The midpoint of the line segment joining (–4, –2) and (2, 8) is calculated to give: (-1, 3)
What is a line's midpoint?The centroid of a line segment is its middle point. Since it is equally far from both ends, it divides the region in half.
How to determine a line segment's midpointIn coordinate geometry, the midpoint formula is the method for calculating the center point of a straight line given its endpoints' coordinates.
The formula is of the form
X= (x₂ + x₁)/2
Y = (y₂ + y₁)/2
For points (–4, –2) and (2, 8).
X= (-4 + 2)/2 = -1
Y = (-2 + 8)/2 = 3
The midpoint is solved to be (-1, 3)
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What is the distance between the points (-8, -3) and (-2, -5)?
The distance between the points (-8, -3) and (-2, -5) is √40 units
How to find distance between two points?Using distance formula,
d = √(x₂ - x₁)² + (y₂ - y₁)²
Therefore, using (-8, -3) and (-2, -5).
x₁ = -8
x₂ = -2
y₁ = -3
y₂ = -5
d = √(-2 + 8)² + (-5 + 3)²
d = √(6)² + (-2)²
d = √36 + 4
d = √40
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Which of the following is the solution to the differential equation dy over dx equals 2 times x times y all over quantity x squared plus 1 end quantity comma with the initial condition y(1)
The solution of the differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex] is y=[tex]-x^{2} +1[/tex].
Given a differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex].
We are required to find the solution of the differential equation when y(0)=1.
dy/dx=[tex]2xy/(x^{2} -1)[/tex]
Taking y to left side and dx to right side.
1/y dy=2x/[tex](x^{2} -1)[/tex] dx
Integrating both sides.
[tex]\int\limits {1/y} \, dy[/tex]=[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]----------1
log y=[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]
Solving right side.
[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]
let [tex]x^{2} -1[/tex]=z
differentiating both sides with respect to x.
2x=dz/dx
2x dx=dz
Put 2x dx=dz in 1.
[tex]\int\limits {1/y} \, dy[/tex]=[tex]\int\limits {1/z } \, dz[/tex]
log y=log z+log c
Put z=[tex]x^{2} -1[/tex]
log y=log([tex]x^{2} -1[/tex])+log c
log y=log [{[tex]x^{2} -1[/tex])c]
y=([tex]x^{2} -1[/tex])c------------2
Put x=0 and y=1
1=(0-1)c
1=-c
c=-1
Put c=-1 in 2 to get the solution.
y=-1([tex]x^{2} -1[/tex])
y=[tex]-x^{2} +1[/tex]
Hence the solution of the differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex] is
y=[tex]-x^{2} +1[/tex].
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Is someone able to help me? You don’t have to explain just give answers
a. The continuous growth rate of the bacteria is 21%
b. The initial population of bacteria is 715
c. The culture will contain 2043 bacteria after 6 × 10⁻⁴ years
a. What is the continuous rate of growth of this bacteria population?Since [tex]n(t) = 715e^{0.21t}[/tex] represents the number of bacteria in the culture.
This function is similar to an exponential function of the form [tex]y(t) = Ae^{\lambda t}[/tex] where λ = growth rate
Comparing n(t) and y(t), we see that λ = 0.21
So, the continuous growth rate of the bacteria is 0.21 = 0.21 × 100 %
= 21%
So, the continuous growth rate of the bacteria is 21%
b. What is the initial population of the culture?Since [tex]n(t) = 715e^{0.21t}[/tex] represents the number of bacteria in the culture, the initial population of bacteria is obtained when t = 0.
So, [tex]n(t) = 715e^{0.21t}[/tex]
[tex]n(0) = 715e^{0.21(0)} \\= 715e^{0} \\= 715 X 1\\= 715[/tex]
So, the initial population of bacteria is 715
c. When will the culture contain 2043 bacteria?To find the time when the number of bacteria will be 2043, this means n(t) = 2043.
Since [tex]n(t) = 715e^{0.21t}[/tex]
Making t subject of the formula, we have
t = ㏑[n(t)/715]/0.21
So, substituting n(t) = 2043 into the equation, we have
t = ㏑[n(t)/715]/0.21
t = ㏑[2043/715]/0.21
t = ㏑[2.8573]/0.21
t = 1.05/0.21
t = 4.99
t ≅ 5 hours
Converting this to years, we have t = 5 h × 1 day/24h × 1 year/365 days
= 5/8760
= 5.7 × 10⁻⁴ years
≅ 6 × 10⁻⁴ years
So, the culture will contain 2043 bacteria after 6 × 10⁻⁴ years
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Your team is adding a new external feature to increase daily active users. What metrics would you consider to determine if the new feature will be successful
Some of the metrics that I would look at to determine whether or not a new feature will be successful are as follows:
How many people use the feature on a daily basis.How long do people spend using the feature.How often do people use the feature.How many people finish tasks using the feature.What are metrics?It should be noted that metrics are the measures of quantitative assessment used for comparing, and tracking performance or production.
Metrics are heavily relied on in the financial analysis of companies to make decisions.
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Suppose you are an engineer trying to recreate an experiment involving a weight on the end of a spring. This simulation will give you an idea of what the experiment will look like. For more information, you can visit this simple harmonic motion website. You are given the equation y(t)=2 sin 4 pi t + 5 cos 4pi t, which models the position of the weight, with respect to time. You need to find the amplitude of the oscillation, the angular frequency, and the initial conditions of the motion. You will also be required to find the time(s) at which the weight is at a particular position. To find this information, you need to convert the equation to the first form, y(t) = A sin (wt+0).
The canonical expression equivalent to sinusoidal model y(t) = 2 · sin (4π · t) + 5 · cos (4π · t) is y(t) = (√ 29) · sin (4π · t + 0.379π) .
How to find the canonical form of the equation for simple harmonic motion
Herein we have a simple harmonic motion model represented by a sinusoidal expression of the form y(t) = A · sin (C · t) + B · cos (C · t), which must be transformed into its canonical form, that is, y(t) = A' · sin (C · t + D). We proceed to perform the procedure by algebraic and trigonometric handling.
The amplitude of the canonical function is determined by the Pythagorean theorem:
A' = √(2² + 5²)
A' = √ 29
The angular frequency C is the constant within the trigonometric functions from the non-canonical formula:
C = 4π
Then, we find the initial position of the weight in time: (t = 0)
y(0) = 2 · sin (4π · 0) + 5 · cos (4π · 0)
y(0) = 5
And now we calculate the angular phase below: (A' = √ 29, C = 4π, y = 5)
5 = √ 29 · sin (4π · 0 + D)
5 / √ 29 = sin D
D ≈ 0.379π rad
The canonical expression equivalent to sinusoidal model y(t) = 2 · sin (4π · t) + 5 · cos (4π · t) is y(t) = (√ 29) · sin (4π · t + 0.379π) .
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Order the number from least to greatest square root of 1, 1/3,2.5,square root of 2
The required order of the number from least to greatest square root is
1/√3 < √1 < √2 < √2.5
Which number is greatest in value:
In the above numbers 1, 1/3 and 2.5 do not have square roots.
So, we will write 1, 1/3 and 2.5 inside the square root as shown below.
√1 = 1
√(1/3) = 1/√3 = 0.577350269
√2.5 = 1.58113883
√2 = 1.414
Arranging these numbers according to their value, we get the order as-
0.577350269 < 1 < 1.414 < 1.581138831
Hence, the required order of the number from least to greatest square root is 1/√3 < √1 < √2 < √2.5.
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True or false: If neither variation in an A/B is statistically better, you pick the variation you like best and proceed to make the change.
It is false to state that " If neither variation in an A/B is statistically better, you pick the variation you like best and proceed to make the change."
What is A/B Testing?A/B testing compares two variations of a website element, often by evaluating users' responses to variant A vs. variant B and determining which of the two variants is more successful.
When the variation seems to be equal, then another factor must be introduced into the metric analysis that helps to make the testing objective.
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An Independent group experiment or between-subjects experiment comparing four treatment conditions produces 20 scores in each treatment condition. How many individuals participated in the entire experiment
The number of individuals who participated in the entire experiment was 80.
In the question, we are informed that an Independent group experiment or between-subjects experiment comparing four treatment conditions produces 20 scores in each treatment condition.
We are asked to find the number of individuals who participated in the entire experiment.
The number of treatment conditions in the experiment is given to be 4.
The scores in each treatment condition for the experiment is given to be 20.
The total number of individuals who participated in the experiment will be the product of the number of treatment conditions in the experiment and the scores in each treatment condition for the experiment.
Thus, the number of individuals who participated in the entire experiment = 4*20 = 80.
Thus, the number of individuals who participated in the entire experiment was 80.
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Volume=
Help me please
I appreciate it so much :)
The volume of the given solid is 6322.75 cubic units.
What is the volume of the given figure?
It is given that,
The area of the regular pentagonal base, a = 35 units
Altitude of the given pyramid, h = 9 units
The formula for the volume of a pyramid with regular pentagonal base is given by,
V = (5/12) × tan(54°)ha²
Substituting the given values of a and h, we get the volume as,
V = (5/12) × tan(54°) × 9 × (35)²
V = (5/12) × (1.376) × 9 × 1225
V = (5/4) × (1.376) × 3 × 1225
V = (5/4) × 5056.8
V ≈ 6322.75 units³
Thus, the volume of the given figure comes out to be approximately equal to 6322.75 cubic units.
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The median for the samples from the 30 mile race of cars and SUVs are:
The median of Sample 1 for cars is 132.
The median of Sample 2 for SUVs is 115.
What conclusions can you derive from the random samples?
The sample size was too small to derive a valid conclusion.
SUVs can perform well under testing conditions.
Cars and SUVs performed equally well.
Cars are slower than SUVs.
Cars are faster than SUVs.
A conclusion which can be derived from these random samples is that: E. Cars are faster than SUVs.
What is a median?A median can be defined as the middle number (center) of a sorted data set, which is typically when the data set is arranged in from the least to greatest or the greatest to least.
In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there's an outlier in the data set.
Based on the information provided for these random samples from the race, we can infer and logically conclude that Cars are faster than SUVs because a median speed of 132 is greater than a median speed of 115.
In conclusion, it is important to note that the Cars used in this survey (research) are faster than SUVs because the median for the SUVs in Sample 2 is equal to 115 while the median for the Cars in Sample 1 is equal to 132.
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Consider a standard deck of playing cards. If 5 cards are selected randomly without replacement from this deck then what is the probability that all of these are red
The probability that all of the cards drawn are red is 0.0253.
How can we find the probability?A standard deck of playing cards has 52 cards.
Of the 52 cards, 26 of the cards are red cards.
When we draw the first card, the probability of getting red is 26/52.
When we draw the second card, the probability of getting red is 25/51.
When we draw the third card, the probability of getting red is 24/50.
When we draw the fourth card, the probability of getting red is 23/49.
When we draw the fifth card, the probability of getting red is 22/48.
Therefore, the probability of drawing 5 red cards without replacement is
= [tex]\frac{26}{52}* \frac{25}{51}* \frac{24}{50} *\frac{23}{49}* \frac{22}{48}[/tex]
= 26*25*24*23*22/52*51*50*49*48
= 0.0253
Therefore, we have found that the probability that all cards drawn are red is 0.0253.
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Which options reflect the requirements for factoring using quadratic form? (Select all that apply.)
Answer:
The exponent of the first term must have twice the value of the exponent of the second term.
Step-by-step explanation:
Evaluate 5a + 5b, where a
=
-6 and b = -5.
Substitute -6 in a and -5 in b
5(-6) + 5(-5)
-30+(-25)
=-55
Hope it helps!
Answer:
-55
5x-6 = -30
5 x -5 = -25
-25 + -30 = -55
Step-by-step explanation:
hope this helps
Word Problem
Beau Thai has a rectangular mirror with a length of 6 inches and a width of 10 inches.
a) How much ribbon could Beau wrap around the outside of the mirror?
b) What is the area of Beau Thai's mirror?
10in
Beau can wrap 32 inches of ribbon outside the mirror.
Area of Beau Thai's mirror is 60 sq. inches.
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The word "area" refers to a free space. A shape's length and width are used to compute its area.
Given information:
Length of mirror = 6 inches
Width of mirror = 10 inches
To Find:
The amount of ribbon Beau could wrap around the outside of the mirror.
Perimeter of the mirror = 2(6+10)
= 2(16)
= 32 inches
The area of Beau Thai's mirror.
Area of the mirror = 6*10
= 60 sq. inches
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Suppose the average commute time of your employees is unknown. The standard deviation of their commute time is estimated as 24.5 minutes. How many employees must be included in a sample to create a 90 percent confidence interval for the average commute time with a confidence interval width of no more than 13 minutes
The number of employees is 91.
According to the statement
Given that the standard deviation = 24.5
The width in the question = 13
We solve for the margin of error E.
E = width / 2
E= 13/2 = 6.5
At 90%
Alpha = 1-0.90
= 0.1
Alpha/2 = 0.1/2 = 0.05
Z 0.05 = 1.576
Now find the Sample size n
= ((1.576x24.5)/2)²
= 90.8
= 91
So, The number of employees is 91.
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At a high school basketball game the lions and the eagles are playing. the lions attempted 16 free throws and made 13, attempted 51 two-point shots and made 22, and attempted 16 three-point shots and made 10. the eagles attempted 27 free throws and made 7, attempted 41 two-point shots and made 19, and attempted 16 three-point shots and made 7. (free throws are worth 1 point each, two-point shots worth 2 points each, and three-point shots worth 3 points each) what is the free throw percentage for the lions? number % (round the final percentage to one decimal place) what is the free throw percentage for the eagles? 025.9 % (round the final percentage to one decimal place) what is the field goal percentage (two-point and three-point shots combined) for the lions? number % (round the final percentage to one decimal place) what is the field goal percentage (two-point and three-point shots combined) for the eagles? number % (round the final percentage to one decimal place) how many points did the lions score? number how many points did the eagles score?
Answer:
a. The free throw percentage obtained by the Lions is of 81.25%.
b. The free throw percentage for the Eagles was of 37.04%.
c. The field goal percentage for the Lions was of 56.01%.
d. The field goal percentage for the Eagles was of 34.43%.
e. The Lions scored 96 points.
f. The Eagles scored 64 points.
Solution:
a. The lions attempted 16 free throws and made 13, which means lions scored 13 out of 16,
The free throw percentage obtained by the Lions = [tex]\frac{13}{16}[/tex] × 100 = 81.25%
The free throw percentage obtained by the Lions is 81.25%
b. The eagles attempted 27 free throws and made 7 which means 7 out of 27, so:
The free throw percentage obtained by the eagles = [tex]\frac{7}{27}[/tex] × 100 = 25.92 %
The free throw percentage obtained by the eagles is 25.92 %
c. The lions attempted 51 two-point shots and made 22, and attempted 16 three-point shots and made 10.
Total attempted = 51 + 16 = 67
Total shots made = 22 + 10 = 32
The field goal percentage (two-point and three-point shots combined) for the Lions = [tex]\frac{32}{67}[/tex] × 100 = 47.76 %
The field goal percentage for the Lions was of 47.76 %.
d. The eagles attempted 41 two-point shots and made 19, and attempted 16 three-point shots and made 7.
Total attempted = 41 + 19 = 60
Total shots made = 19 + 7 = 26
The field goal percentage (two-point and three-point shots combined) for the eagles= [tex]\frac{32}{67}[/tex] × 100 = 43.33 %
The field goal percentage for the eagles was of 43.33 %.
e. Total goals secured by lions 13 free throws, 22 two's and 10 three's. So
Total points = 10 × 1 + 22 × 2 + 10 × 3 = 84
The Lions scored 84 points.
f. Total goals secured by eagles 7 free throws, 19 two's and 7 three's. So
Total points = 7 × 1 + 19× 2 + 7 × 3 = 66
The eagles scored 66 points.
What is percentage?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
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What is the domain and range of the following graph?
Using it's concepts, the domain and the range of the graph are given as follows:
Domain: all real values except x = -1.Range: All real values.What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input. In a graph, it is given by the values of x, which is the horizontal axis of the graph.The range of a function is the set that contains all the values of the output. In a graph, it is given by the values of y, which is the vertical axis of the graph.In this graph, have that the function is defined for all values of x except x = -1, and assumes all real values, hence the domain and the range of the graph are given as follows:
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URGENT WILL GIVE BRAINLIEST
Answer:
27.7 m²
Step-by-step explanation:
Area of equilateral triangle:In regular polygon, all the sides and angles are equal. The polygon in the picture is a equilateral triangle.
a = 8 m
√3 = 1.732
[tex]\sf \boxed{\bf Area \ of \ equilateral \ triangle= \dfrac{\sqrt{3}a^2}{4}}[/tex]
[tex]\sf =\dfrac{1.732 * 8 * 8 }{4}\\\\ = 1.732*2*8\\\\= 27.71\\\\= 27.7 \ m^2[/tex]
What is the point-slope form of a line with slope that contains the point
(-2, 1)?
Answer:
d; y - 1 = 4/5(x + 2)
Step-by-step explanation:
the equation for a point-slope form line is y - y1 = m(x - x1)
plug in the points and you will get your answer
y - 1 = 4/5(x + 2)
that is your answer
Write an equivalent expression by distributing the "-−" sign outside the parentheses: -(-8r-9.8s)+8.1
Answer: 8r + 9.8s + 8.1
Step-by-step explanation:
Given:
-(-8r-9.8s)+8.1
Distribute:
↳ A - times a - becomes a +, a -times a + stays a -
8r + 9.8s + 8.1
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Please help!
I don't understand part B.
The median value of x is 2.
According to the statement
we have given the values of x at some points then
and we have to find the median for the x.
We know that the median formula is {(n + 1) ÷ 2}th, where “n” is the number of items in the set and “th” just means the (n)th number.
and after put the values in this formula we get our median value for x.
So,
we have given that the f(x) is 0.2 when x is from -1 to 0
and f(x) is 0.2 +1.2x when x is grater than 0 but less than 1
and f(x) is 0 when x is less than -1 or grater than 1
From these statements it is clear that the the f(x) is only exist when the x lies in between from the -1 to 1.
So, the total value of x becomes is -1,0,1
Then according to the median formula
median = (n + 1) ÷ 2
median = (3+1) / 2
median = 2.
So, The median value of x is 2.
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The vehicle preference of police officers and firefighters is given in the table.
Police Officers Firefighters
Cars 12 3
Trucks 9 4
SUVs 15 2
Based on the information in the table, which of the following is an example of independent events.
Based on the information in the table, an example of independent events is the: P(policer officer and chooses car).
What is an independent event?An independent event can be defined as an event that isn't dependent on other events. Thus, it isn't affected by any previous event.
Based on the information provided, we can infer and logically deduce that an example of independent events is the probability of being a policer officer and chooses a car because they aren't overlapping probabilities.
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Roco draws two shapes. one of his shapes is 4 times longer and 4 times wider than the other. he found that the perimeter of the larger shape is 6 times larger than the perimeter of the smaller shapes and that the area is 16 times larger. is he correct? what did he calculate correctly: area, perimeter or both?
If two squares have different perimeters, the one with the larger perimeter will have a larger area. If two polygons have the same perimeter, then they must have the same shape. If two polygons have the same shape but are different sizes, then they must have different perimeters.
If two squares have equal areas, they will also have sides of the same length. But although "equal areas mean equal sides" is true for squares, it is not true for most geometric figures.
In order to find the perimeter or distance around the rectangle, we need to add up all four side lengths. This can be done efficiently by simply adding the length and the width, and then multiplying this sum by two since there are two of each side length.
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What are the domain and range of the function below? graph
domain: [0,00)
range: (-00,00) domain [0,00) range: (-00,4] domain: (0,4) range:(-00,00) domain: (-00,4] range: [0,00)
The domain and range of the function is D) Domain: (-∞, ∞); Range: (-∞, ∞)
How to illustrate the information?The domain is the input values, or the x values. We can put in any x values for this function.
Domain : (-∞, ∞)
The range is the output values or the y values. We can get any output values for this function
Range: (-∞, ∞)
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Complete question:
What are the domain and range of the function below?
A) Domain: (-∞, -5)
Range: (5, ∞)
B) Domain: (-5, -10)
Range: (5, 10)
C). Domain: (-5, 10)
Range: (-10, 5)
D) Domain: (-∞, ∞)
Range: (-∞, ∞)
What steps may be necessary to predict data not included in a data set using a scatter plot and line of best fit? Select all that apply.
the necessary steps to predict data not included in a data set using a scatter plot and line of best fit are Options 2, 3, 4
Graph the data in a scatter plotExtend the line of best fit beyond the dataFind the average of the dataSteps involved in predicting dataIn using the line of best fit also known as the slope, they following steps are involved;
Draw the line of best fitFind the direction of association between the two variablesIn using scatterplot, they following steps are involved;
Draw line of best fit that passes close to most of the data pointsApproximately half of the data points should be below the line and half of the points above the lineThis explains that the average of the set of data is found from the scatter plot and line of best fit.
Thus, the necessary steps to predict data not included in a data set using a scatter plot and line of best fit are Options 2, 3, 4
Graph the data in a scatter plot
Extend the line of best fit beyond the data
Find the average of the data
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Use this information to answer the questions.
You are helping plan your sister's wedding. You decide to help set up a night to prepare the decorations and gift bags, but worry it all won't get done and you will be stuck doing the rest by yourself. Use the information below to help you know how long it will take to get everything done.
1.
You plan to have 2 people work on each task. How would you pair them up to complete each task in the shortest amount of time? Explain using rational expressions.
2.
What is the shortest amount of time it would take to complete all the tasks? If you know people have to leave your house by 9pm, what time should they come over to get started? Explain using rational expressions.
The shortest possible time to perform the tasks is 30 minutes, these activities would be performed in this time by the couple made up of you and your aunt 1.
How to calculate the shortest time to perform the wedding tasks?To calculate the shortest time to complete the wedding tasks, we must carefully observe the information in the table and identify the time that each person takes to complete the tasks. Subsequently, we must identify the people who take the shortest time, in this case it is you and your aunt 1 as shown below:
You
2.5 + 5 + 1.5 = 9 hoursaunt 1
1.5 + 4 + 3 = 8.5 hours.Additionally, we must subtract the two values, to know how long it will take in total for both people to perform the three required activities.
9 - 8.5 = 0.5 hours = 30 minutesAccording to the above, the most efficient couple is your aunt 1 and you because you will take 30 minutes to complete the activities.
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PLEASE HELP VERY URGENT Let p represent "Two angles have the same measure," and let q represent "The angles are congruent."
Which symbolic statement represents the following conditional: "If two angles are not congruent,
then they have the same measure"?
answer choices:
~q->p
p->q
q->p
q->~p
The symbolic representation for the given statement " If two angles are not congruent, then they have the same measure" is ~q → p. So, option A is correct.
How a conditional statement is represented?The conditional statement consists of a hypothesis sentence and a conclusion statement. A conditional statement can be written as " If p then q" where p is called the hypothesis and q is called the conclusion.The statement "If p then q" - means q must be true whenever p is true.Calculation:It is given that,
p - "Two angles have the same measure"
q - "The angles are congruent"
Statement: " If two angles are not congruent, then they have the same measure"
So, symbolically it is written as,
The hypothesis "two angles are not congruent" is represented by ~q and the conclusion "they have the same measure" is represented by p.
That is,
The representation is "If ~q then p i.e., ~q → p. So, option A is correct".
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Which expression is equivalent to 21/15 - 915?
A. 12
B. 30 15
c. 125
D. 12 15
[tex]\textbf{Heya !}[/tex]
the denominators are equal, so subtracting these two fractions is a piece of cake:-
[tex]\sf{\cfrac{21}{15}-\cfrac{9}{15}}[/tex]
[tex]\sf{\cfrac{21-9}{15}}[/tex]
[tex]\sf{\cfrac{12}{15}}[/tex]
`hope it's helpful to u ~
4. Alex is painting a house. He uses 1/3 of the
paint he bought on the dining room. He uses
twice as much on the living room as on the
kitchen, where he uses 1 ½ gallons. He has 12
gallons of paint left. How much paint did Alex
buy?
Alex bought 24.75 gallons of paint to use for the house painting.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the amount of paint bought by Alex, hence:
(1/3)x + 3/2 + 2(3/2) + 12 = x
X = 24.75 GALLONS
Alex bought 24.75 gallons of paint to use for the house painting.
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A quantity with an initial value of 570 grows exponentially at a rate of 35% every 2
decades. what is the value of the quantity after 39 years, to the nearest hundredth?
After 39 years, the value of this quantity is 1,023.35
What is the value after 39 years?Here we know that:
The initial value is 570.There is an exponential growth.The rate of growth is 35% for every 2 decades (20 years).Then the exponential equation is:
[tex]A(t) = 570*(1 + 0.35)^{t/20}[/tex]
Where t is the time in years.
So, after 39 years, the value of this quantity is given by:
[tex]A(39) = 570*(1 + 0.35)^{39/20} = 1,023.35[/tex]
After 39 years, the value of this quantity is 1,023.35
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