Larry could have about $139,827 in his IRA if he invests $250 at the beginning of each month and earns 3.5% interest compounded monthly, rounded to the nearest dollar
Assuming that Larry is starting his IRA at the beginning of his 32nd year, he could have 26 years until he retires at age 58.
Because he is investing $250 at the beginning of each month, that means he will be making an investment a complete of $3,000 consistent with year.
We are able to use the formula for compound interest to calculate the future value of his IRA:
[tex]FV = P * ((1 + r/n)^{(n*t)} - 1) / (r/n)[/tex]
Where FV is the future value, P is the primary (the quantity he invests every month), r is the interest charge (3.5%), n is the wide variety of times the interest is compounded consistent with year (12 for monthly), and t is the quantity of years.
Plugging within the numbers, we get:
[tex]FV = 250 * ((1 + 0.0.5/12)^{(12*26)} - 1) / (0.0.5/12) \approx $139,827[/tex]
Therefore, Larry could have about $139,827 in his IRA.
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if r=11 units and x = 15 units, then what is the volume of the cylinder shown above?
The volume of the cylinder V = πr²h. Therefore, we need to have more information about the cylinder's height in order to solve this problem.
To find the volume of the cylinder, we first need to know the height of the cylinder. However, the height is not given in the question. Therefore, we cannot determine the volume of the cylinder with the given information.
We can use the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height.
Since r = 11 units and x = 15 units, we can find the diameter of the base of the cylinder by multiplying r by 2, which gives us 22 units. However, we still do not know the height of the cylinder.
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13) a 95 percent confidence interval estimate will have a margin of error that is approximately + or - 47.5 percent of the size of the population mean. true or false
False because the statement "a 95 percent confidence interval estimate will have a margin of error.
How to Calculate 95% confidence interval with margin?A 95% confidence interval (CI) estimate is a range of values that is likely to contain the true population mean with 95% confidence. The margin of error for a confidence interval depends on the sample size, the variability of the data, and the desired level of confidence.
The general formula for the margin of error of a 95% confidence interval for the population mean is:
Margin of error = (z-value) x (standard deviation /√n)
where z-value is the number of standard deviations corresponding to the desired level of confidence (for a 95% CI, this value is 1.96), standard deviation is the standard deviation of the sample data, and n is the sample size.
The margin of error is usually expressed as a percentage of the sample mean, not the population mean. Moreover, the percentage of the margin of error is not fixed, but it varies depending on the data and the sample size.
Therefore, the statement "a 95 percent confidence interval estimate will have a margin of error that is approximately + or - 47.5 percent of the size of the population mean" is not correct.
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Based on the box-and-whisker plot shown below, match each term with the correct value. PLEASE ANSWER QUICKLY!!!
The value of the median is 18. The range of this plot is 6. The 25th percentile is 17 and the 75th percentile is 20. The interquartile range is 3.
We are given a box-and-whisker plot and we have to find the correct value of the median, range, 25th percentile, 75th percentile, and inter-quartile range with the help of this box-and-whisker plot.
We find the median with the help of the box. The line which splits the box into two halves is the median for the given data. Therefore, the median will be 18. To find the range, we subtract the minimum value from the maximum value. The minimum value is 15 and the maximum value is 21. Therefore, the range will be (21 - 15) = 6.
From the plot, we can see that the 25th percentile is 17, Q1, and the 75th percentile is 20, Q3. Now, we have to find the interquartile range. To find the interquartile range, we subtract Q1 from Q3. Therefore, our interquartile range will be (20 -17) = 3.
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Ver en español
Of the last 20 contestants on a game show, 8 won a prize. What is the experimental probability that the next contestant will win a prize?
The probability that the next contestant will win a prize is 2/5.
What is probability?
Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.
Experimental probability is based on the result of an experiment that has been carried out multiples times.
probability that the next contestant will win a prize = number of contestants that won in the last games / total number of contestants in the last games
=> 8/20
To transform to the simplest form. divide both the numerator and the denominator by 4
=> 2/5
Hence the probability that the next contestant will win a prize is 2/5.
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Geometry!! will mark brainliest if correct!!!
Sierra is constructing an inscribed square. Keaton is constructing an inscribed regular hexagon. In your own words, describe one difference between Sierra's construction steps and Keaton's construction steps
The main difference is that Sierra needs to create two equal arcs, while Keaton needs to create six equal arcs to form the vertices of their respective shapes.
For Sierra's inscribed square:
1. Draw a circle with a compass.
2. Mark a point on the circle as one vertex of the square.
3. Draw a diameter passing through the marked point.
4. Use the compass to create two equal arcs, one on each end of the diameter, intersecting the circle.
5. Connect the intersection points to create the square.
For Keaton's inscribed regular hexagon:
1. Draw a circle with a compass.
2. Mark a point on the circle as one vertex of the hexagon.
3. Use the compass to create six equal arcs around the circle, each arc intersecting the end of the previous arc.
4. Connect the intersection points to create the hexagon.
The main difference is that Sierra needs to create two equal arcs, while Keaton needs to create six equal arcs to form the vertices of their respective shapes.
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Consider this equation
(4x)^1/3 - x =0
The first step in solving this equation is to ____
The second step is to____
Solving this equation for x initially yields____
Checking the solutions shows that____
The first step in solving the equation is to isolate the radical term, and the second step is to eliminate the radical by raising both sides to the power of 3. Solving this equation for x initially yields x = 0, x = 2, and x = -2. Checking the solutions shows that it is not a real solution.
The first step in solving the equation (4x)[tex]^{1/3}[/tex] - x = 0 is to isolate the radical term by adding x to both sides of the equation. This gives us
(4x)[tex]^{1/3}[/tex]= x.
The second step is to raise both sides of the equation to the power of 3, which eliminates the radical. This results in 4x = x³.
Solving this equation for x initially yields x = 0, x = 2, and x = -2.
Checking the solutions shows that only x = 2 is a valid solution, as plugging it back into the original equation yields (4*2)[tex]^{1/3}[/tex] - 2 = 0. However, plugging in x = 0 results in a division by zero, and plugging in x = -2 yields a negative number under the radical, which is not a real solution.
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If x-2 and x+2 are the factors of the polynomial p(x) = x³− 4mx²− 2nx + 1 = 0, then find the values of m and n.
If x-2 and x+2 are the factors of the polynomial p(x) = x³− 4mx²− 2nx + 1 = 0, then the values of m and n are 5/4 and 1/2, respectively.
Given that the factors of the polynomial p(x) = x³ - 4mx² - 2nx + 1 are x - 2 and x + 2, we can write:
p(x) = (x-2)(x+2)(x-a)
where a is the remaining root of p(x).
Expanding this equation, we get:
p(x) = (x²-4)(x-a) = x³ - (4+a)x² + 4ax - 4a
Comparing the coefficients of this expression with the coefficients of the original polynomial, we get the following system of equations:
4+a = 4m
4a = -2n
-4a = 1
Solving these equations, we get:
a = -1/4, m = 5/4, n = -2a = 1/2
Therefore, the values of m and n are 5/4 and 1/2, respectively.
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How much would it cost to buy a cover for the pool that cost $0.30 per square foot
It would cost $735 to buy a cover for the pool at $0.30 per square foot
How much would it cost to buy a cover for the poolFrom the complete question (see attachment), we have the following parameters that can be used in our computation:
Unit rate = $0.30 per square foot
Dimensions = 10 inches by 20 inches
Scale = 2 inches : 7 feet
Using the above as a guide, we have the following:
Total cost = Unit rate * Area of pool
Where
Area of the pool = 10 inches * 20 inches
Using the scale, we have
Area of the pool = (10 * 7/2)* (20 * 7/2) square feet
Area of the pool = 2450 square feet
Substitute the known values in the above equation, so, we have the following representation
Total cost = $0.30 per square feet * 2450 square feet
This gives
Total cost = $735
Hence, it would cost $735 to buy a cover for the pool
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Complete question
The blueprint of a pool has a scale of 2 inches equals 7 feet. The scale drawing is shown below (see attachment)
How much would it cost to buy a cover for the pool that cost $0.30 per square foot
Jack bought 540 shares of Sound Foundations stock years ago for $44.50 per share. He sold them yesterday for $49.54 per share. What was the percent capital gain for the 540 shares, rounded to the nearest percent?
Answer:
11.325 %
Step-by-step explanation:
44.50 . . ... .. 100%
0.445. . . . . . . . .1 %
49.54 . . . . . . . .?%
49.54 : 0.445=111.325 %
111.325-100 = 11.325%
Answer:
Step-by-step explanation:
EXAMPLE 1 A spring with a mass of 6 kg has a natural length of 0.3 m. A force of 38.4 N is required to maintain it stretched to a length of 0.7 m. If the spring is stretched to a length of 0.7 m and then released with initial velocity 0, find the position of the mass at time t. SOLUTION From Hooke's Law, the force required to stretch the spring is k(0.4) = 38.4 so k = 38.4/0.4 = 96. Using this value of the spring constant k, together with m = 6, we have d²x 6 = 0. + dt2 As in the earlier general discussion, the solution of this equation is X(t) = ( cos(4t) + C2 sin(4t). We are given the initial condition that x(0) = 0.4. But, from the previous equation, x(0) = cz. Therefore cn = . Differentiating, we get x'(t) = -4c sin(4t) + 4c2 cos(4t). Since the initial velocity is given as x'(O) = 0, we have cz = 0 and so the solution is = x(t) =
The equation given in the solution is X(t) = (cos(4t) + C2sin(4t)). This equation represents the position of the mass at time t after the spring has been released with an initial velocity of 0. The terms "spring" and "stretch" indicate that Hooke's Law is being used to determine the spring constant k.
The term "velocity" is used to describe the initial velocity of the mass, which is given as 0. The position of the mass at time t is determined by the value of X(t), which is a function of time. Therefore, the position of the mass at any given time can be found by plugging in the value of t into the equation X(t) = (cos(4t) + C2sin(4t)).
Hi! Based on the information provided, you have a spring with a mass of 6 kg and a natural length of 0.3 m. A force of 38.4 N is required to stretch it to 0.7 m. The spring constant, k, is determined to be 96. The spring is then stretched to 0.7 m and released with an initial velocity of 0. To find the position of the mass at time t, you can use the equation:
x(t) = C1 * cos(4t) + C2 * sin(4t)
Given the initial condition x(0) = 0.4, we find that C1 = 0.4. The initial velocity x'(0) is 0, leading to the conclusion that C2 = 0. Therefore, the equation for the position of the mass at time t is:
x(t) = 0.4 * cos(4t)
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In 2016 there were approximately 7,040 college and university libraries in the United States. A survey found that 65% of those libraries participated in an electronic "book-sharing" program. Based on this information, how many college and university libraries participated in the electronic "book-sharing" program in 2016?
To calculate the approximate number of libraries that participated in the book-sharing program in 2016, we multiply the total number of college and university libraries (7,040) by the percentage of libraries participating (65%).
By multiplying 7,040 by 0.65, we find that approximately 4,576 libraries participated in the book-sharing program in 2016.
This calculation assumes that the percentage given accurately represents the proportion of libraries participating in the program. However, it's important to note that this is an approximation based on the given information. The actual number of participating libraries may vary slightly due to factors such as reporting discrepancies or changes in participation rates over time.
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The point guard of a basketball team has to make a decision about whether or not to shoot a three-point attempt or pass the ball to another player who will shoot a two-point shot. The point guard makes three-point shots 30 percent of the time, while his teammate makes the two-point shot 48 percent of the time.
The point guard has to decide whether to shoot a three-point attempt or pass the ball to another player for a two-point shot. The point guard has a 30% success rate for three-point shots, while the teammate has a 48% success rate for two-point shots.
To determine the best option, we can compare the expected values for each decision. Here's a step-by-step explanation:
1. Calculate the expected value of the point guard's three-point attempt:
- Success rate: 30% (0.3)
- Point value: 3
- Expected value: 0.3 (3 )= 0.9
2. Calculate the expected value of the teammate's two-point shot:
- Success rate: 48% (0.48)
- Point value: 2
- Expected value: 0.48 (2) = 0.96
3. Compare the expected values:
- Three-point attempt: 0.9
- Two-point shot: 0.96
Since the expected value of the teammate's two-point shot (0.96) is higher than the point guard's three-point attempt (0.9), it would be a better decision for the point guard to pass the ball to the teammate for a two-point shot.
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4. Use the data below for the calculations.
Average hours sleeping per weeknight: 4, 5, 8, 12, 10, 6, 7, 9, 8, 8, 6, 6, 4, 3, 9
Mean:
Median:
Mean Absolute Deviation:
Absolute Deviation from Median:
The mean is 7
The median is the middle value, which is 7.
Mean Absolute Deviation: 2
How to solve for the mean absolute deviationStep 3: Find the absolute deviation of each value from the mean:
|4-7.067|, |5-7.067|, |8-7.067|, |12-7.067|, |10-7.067|, |6-7.067|, |7-7.067|, |9-7.067|, |8-7.067|, |8-7.067|, |6-7.067|, |6-7.067|, |4-7.067|, |3-7.067|, |9-7.067|
These absolute deviations are: 3.067, 2.067, 0.933, 4.933, 2.933, 1.067, 0.067, 1.933, 0.933, 0.933, 1.067, 1.067, 3.067, 4.067, 1.933.
Step 4: Find the mean of these absolute deviations to find the mean absolute deviation:
Mean Absolute Deviation = (3.067+2.067+0.933+4.933+2.933+1.067+0.067+1.933+0.933+0.933+1.067+1.067+3.067+4.067+1.933) / 15 = 2
Step 5: Find the absolute deviation of each value from the median:
|4-8|, |5-8|, |6-8|, |6-8|, |6-8|, |7-8|, |8-8|, |8-8|, |8-8|, |9-8|, |9-8|, |10-8|, |12-8|, |8-8|, |3-8|
These absolute deviations are: 4, 3, 2, 2, 2, 1, 0, 0, 0, 1, 1, 2, 4, 0, 5.
Therefore, the absolute deviation from the median is 5.
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A $750 gift was shared equally by 5 people. After spending $90 of her share, Clarissa divided the amount remaining into 2 equal parts. What amount of money is now in each part of Clarissa's money?
Answer:
$30 for each part
Step-by-step explanation:
$750 ÷ 5 = $150 each people
Clarissa's money is $150
$150 - $90 = $60
Clarissa's money after she spent is $60
$60 ÷ 2 = $30
Clarissa's money for each part out of 2 parts is $30
Chad buys pineapples, watermelons, and a bag of grapes for a fruit salad. He spends a total of $29.68 on the fruit salad. Pineapples
cost $2.15 each, and watermelons cost $3.75 each. The bag of grapes costs $4.48.
Create an equation to model this situation, where p represents the number of pineapples Chad can purchase and w represents the
number of watermelons he can purchase.
An equation that models the situation, where p represents the number of pineapples Chad can purchase and w represents the number of watermelons he can purchase will be; 2.15p + 3.75w = 25.20.
Let's use the given information to create an equation to model this situation. We know that Chad spends a total of $29.68 on the fruit salad, so we can start with;
2.15p + 3.75w + 4.48 = 29.68
This equation represents the total cost of the fruit salad, which includes the cost of the pineapples (2.15p), the cost of the watermelons (3.75w), and the cost of the bag of grapes (4.48).
To make this equation more specific to the problem of finding the number of pineapples and watermelons Chad can purchase, we need to use the variables p and w to represent those quantities. We can set up a second equation based on the information given about the total number of fruits;
p + w + 1 = T
Here, T represents the total number of fruits in the salad, and we add 1 to account for the bag of grapes.
Now we can use substitution to eliminate the variable T. Solving for T in terms of p and w;
T = p + w + 1
Substitute this expression for T into first equation;
2.15p + 3.75w + 4.48 = 29.68
Simplify;
2.15p + 3.75w = 25.20
Therefore, the model of this situation is; 2.15p + 3.75w = 25.20
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If i walked 14 out of the 20 days in February, which value is equivalent to the fraction of the school days in February that i walked to school?
The fraction of the school days in February that you walked to school is 7/10 or 0.7 when expressed as a decimal.
What is the fraction of school days in February that you walked to school if you walked 14 out of 20 days?
The fraction of the school days in February that you walked to school can be represented as:
(number of days you walked) / (total number of school days in February)
Since you walked 14 out of 20 days in February, we can substitute these values into the formula:
(number of days you walked) / (total number of school days in February) = 14 / 20
Simplifying the fraction by dividing both the numerator and denominator by their greatest common factor (2), we get:
(number of days you walked) / (total number of school days in February) = 7 / 10
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Which statement is true about all perfect cubes?
A
A perfect cube represents 3 times the area of a face of the cube.
B
A perfect cube represents the sum of 9 edge lengths of the cube.
A perfect cube represents the volume of a cube with equal integer side lengths.
D
A perfect cube represents the surface area of a cube with equal integer side lengths.
C
A cylindrical jar of peanut butter has a height of 4 inches and a diameter of 3 inches. How many cubic inches of peanut butter can the jar hold? Use π = 3.14.
28.26 in3
37.68 in3
113.04 in3
150.72 in3
The jar can hold 28.26 cubic inches of peanut butter
How to calculate the amount of cubic inches of peanut butter?The first step is to write out the parameters
A cylindrical jar of peanut has a height of 4 inches
The diameter is 3 inches
The next step is to calculate the radius, this is done by dividing the diameter by 2
radius= 3/2
= 1.5
The formula used to calculate the cubic inches of peanut butter is
V= πr²h
= 3.14 × 1.5² × 4
= 3.14 × 2.25 × 4
= 28.26
Hence the jar can hold 28.26 cubic inches of peanut butter
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The notation (x,y)→(−x,y) means a reflection across the y axis.
Answer:
This is true.
Step-by-step explanation:
To prove this as true what we can do is draw a graph. On one of the graphs, we will have a point at (-7,1). If we were going to reflect it over the y-axis by counting the distance it is from the y-axis and counting it in the other direction. When we do this we get a point of (7,1). We can infer that because it was flipped in the y-axis the y value stayed the same while the x-axis changed.
This is how we can prove this to be true.
QR has endpoints at Q(5, –6) and R(6, 3). Find the midpoint M of QR.
Answer:
(5.5, -1.5)
Step-by-step explanation:
(x, y)midpoint = (x1 + x2)/2 , (y1 + y2)/2
= (6 + 5)/2, (3 - 6)/2
= (11/2, -3/2)
= (5.5, -1.5)
Which is the better deal: an account that pays 4% interest compounded daily or one that pays 3.95% compounded continuously?
Answer:
compounded continuously
Step-by-step explanation:
compounded continuously occurs more frequently than daily
A survey of North middle school staff included staff members ages the ages were complied and displayed in a histogram which of the following statements best describes the data
The number of staff members under the age of 40 are 28 and the number of staff members 40 and older are 22.
From the given histogram,
A. Between the age 20-29 there are 10 members.
B. Under the age of 40 = 10+18
= 28
40 and older = 12+7+2+1
= 22
C) Total staff members = 28+22=50
D) Number of staff members are 50 years or older
= 7+2+1
= 10
Therefore, the number of staff members under the age of 40 are 28 and the number of staff members 40 and older are 22.
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D. Larry has a new plan. Whenever his need for the car exceeds the number of slots he has rented the car for, he returns the car on time to avoid the fine, and uses his bicycle for the remaining deliveries. Unfortunately, bike deliveries take 3 times longer than car deliveries. Suppose he rents the car for 5 slots (75 minutes). If he needs 7 slots, then he uses the car for 5 slots, and the remaining 2 slots are done by bicycle, which take 6 slots (1. 5 hours). How much time does he expect to bicycle on average (in terms of slots)
Larry uses the car for the first 5 slots (75 minutes) and returns it on time to avoid any fine. He then uses his bike for the remaining 2 slots, which takes 6 slots (3 times longer than using the car).
Therefore, in total, Larry uses the car for 5 slots and the bike for 6 slots, for a total of 11 slots.
On average, Larry expects to use the bike for (6/11) of his total slots. Since each bike delivery takes 3 times longer than a car delivery, we can say that Larry expects to spend 3 times as much time on the bike as he would in the car. Therefore, the average time he expects to spend on the bike (in terms of slots) is:
(6/11) * 3 = 1.636 slots
So, Larry expects to spend an average of 1.636 slots (or about 24.5 minutes) on the bike for each delivery.
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Please upload a picture of a piece of paper with the problem worked out, and draw the graph for extra points, there will be 6 of these, so go to my profile and find the rest, and do the same, for extra points.
for questions 3 and 4, solve the system using the substitution method.
The value of X and y using substitution method for the quadratic equation given above would be = -3.6 and - 2.8 respectively.
How to calculate the unknown values using substitution method?The equations given are;
2x - 7y = 13. ----> equation 1
3x + y = 8 --------> equation 2
From equation 2 make y that subject of formula;
y = 8 - 3x
Substitute y = 8 - 3x into equation 1
2x - 7(8 - 3x) = 13
2x - 56 - 21x = 13
-19x = 13+56
-19x = 69
X = -69/19
X = - 3.6
Substitute X = -3.6 into equation 2
3(-3.6) + y = 8
y= 8 - 10.8
= - 2.8
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1. Direct or indirect characterization? "Nina was so annoyed at her little brother for bothering her. " Direct Indirect 2. Direct or indirect characterization? "Tim's room was a mountain of dirty clothes and used dishes that had been piled up for weeks. " Direct Indirect 3. An author can show indirect characterization through a character's thoughts, feelings, actions, and the setting of the story. Their effect on others. The rising action. Do all 3
An author can show indirect characterization through a character's thoughts, feelings, actions, and the setting of the story, as well as through their effect on others and their role in the rising action of the plot.
All of these elements can provide insights into a character's personality, motivations, and values, without the author explicitly stating them.
By carefully observing the character's interactions with others, their reactions to events, and the situations in which they find themselves, readers can draw conclusions about who the character is and what drives them.
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Color the stars so it would be likely but not certain you would choose a yellow one.
what's the solution?
Answer:
(1, 1.5)
Step-by-step explanation:
If x = 1, plug it into the other equation, y = 1/2x + 1, and y = 1.5.
Randy divides (2x4 – 3x3 – 3x2 7x – 3) by (x2 – 2x 1) as shown below. what error does randy make? x squared minus 2 x 1 startlongdivisionsymbol 2 x superscript 4 baseline minus 3 x cubed minus 3 x squared 7 x minus 3 endlongdivisionsymbol. minus 2 x superscript 4 baseline minus 4 x cubed 2 x squared to get a remainder of x cubed minus 5 x squared 7 x. minus x cubed minus 2 x squared x to get a remainder of negative 3 x squared 6 x minus 3. minus negative 3 x squared 6 x minus 3 to get a remainder of 0 and a quotient of 2 x squared x 3. he makes a subtraction error. he makes an error writing the constant term in the quotient. he makes an error choosing the x-term in the quotient. he makes an error rewriting the problem in long division.
By subtracting this from the dividend, the next step would be:
[tex](2x^4 - 3x^3 - 3x^2 + 7x - 3) - (-5x^3 + 10x^2 - 5x) = 2x^4 + 2x^3 - 13x^2 + 12x - 3[/tex]
This error occurs because he forgets to distribute the -2 in [tex]-2(x^2 - 2x + 1)[/tex]when subtracting from [tex]2x^4[/tex]. This leads to a mistake in the next step when he subtracts [tex]x^3 - 2x^2[/tex] from [tex]x^3 - 5x^2[/tex] to get [tex]-3x^2[/tex]instead of [tex]-3x^2 + 6x[/tex]. This error then leads to the incorrect constant term in the quotient.
Therefore, the error Randy makes is a subtraction error in the first step of the long division. It is important to pay attention to signs and distribute coefficients correctly when performing long division with polynomials.
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Answer: A. x + 2
Step-by-step explanation:
Edge 2023
Which are equal to the following? Check all that
apply.
Rewrite the following with lower index 0
To rewrite a given expression with lower index 0, which involves changing the subscript of any variable or quantity to 0.
How to rewrite with lower index 0?To rewrite a given expression with lower index 0. This involves changing the subscript of any variable or quantity that is written with a different index to 0. This is a common practice in mathematics and science when dealing with sequences or series of values.
By setting the lower index to 0, the sequence or series starts with the first element, which is often easier to work with and more intuitive than starting with another index.
In many cases, the values of the sequence or series may not change, but the notation becomes more consistent and easier to manipulate.
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Answer:
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Step-by-step explanation:
Compute the number of 12 letter combination of the 26 letters in alphabet.
key answer:
9,675,700
To compute the number of 12 letter combinations of the 26 letters in the alphabet, we can use the formula for combinations, which is:
nCr = n! / r!(n-r)!
where n is the total number of items (26 letters in this case), r is the number of items to choose (12 letters in this case), and ! means factorial (the product of all positive integers up to that number).
Using this formula, we can plug in the numbers:
26C12 = 26! / 12!(26-12)!
= (26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15) / (12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
= 9,675,700
Therefore, there are 9,675,700 possible 12 letter combinations of the 26 letters in the alphabet.
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