Answer:
[tex]3^{-14}[/tex] or [tex]\displaystyle \frac{1}{3^{14}}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{3^{-10}}{3^4*3^0}=\frac{3^{-10}}{3^4}=3^{-10-4}=3^{-14}[/tex]
Solve for each variable.
a = ___
b = ___
c = ___
d = ___
Answer:
a=55°
b=123°
c=55°
d=123°
Jade decided to rent movies for a movie marathon over the weekend. The function g(x) represents the amount of money spent in dollars, where x is the number of movies. Does a possible solution of (6.5, $17.50) make sense for this function? Explain your answer.
Yes. The input and output are both feasible.
No. The input is not feasible.
No. The output is not feasible.
No. Neither the input nor output is feasible.
The output value is feasible. The input value is not feasible, the possible solution of (6.5, $17.50) does not make sense for this function. The correct answer is No. The input is not feasible.
Jade decided to rent movies for a movie marathon over the weekend.
The function g(x) represents the amount of money spent in dollars, where x is the number of movies.
The given function is g(x) which represents the amount of money spent in dollars, where x is the number of movies.
The solution given is (6.5, $17.50).
We need to find whether the solution makes sense for the given function or not.
The input is given as 6.5 and the output is given as $17.50.
This means that Jade rented 6.5 movies and spent $17.50 on renting those movies.
To check whether the solution makes sense or not, we need to see if the input and output values are feasible or not.
The input value 6.5 is not a feasible value because it is not possible to rent half a movie.
Jade can rent 6 movies or 7 movies but not 6.5 movies.
Therefore, the input value is not feasible.
On the other hand, the output value $17.50 is a feasible value because it is possible for Jade to spend $17.50 on renting 6 movies.
The output value is feasible.
Since the input value is not feasible, the possible solution of (6.5, $17.50) does not make sense for this function. The correct answer is No. The input is not feasible.
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Is a point imaginary or real?
Answer:
it is real or imaginary depending on what u are talking about.
Predict the population in 2016, as a decreases at a constant rate
Answer:
We need more information to accurately predict the population in 2016. The following information is needed:
The initial population (population in a given baseline year)
The known population decrease rate as a percentage or absolute number per year
For example, if:
The initial population (in 2010) was 10,000
The population is decreasing at a constant rate of 100 people per year
Then we can calculate the population in 2016 as follows:
2010 population: 10,000
2011 population: 10,000 - 100 = 9,900
2012 population: 9,900 - 100 = 9,800
2013 population: 9,800 - 100 = 9,700
2014 population: 9,700 - 100 = 9,600
2015 population: 9,600 - 100 = 9,500
2016 population: 9,500 - 100 = 9,400
Therefore, based on this information, the predicted population in 2016 would be 9,400.
In summary, to accurately predict population changes over time, we need to know the initial population and population decrease rate. With that information, we can calculate the population for each subsequent year by subtracting the decrease amount from the population in the previous year.
Hope this helps! Let me know if you have any other questions.
Step-by-step explanation:
Rewrite 9 2/7 as an improper fraction. 25/2 65/7 25/7 23/7 Rewrite 2 4/5 as an improper fraction. 10/4 13/5 14/5 22/5 Find the product of 9 2/7 and 2 4/5. Express your answer in simplest form. 26 130/5 910/35 15
Answer:
1. 9 2/7 = (63+2)/7 = 65/7
2. 2 4/5 = (10+4)/5 = 14/5
3. 65/7 * 14/5 = 910/35 = 26
Use traces to sketch the surface. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.)
9x2 − y2 + 3z2 = 0
(Write an equation for the cross section at
z = 0
using x and y.)
(Write an equation for the cross section at
y = −9
using x and z.)
(Write an equation for the cross section at
y = 9
using x and z.)
(Write an equation for the cross section at
x = 0
using y and z.)
Answer:
Step-by-step explanation:
To sketch the surface represented by the equation 9x² - y² + 3z² = 0 and find the equations for the cross sections, we can start by isolating each variable and considering different values for the fixed variables.
(1) - Cross section at z = 0:
Substituting z = 0 into the equation, we get 9x² - y² = 0 . Rearranging this equation, we have:
9x² = y²
Taking the square root of both sides, we get:
y = ±3x
So the equation for the cross section at z = 0 is y = ±3x and our trace is a line in the xy-plane.
(2) - Cross section at y = -9:
Substituting y = -9 into the equation, we get 9x² - (-9)² + 3z² = 0. Simplifying this equation, we have:
9x² - 81 + 3z² = 0
Rearranging, we obtain:
9x² + 3z² = 81
Dividing by 3, we get:
3x² + z² = 27
So the equation for the cross section at y = -9 is 3x² + z² = 27 and our trace is an ellipse in the xz-plane.
(3) - Cross section at y = 9:
Substituting y = 9 into the equation, we get 9x² - (9)² + 3z² = 0. Simplifying this equation, we have:
9x² - 81 + 3z² = 0
Rearranging, we obtain:
9x² + 3z² = 81
Dividing by 3, we get:
3x² + z² = 27
So the equation for the cross section at y = -9 is 3x² + z² = 27 and our trace is an ellipse in the xz-plane.
(4) - Cross section at x = 0:
Substituting x = 0 into the equation, we get - y² + 3z² = 0. Rearranging this equation, we have:
y² = 3z²
Taking the square root of both sides, we get:
y = ±√3z
So the equation for the cross section at x = 0 is y = ±√3z and our trace is a parabola in the yz-plane.
Is there a difference between shapes when plotting Uniform acceleration towards (+)directtion,Uniform acceleration towards (-)direction, Uniform deceleration towards (+) direction and Uniform deceleration towards (-) direction in displacement time graph
Yes, there is a difference in the shapes of the displacement-time graphs for uniform acceleration towards the positive direction, uniform acceleration towards the negative direction, uniform deceleration towards the positive direction, and uniform deceleration towards the negative direction.
Uniform acceleration towards the positive direction:
In this case, the object's velocity increases in the positive direction over time. The displacement-time graph will have a concave-upward shape, forming a curve that starts with a small slope and gradually becomes steeper as time progresses.
Uniform acceleration towards the negative direction:
Here, the object's velocity increases in the negative direction, meaning it accelerates in the opposite direction to its positive direction.
The displacement-time graph will have a concave-downward shape, forming a curve that starts with a steep slope and gradually becomes less steep as time progresses.
Uniform deceleration towards the positive direction:
In this scenario, the object's velocity decreases in the positive direction, but it still moves towards the positive direction.
The displacement-time graph will show a curve with a decreasing slope, forming a concave-downward shape, indicating that the object is slowing down.
Uniform deceleration towards the negative direction:
Here, the object's velocity decreases in the negative direction, opposing its initial direction.
The displacement-time graph will have a curve with a decreasing slope, forming a concave-upward shape, indicating that the object is slowing down but still moving in the negative direction.
In summary, the shapes of the displacement-time graphs differ based on the direction and type of acceleration (positive or negative) and whether the object is undergoing uniform acceleration or uniform deceleration. These differences can be observed through the concavity and slope of the graphs.
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Which of the following is the prime factorization of 15?
01x15
03x5
02x2x5
05x2
Answer: The second one, 3×5
Step-by-step explanation:
We can use a factor tree to determine the prime factorization of 15. We first choose factors of 15, and the only factors we can use besides 1 and 15 are 3 and 5.
15
3×5
That is all, because the final numbers listed are prime and we cannot perform any further actions. The prime factorization of 15 is 3×5, or in exponential form, [tex]3^1[/tex]×[tex]5^1[/tex].
Note: You may notice with other numbers that there are several factors to choose from. That's okay, because in the end it will give you the same result.
Hope this helps!
What is the surface area of this cone?
Use 3.14 and round your answer to the nearest hundredth.
15 cm
9 cm
Answer:
answer is 749.07
just use the formula and put values for radius and height. you can find formula online or leave me a comment if you can't find it.
Kemani Walker
Law of Sines
Jun 15, 9:29:00 PM
?
In ATUV, t = 820 inches, m/U=132° and m2V=25°. Find the length of u, to the
nearest inch.
Answer: u =
Submit Answer
The length of u, to the nearest inch, is 1818 inches.
To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.
In this case, we'll use the following formula:
a/sin(A) = b/sin(B) = c/sin(C)
Let's label the sides and angles of the triangle:
Side a = u (length of u)
Side b = t (820 inches)
Side c = v (length of v)
Angle A = m/U (132°)
Angle B = m2V (25°)
Angle C = 180° - A - B (as the sum of angles in a triangle is 180°)
Now, we can use the Law of Sines to set up the equation:
u/sin(A) = t/sin(B)
Plugging in the given values:
u/sin(132°) = 820/sin(25°)
To find the length of u, we'll solve this equation for u.
u = (820 [tex]\times[/tex] sin(132°)) / sin(25°)
Using a calculator, we can evaluate the right side of the equation to get the approximate value of u:
u ≈ (820 [tex]\times[/tex] 0.9397) / 0.4226
u ≈ 1817.54 inches
Rounding to the nearest inch, we have:
u ≈ 1818 inches
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Answer the equation 2.5p + 1 = 1.4p
Answer:
p ≈ -0.9
Step-by-step explanation:
2.5p + 1 = 1.4p
2.5p = 1.4p - 1
1.1p = -1
p ≈ -0.9
So, p ≈ -0.9
Jennifer Aniston bought a property for $2,000,000. One year later, she sold it for $2,200,000. Jennifer invested only $1,000,000 of her own money and borrowed the rest interest-free from her friend, Brad Pitt. What was her return on this investment?
This means that she made a 20% return on the money she invested in the property. For every dollar she invested, she earned 20 cents in profit.
To calculate Jennifer Aniston's return on investment (ROI), we can use the formula:
ROI = (Net Profit / Initial Investment) * 100
First, let's calculate the net profit. The net profit is the selling price minus the initial investment:
Net Profit = Selling Price - Initial Investment
Net Profit = $2,200,000 - $2,000,000
Net Profit = $200,000
Next, we calculate the ROI:
ROI = (Net Profit / Initial Investment) * 100
ROI = ($200,000 / $1,000,000) * 100
ROI = 0.2 * 100
ROI = 20%
Jennifer Aniston's return on investment for this property is 20%.
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Find the slope of the line graphed below.
Answer:
m = 3
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (-1,-1) (0,2)
We see the y increase by 3 and the x increase by 1, so the slope is
m = 3
Answer:
slope = 3
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, - 1) and (x₂, y₂ ) = (0, 2) ← 2 points on the line
m = [tex]\frac{2-(-1)}{0-(-1)}[/tex] = [tex]\frac{2+1}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3
El resultado de (6+9i) +(4-5i) es/
?
Answer:
es 362770
Step-by-step explanation:
saque esta imformacion de la calculadora
Answer:
10 + 4i
Step-by-step explanation:
To solve this, just combine the like terms:
[tex]\sf{(6+9i)+(4-5i)}[/tex]
[tex]\sf{6+9i+4-5i}[/tex]
[tex]\sf{6+4+9i-5i}[/tex]
[tex]\sf{10+4i}[/tex]
Hence, the answer is 10 + 4i
Pablo solved the polynomial equations given in the table. Determine whether each polynomial is correct. Select Correct or Incorrect for each equation.
Equation
(b²+7b-9)+(4b-6b²) = -8b² + 14b-9
(4a+6)-(3a²-9a+1)=-3a²+ 13a +5
(12c-8c²)+(5c²- 10c) = -3c²+2c
The first equation is incorrect.
The second equation is correct.
The third equation is correct.
Let's go through each equation and determine whether it is correct or incorrect:
(b²+7b-9)+(4b-6b²) = -8b² + 14b-9
To determine if this equation is correct, we need to simplify both sides and check if they are equal.
On the left side:
(b²+7b-9)+(4b-6b²) = b² - 6b² + 7b + 4b - 9 = -5b² + 11b - 9
On the right side:
-8b² + 14b - 9
Comparing both sides, we can see that -5b² + 11b - 9 is not equal to -8b² + 14b - 9. Therefore, the equation is incorrect.
(4a+6)-(3a²-9a+1)=-3a²+ 13a +5
Again, we need to simplify both sides of the equation and check if they are equal.
On the left side:
(4a+6)-(3a²-9a+1) = 4a + 6 - 3a² + 9a - 1 = -3a² + 13a + 5
On the right side:
-3a² + 13a + 5
Comparing both sides, we can see that -3a² + 13a + 5 is equal to -3a² + 13a + 5. Therefore, the equation is correct.
(12c-8c²)+(5c²- 10c) = -3c²+2c
Again, let's simplify both sides and compare them.
On the left side:
(12c-8c²)+(5c²- 10c) = 12c - 8c² + 5c² - 10c = -3c² + 2c
On the right side:
-3c² + 2c
Comparing both sides, we can see that -3c² + 2c is equal to -3c² + 2c. Therefore, the equation is correct.
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Help, please !!!!
A scatter plot is shown on the coordinate plane.
scatter plot with points at 1 comma 9, 2 comma 7, 3 comma 5, 3 comma 9, 4 comma 3, 5 comma 7, 6 comma 5, and 9 comma 5
Which two points would a line of fit go through to best fit the data?
(1, 9) and (9, 5)
(1, 9) and (5, 7)
(2, 7) and (4, 3)
(2, 7) and (6, 5)
Answer:
(2,7) and (6,5)
Step-by-step explanation:
The line of best fit would be approximately:
y = -.4x + 8
(1,9)
9 = -.4(1) + 8
9 = 7.6
(9,5)
y = -.4x + 8
5 = -.4(9) + 8
5 = 4.4
(5,7)
y = -.4x + 8
7 = -.4(5) + 8
7 = 6
(2,7)
y = -.4x + 8
7 = -.4(2) + 8
7 = 7.2
(4,3)
y = -.4x + 8
3 = -.4(4) + 8
3 = 6.4
(6,5)
y = -.4x + 8
5 = -.4(6) + 8
5 = 5.6
Using a linear model, the predicted calories in food items based on grams of carbs are represented by the residual plot.
Residuals
30.00
20.00
10.00
0.00
-10.00
-20.00
-30.00
0
2
8
Carbs in grams
10
12
16
What does the pattern in the residual plot indicate about the type of model?
The pattern in the residual plot indicates the following about the type of model: C. The pattern is random, indicating a good fit for a linear model.
What is a residual plot?In Mathematics and Geometry, a residual plot is sometimes referred to as scatter plot and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association or correlation (relationship) between the data set.
In Mathematics, a residual value is a difference between the measured (given or observed) value from a residual plot (scatter plot) and the predicted value from a residual plot (scatter plot).
By critically observing the residual plot which shows a relationship between the residuals and carbs in grams, we can logically deduce that a linear model is the most appropriate because there isn't a clear pattern between the data points i.e a random pattern.
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Complete Question:
What does the pattern in the residual plot indicate about the type of model?
A. The pattern is random, indicating a good fit for a nonlinear model.
B. The pattern shows the points are far from the zero line, indicating a good fit for a linear model.
C. The pattern is random, indicating a good fit for a linear model.
D. The pattern shows the points are far from the zero line, indicating a good fit for a nonlinear model.
E. The pattern is random, indicating that the model is unable to be determined.
Washington, DC is 389 miles from Statesville, NC. If you wanted to drive there,
how long would it take you driving on interstates with an average of 65 mph?
O 5.98 hours
07.07 hours
O 5.56 hours
07.78 hours
O 6.48 hours
Suppose your car gets 29 miles per gallon on the interstate and gas costs
$3.89/gallon. How much will it cost you to drive to Washington, DC?
O $0.29
O $43,883.09
$52.18
O $3.45
O $2,900.00
It would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.
To calculate the time it would take to drive from Statesville, NC to Washington, DC, we can divide the distance of 389 miles by the average speed of 65 mph.
Time = Distance / Speed
Time = 389 miles / 65 mph
Time ≈ 5.98 hours
Therefore, it would take approximately 5.98 hours to drive from Statesville, NC to Washington, DC on interstates with an average speed of 65 mph.
To calculate the cost of driving to Washington, DC, we need to know the number of gallons of gas required for the trip. We can find this by dividing the distance by the car's mileage, which is 29 miles per gallon.
Number of gallons = Distance / Mileage
Number of gallons = 389 miles / 29 miles per gallon
Number of gallons ≈ 13.41 gallons
The cost of gas can be calculated by multiplying the number of gallons by the cost per gallon, which is $3.89.
Cost = Number of gallons * Cost per gallon
Cost ≈ 13.41 gallons * $3.89/gallon
Cost ≈ $52.18
Therefore, it would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.
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How to represent 7/3 as a decimal
Fraction 7/3 is convertible to a decimal. It is a proper fraction. Because here the numerator is lesser than the denominator. Any fraction can be represented as a decimal number.
To transform the fraction into a decimal, it has to go through a process of division. It will be like this, 7÷3.
During the process of the division after the use of the decimal point, the same number will keep repeating. The number that keeps repeating is known as the recurring number.
If 7 is divided by 3, the result is 2.333333. Here the digit 3 is recurring. So the representation of 7/3 as a decimal is 2.333333.
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The cycling tour has a $6,500 budget. This includes travel, accommodation and food. If $1,870 is spent to cover the first week’s travel and accommodation, how much money is left
Answer:
4710
Step-by-step explanation:
6580 minus
1870
4710
Need this soon!! AP Calc AB
Answer:
(Look at the picture)
Drag each shape to the correct location on the table. Each shape can be used more than once, but not all shapes will be used.
Consider the given square pyramid.
The descriptions and the cross-sectional images formed are as follows:
1. Description: a vertical plane that cuts through the top vertex perpendicular to the base
Cross-sectional image: The rectangle
2. Description: A horizontal plane that cuts through the pyramid parallel to the base
Cross-sectional image: A triangle
3. Description: A vertical plane that cuts through the base and two opposite lateral faces.
Cross-sectional image: The square
How to describe the shapesTo determine the cross-sectional images of the shapes, we will start by representing the shapes and the results obtained when the descriptions are applied to them. For the first one, running a vertical plane through the square pyramid will give us a rectangle.
Next, cutting a horizontal plane through the pyramid parallel to the base will give a triangle. Finally, running a vertical plane through the base and two lateral faces will give a square.
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Ayesha is the marketing manager for Superior Stationery Suppliers, a company that supplies a variety of stationery items to its customers, mostly businesses. Ayesha has started a process to understand the key buying motivations for customers. Ayesha must consider each of the following variables in the process, except...
(4x³+6x²+20x+9)/2x+1
divide using long polynomial division
The result of dividing (4x³ + 6x² + 20x + 9) by (2x + 1) using long polynomial division is 2x² + 2x + 9 with a remainder of 0.
To divide the polynomial (4x³ + 6x² + 20x + 9) by (2x + 1) using long polynomial division.
Arrange the terms of the dividend and the divisor in descending order of the degree of x:
2x + 1 | 4x³ + 6x² + 20x + 9
Divide the first term of the dividend by the first term of the divisor and write the result on the top line:
2x + 1 | 4x³ + 6x² + 20x + 9
| 2x²
Multiply the divisor (2x + 1) by the quotient obtained in the previous step (2x²) and write the result below the dividend:
2x + 1 | 4x³ + 6x² + 20x + 9
- (4x³ + 2x²)
---------------
4x² + 20x + 9
Subtract the result obtained in the previous step from the dividend and bring down the next term.
2x + 1 | 4x³ + 6x² + 20x + 9
- (4x³ + 2x²)
---------------
4x² + 20x + 9
- (4x² + 2x)
---------------
18x + 9
Repeat the process by dividing the term brought down (18x) by the first term of the divisor (2x):
2x + 1 | 4x³ + 6x² + 20x + 9
- (4x³ + 2x²)
---------------
4x² + 20x + 9
- (4x² + 2x)
---------------
18x + 9
- (18x + 9)
---------------
0
The division is complete when the degree of the term brought down becomes less than the degree of the divisor.
In this case, the degree of the term brought down is 0 (a constant term). Since we can no longer divide further, the remainder is 0.
Therefore, the result of the division is:
Quotient: 2x² + 2x + 9
Remainder: 0
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D = {x|x is a whole number} E = {x|x is a perfect square between 1 and 9} F = {x|x is an even number greater than or equal to 2 and less than 9} Which of the following is an element of D ∩ (E ∩ F)? 16 3 6 4
The element 4 is an element of D ∩ (E ∩ F).
To find the intersection of sets D, E, and F, we need to determine the elements that are common to all three sets.
Set D consists of all whole numbers, so any whole number can be an element of set D.
Set E consists of perfect squares between 1 and 9. The perfect squares in this range are 1, 4, and 9.
Set F consists of even numbers greater than or equal to 2 and less than 9.
The even numbers in this range are 2, 4, 6, and 8.
Taking the intersection of sets E and F, we find that the common element is 4, as it is the only number that satisfies both conditions of being a perfect square and an even number in the given range.
Finally, taking the intersection of set D with the intersection of sets E and F, we find that the element 4 is also an element of set D ∩ (E ∩ F).
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Arc BC on circle A has a length of 115,
- inches. What is the radius of the circle?
115/6 pi
138°
The radius of the circle is 25 inches. The length of arc with a central angle of 138° is 115π/6 in
What is an equation?An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.
The length of an arc with a central angle Ф with circle radius (r) is given by:
Length of arc = (Ф/360) * 2πr
Given the length of arc as 115π/6 in and angle of 138°, hence:
Length of arc = (Ф/360) * 2πr
Substituting:
115π/6 = (138/360) * 2πr
r = 25 inches
The radius of the circle is 25 inches.
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Refer to the table summarizing service times (seconds) of dinners at a fast food restaurant. How many individuals are included in the summary? Is it possible to identify the exact values of all of the original service times?
Time (sec) Frequency
60 to 119 7
120 to 179 24
180 to 239 14
240 to 299 1
300 to 359 4
Answer:
Based on the provided information, the table summarizes service times (in seconds) of dinners at a fast food restaurant. To determine the number of individuals included in the summary, we can sum up the frequencies listed in the table:
7 + 24 + 14 + 1 + 4 = 50
Therefore, there are 50 individuals included in the summary.
Regarding the exact values of all the original service times, it is not possible to determine them precisely based on the given information. The table only provides ranges of service times and their corresponding frequencies. We can determine the range within which each individual's service time falls, but we cannot determine the exact value within that range.
What is the coefficient of x^2y^3 in the expression of (2x+y)^5
The coefficient of [tex]x^2y^3[/tex] in the expression [tex](2x+y)^5[/tex] is 10
To find the coefficient of the term containing [tex]x^2y^3\\[/tex] in the expansion of [tex](2x+y)^5[/tex], we can use the binomial theorem. The binomial theorem states that the expansion of [tex](a + b)^n[/tex] can be written as the sum of the binomial coefficients multiplied by the respective powers of a and b, where n is a positive integer.
In this case, we have [tex](2x + y)^5[/tex]. The term [tex]x^2y^3[/tex] can be obtained by selecting two x's from [tex](2x)^2[/tex] and three y's from [tex]y^3[/tex]. The coefficient of [tex]x^2y^3[/tex] will be the product of the corresponding binomial coefficients.
The binomial coefficients for this term can be calculated as follows:
Coefficient = C(5, 2) * C(3, 3)
C(n, k) represents the binomial coefficient, which is calculated as n! / (k! * (n - k)!), where "!" denotes the factorial operation.
Plugging in the values, we have:
Coefficient = C(5, 2) * C(3, 3)
[tex]= (5! / (2! * (5 - 2)!)) * (3! / (3! * (3 - 3)!))\\= (5! / (2! * 3!)) * (3! / (3! * 0!))\\= (5 * 4 * 3! / (2 * 1 * 3!)) * 1\\= (5 * 4) / (2 * 1)\\= 10.[/tex]
Therefore, the coefficient of [tex]x^2y^3[/tex] in the expression [tex](2x+y)^5[/tex] is 10.
To learn more about binomial theorem, refer:
brainly.com/question/222308
really need help with is problem if any math wizards are on
[tex]f(4)=4\\f(-5)=1\\x=-4,2[/tex]
7. At age 20, Heather began investing $3000 annually
into an account earning 7.5% interest compounded
annually. Lesley invested $6000 annually into a similar
account but began at age 40. They both stopped
contributing at age 65.
a) How much money did Heather and Lesley contribute
to their account?
b) What is the value of each of their investments when
they are 65 years old?
c) At age 65, when the investments mature, who has
more money and by how
much?
a) Heather contributed $135,000 and Lesley contributed $150,000 to their accounts.
b) Heather's investment is approximately $273,714.17, while Lesley's investment is approximately $191,048.18 when they are 65 years old.
c) Heather has more money by approximately $82,665.99 at age 65.
a) To find out how much money Heather and Lesley contributed to their accounts, we need to calculate the total contributions made by each of them.
Heather:
Heather started investing at age 20 and stopped at age 65, contributing $3000 annually. The number of years she contributed is (65 - 20) = 45 years.
Total contributions by Heather = $3000 × 45 = $135,000.
Lesley:
Lesley started investing at age 40 and stopped at age 65, contributing $6000 annually. The number of years she contributed is (65 - 40) = 25 years.
Total contributions by Lesley = $6000 × 25 = $150,000.
Therefore, Heather contributed $135,000 and Lesley contributed $150,000 to their respective accounts.
b) To calculate the value of their investments at age 65, we can use the formula for compound interest:
Future Value = Principal × (1 + interest rate)^number of years
Heather:
Principal (initial investment) = $3000
Interest rate = 7.5% = 0.075 (converted to decimal)
Number of years = 65 - 20 = 45
Future Value of Heather's investment = $3000 × (1 + 0.075)^45
Lesley:
Principal (initial investment) = $6000
Interest rate = 7.5% = 0.075 (converted to decimal)
Number of years = 65 - 40 = 25
Future Value of Lesley's investment = $6000 × (1 + 0.075)^25
Calculating these values:
Future Value of Heather's investment = $3000 × (1.075)^45 ≈ $273,714.17
Future Value of Lesley's investment = $6000 × (1.075)^25 ≈ $191,048.18
c) To determine who has more money at age 65 and by how much, we compare the future values of their investments.
Heather's investment value at age 65 = $273,714.17
Lesley's investment value at age 65 = $191,048.18
Therefore, Heather has more money at age 65, and the difference in their investments is approximately $273,714.17 - $191,048.18 = $82,665.99.
for such more question on Heather's investment
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