed by it. If one side of the rectangle is x meters long, the other side is (110 - x) meters long (because we have one straight wall to use as a side).The perimeter of the rectangle can be calculated by adding up all four sides of the rectangle. Hence:2x + (110 - x) + (110 - x) = 220We simplify the equation to solve for x:2x + 220 - 2x = 220-x = 55Therefore, one side of the rectangle is 55 meters long, and the other side is (110 - 55) = 55 meters long as well. The area of a rectangle is given by its length multiplied by its width. In this case, the area is:55 x 55 = 3025.
Therefore, the largest area that can be enclosed is 3025 square meters.
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What does y equal?
5(2y-1)<-15
Answer:
To solve for y in the inequality 5(2y - 1) < -15, we can simplify the expression on the left-hand side as follows:
5(2y - 1) < -15
10y - 5 < -15 // Distribute the 5 on the left side
10y < -10 // Add 5 to both sides
y < -1 // Divide both sides by 10 and flip the inequality
Therefore, the solution is y < -1.
Determine the unknown angle measures of △def. round to the nearest degree. m∠d = ° m∠f = °
Answer: [tex]\angle F = 44\°\\angle D= 46\°[/tex]
Step-by-step explanation:
a group of seven people are attending the movies together. (a) two of the seven insist on sitting side-by-side. in how many ways can the seven be seated together in a row?
The total number of ways in which the group of seven people can be seated together in a row are 1440.
The group of seven people are attending the movie together and two of them are insisting that they will sit side by side to each other.
Now if all the people were to be seated in any random order then the number of positions would have been seven but now as two people are sitting side by side so we will consider only six positions in which we have to make the combinations.
And as we know that the seven people will be unique and there will be no repetition total number of ways in which the seven can be fitted together in a row is,
= 6 x 5 x 4 x 3 x 2 x 1 x 2
= 1440
It is to be noted that we have multiplied by the number of positions with to because the two people who are sitting together can be seated in two possible ways.
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What is the volume for the following figure? Round your answer to the nearest whole.
The volume of the give cone is 4.0913 π m³.
What is volume ?
Volume is the measure of the amount of three-dimensional space enclosed by a closed surface or shape. It is usually expressed in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³). The volume of an object can be calculated by multiplying its length, width, and height, or by using a formula specific to the shape of the object, such as the formula for the volume of a sphere or a cylinder. Volume is an important concept in geometry, physics, and engineering, and is used to measure the capacity of containers, the displacement of liquids, and the size of solid objects.
We know that, volume of cone = 1/3 πr²h
here, h = 3.4 cm
r = 1.9 cm
so, volume of given cone = 1/3 πr²h
= 1/3 π × 1.9² × 3.4
= 4.0913 π m³
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what is the equation of a line that passes through 1,3 and has a slope of 5/4
Answer: y-3= 5/4(x-1) is the point slope form answer, y = 1.25x + 1.75 is the slope intercept form answer.
Step-by-step explanation:
Solve for x. Round your answer to the nearest tenth
Hence, value of variable y in the triangle is 7.5
Define triangle proportionalityTriangle proportionality is a relationship that exists between the sides of a triangle when a line is drawn parallel to one side of the triangle, intersecting the other two sides. Specifically, the line divides the two sides in proportion to the length of the third side.
We know that, if a line is drawn parallel to one side of a triangle, then the line divides the other two sides in proportion.
AB/AC=2y+5/2y+25
We know that
AB=BC=1/2AC
½=2y+5/2y+25
2y+25=4y+10
2y=15
y=7.5
value of variable y in the triangle is 7.5.
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What is the radius of a cone with diameter d? An ice cream cone is filled exactly level with the top of the cone. The cone has a -cm diameter and -cm depth. Approximate how much ice cream (in ) is in the cone? Use 3.14 for .
Answer: radius is 2.5 and volume of ice cream is 58.9 cm cubed
Step-by-step explanation:
the lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. if one such class is randomly selected, find the probability that the class length is more than 51.7 min.
The probability that the class length is more than 51.7 min is 0.3 or 30%.
To solve the problem, we first need to find the total possible outcomes, which is the range of class lengths between 50.0 min and 52.0 min, which is 2.0 min. Since the distribution is uniform, each possible class length within this range is equally likely.
Next, we need to find the favorable outcomes, which is the range of class lengths that are more than 51.7 min. This range is 52.0 min minus 51.7 min, which equals 0.3 min.
To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = (favorable outcomes) / (total outcomes) = 0.3 min / 2.0 min = 0.15 or 15%.
Therefore, the probability of a randomly selected class length being more than 51.7 min is 0.3 or 30%.
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if f(x) = 2x^2 + 3x - 1 and g(x)= 4x+ 10 then (f . g) (x) is whar rype of function?
Linear
Cubic
Quartic
Quadratic
PLSS HELPPP
Answer:
quadratic
Step-by-step explanation:
see image above for explanation.
I need help!!!!!!!!!!!!!!1
Answer:
∠2 = 125°
Step-by-step explanation:
∠1 and ∠2 form a straight angle of 180° (∠3 and ∠4 aswell)
∠1 = ∠3, because they are cross angles (∠3 and ∠4 aswell)
We can write an equation according to this and find y:
(8y - 9)° = (6y + 7)°
8y - 6y = 7 + 9
2y = 16 / : 2
y = 8
∠1 = 8 × 8 - 9 = 55°
∠2 = 180° - 55° = 125°
∠3 =∠1 = 6 × 8 + 7 = 55°
∠4 = 180° - 55° = 125°
1. 3 6 12 24 2. 2 9 16 23 3. 53 46 39 32 4. 5 12 26 54 5. 5 20 50 110
FIND 3 NEXT TERMS
Answer:
Step-by-step explanation:
1. 48 96 192 (multiplying by 2)
2. 30 37 44 ( adding 7)
3. 25 18 11 ( subtracting 7)
4. 110 232 456 ( adding 7, 14, 28, 56 and so on)
5. 230 470 950 (adding 15, 30, 60 120 and so on)