PLEASE ANSWER THEN I'LL MARK U BRAINLY
1. When measuring an angle on a protractor, where must the vertex be placed?
2. What is a statement that is accepted to be true without having to formally prove it?
3. What is the measurement of a straight angle?
Answers
A2. An axiom or postulate is a statement that is accepted without proof.
A3. A straight angle is an angle with measure 180 degrees. It is called a straight angle because if there were an angle that had measure 180 degrees, the three points that form the angle would be in a straight line.
Related Questions
match the turms with the values using this set of data 46, 72, 15, 72, 19, 10 what are the mean medien and range
Answers
Answer:
See below ~
Step-by-step explanation:
Arranging the data in increasing order
10, 15, 19, 46, 72, 72Mean
10 + 15 + 19 + 46 + 72 + 72 / 625 + 65 + 144 / 6234/639Median
In a set with even number of data points, the median is the mean of the middle 2 terms19 + 46 / 265/232.5Range
Difference between highest data point and lowest data point72 - 1062Answer:
Mean: 39
Median: 32.5
Range: 62
George records the number of questions he has answered on DFM per day over 14 days, and puts the data in the bar chart below.
Find the total number of questions.
Answers
Answer:
18 is the total number of questions George answered in 14 days.
Step-by-step explanation:
The given chart:
The x-axis is showing the total number of questions George answered The y-axis is showing the frequency of days on which George answered the questions.The given chart is showing that:
George answered the 5 questions on the first 4 days;George answered the next 6 questions on the next 5 days;George answered the next 7 questions on the last 5 days';Hence, the total questions he answered will be:
5 + 6 + 7 = 18
Therefore, 18 is the total number of questions George answered in 14 days.
Find the measure of KM¯¯¯¯¯¯¯¯¯¯.
Answers
Answer:
12
Step-by-step explanation:
(whole secant) x (external part) = (whole secant) x (external part)
( 7+x+2) * 7 = ( 6+8) * 6
Combine like terms
(9+x) *7 = 14*6
Distribute
63 +7x = 84
Subtract 63
63 +7x -63 = 84-63
7x =21
Divide by 7
7x/7 = 21/7
x = 3
KM = x+2+7
= 3+2+7
=12
Answer:
\(\huge\boxed{KM = 11}\)
Step-by-step explanation:
According to secant - secant theorem:
(MK)(ML) = (MR)(MN)
Where
MK = 7 + x+ 2 = x + 9
ML = 7
MR = 8 + 6 = 14
MN = 6
=> (x+9)(7)= (14)(6)
=> 7x + 63 = 84
Subtracting both sides by 63
=> 7x = 84 - 63
=> 7x = 21
Dividing both sides by 7
=> x = 3
Now,
KM = x + 9
KM = 3 + 9
KM = 11
a dataset on 91 roller coasters lists the duration of the ride in seconds in addition to the drop height in feet for some of the coasters. one coaster, the tower of terror, is unusual for having a large drop but a short ride. after setting it aside, a regression to predict duration from drop for the remaining 90 coasters has r29.4%. complete parts a through c.a) What are the variable and units in this regression? The predictor variable is ___ in units of ___ and the response variable is ___ in units of ___ b) What units does the slope have? Feet, Seconds per foot, Seconds, Feet per second. c) Is the slope probably positive or probably negative? Explain. The slope is probably ____ because ___
Answers
(a) The predictor variable is Fall in feet and the response variable is Duration in seconds.
(b) The slope is in seconds per foot.
(c) The slope may be negative, as greater drop heights generally result in longer travel times.
(a) The predictor variable in this regression is Drop, which represents the drop height of the roller coaster, in feet, in feet. The response variable is Duration, which represents the duration of the trip, in seconds, in seconds.
(b) The units of slope in this regression are seconds per foot. This means that for each unit of increase in descent height in feet, the travel time will increase or decrease the value of the slope, measured in seconds per foot.
(c) The slope can be negative, as greater drop heights generally result in longer ride times, and the Tower of Terror roller coaster, which was exceptionally short despite its large drop height, has were removed from the analysis.
Therefore, the remaining 90 roller coasters in the dataset likely exhibit a negative relationship between drop height and time, meaning that as drop height increases, ride time decreases .
The Low R-value squared 29.4% means that the relationship between roller coaster drop and ride time in the data set is highly variable, but the negative slope indicates a general downward trend.
Learn more about Slope:
https://brainly.com/question/3605446
#SPJ4
If cosA = 24/25 tanB = 4/3 and angles A and B are in Quadrant I, find the value of tan(A−B).
Answers
If cosA = 24/25 tanB = 4/3 and angles A and B are in Quadrant I. The value of tan(A-B) is -23/33.
What is the value of tan(A-B)?We can start by using the identity: tan(A - B) = (tan A - tan B)/(1 + tan A tan B)
From the given information, we have:
cos A = 24/25, which means sin A = sqrt(1 - cos^2 A) = 7/25 (since A is in Quadrant I)
tan B = 4/3, which means sin B = 4/sqrt(4^2 + 3^2) = 4/5 and cos B = 3/sqrt(4^2 + 3^2) = 3/5
Now, we can use the definitions of sine and cosine to find tan A:
tan A = sin A / cos A = (7/25)/(24/25) = 7/24
Substituting the values we have found into the formula for tan(A - B), we get:
tan(A - B) = (tan A - tan B)/(1 + tan A tan B)
= [(7/24) - (4/3)]/[1 + (7/24)(4/3)]
= (-13/72)/(25/72)
= -13/25
Therefore, tan(A - B) = -13/25.
Learn more about tan(A - B) here:https://brainly.com/question/24305408
#SPJ1
Your friend how you a coin collection. In it, 44/50
of the coin are quarter. What percent of the coin are quarter?
Answers
The percentage of the coin are quarter would be 88%.
What is meant by percentage?Since the denominator of percentages is 100, they are effectively fractions. percentage is a relative value that denotes hundredths of any amount. One percent, denoted by the symbol 1%, is equal to one hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified.
In addition to being stated as a decimal or a fraction, a percentage is a number that indicates how many out of 100 it is. Three for the price of one! Simply enter the % as the numerator and 100 as the denominator to convert the percentage to a fraction.
"Out of 100" is what "percentage" means. When describing parts of a whole in mathematics, percentages are employed along with fractions and decimals. The full is divided into one hundred equal portions for the purpose of computing percentages.
To determine, multiply the fraction 44/50 by 100 to convert it to a percentage.
(44/50) × 100 = 88%.
Therefore, the percentage of the coin are quarter would be 88%.
To learn more about percentage refer to:
https://brainly.com/question/24877689
#SPJ4
a box contain 5 white,2 red, 3 blue and 5 yellow marbles. what is the probality of getting: (i) a red marbles (ii) a yellow marbles
Answers
total number of marbles= 5+2+3+5 = 15 marbles
probability of a red marble - 2/15
probability of yellow marble - 5/15 = 1/3
Answer:
i) 2/15 ii) 1/3
Step-by-step explanation:
the number of marbles all together is 15
2 out of the 15 are red, so 2/15
5 out of 15 are yellow,so 5/15, simplified to 1/3
What is the vertex of f(x)=-3(x+1)^2-4
Answers
Answer:
vertex = (- 1, - 4 )
Step-by-step explanation:
the equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
f(x) = 3(x + 1)² - 4 ← is in vertex form
with vertex = (- 1, - 4 )
Answer:
(−1,−4)
Step-by-step explanation:
f(x)=3(x+1)2−4
Can someone PLEASE HELP
Answers
The first box is the the first quartile while the second box is the second quartile and well A and E aren’t in the boxes and A is the first for meaning that’s the minimum and E is the last dot meaning it the maximum
Hope this helps!
A dress pattern calls for 1 1/8 yards of fabric for the top and 2 5/8 yards for the skirt. Mia has 3 1/2 yards of fabric. Does she have enough fabric to make the dress? Explain
Answers
To find out whether Mia has enough fabric to make the dress, you need to add the amount of fabric required for the top and skirt. Then compare it with the amount of fabric she has.
So, let's do that.To make the dress, we need 11/8 yards of fabric for the top2 5/8 yards of fabric for the skirt Total fabric required
= 1 1/8 + 2 5/8
= 3 3/4 yards
Mia has 3 1/2 yards of fabric
So, Mia does not have enough fabric to make the dress because she needs 3 3/4 yards of fabric to make it.
To know more about yards visit :-
https://brainly.com/question/24487155
#SPJ11
If A = (3.1∠63.2°) and B = (6.6∠26.2°) then solve for the sum (A + B) and the difference (A − B).
Part A
Enter the real part of (A + B)
Part B
Enter the imaginary part of (A + B)
Part C
Enter the real part of (A − B)
Part D
Enter the imaginary part of (A − B)
Answers
Part A: The real part of (A + B) is 9.7
Part B: The imaginary part of (A + B) is approximately 5.68
Part C: The real part of (A - B) is -3.5
Part D: The imaginary part of (A - B) is approximately -0.14.
Given that,
A = 3.1∠63.2°
B = 6.6∠26.2°
Part A: To find the real part of (A + B), we add the real parts of A and B.
In this case,
The real part of A is 3.1 and the real part of B is 6.6.
Adding them together, we get:
Real part of (A + B) = 3.1 + 6.6 = 9.7
So, the real part of (A + B) is 9.7.
Part B: To find the imaginary part of (A + B),
Add the imaginary parts of A and B.
In this case,
The imaginary part of A can be calculated using the formula
A x sin(angle),
Which gives us:
Imaginary part of A = 3.1 x sin(63.2°)
≈ 2.77
Similarly, for B:
Imaginary part of B = 6.6 x sin(26.2°) ≈ 2.91
Adding these together, we get:
Imaginary part of (A + B) ≈ 2.77 + 2.91
≈ 5.68
So, the imaginary part of (A + B) is approximately 5.68.
Part C: To find the real part of (A - B),
Subtract the real part of B from the real part of A.
In this case,
The real part of A is 3.1 and the real part of B is 6.6.
Subtracting them, we get:
Real part of (A - B) = 3.1 - 6.6
= -3.5
So, the real part of (A - B) is -3.5.
Part D: To find the imaginary part of (A - B),
Subtract the imaginary part of B from the imaginary part of A.
Using the previously calculated values, we have:
Imaginary part of (A - B) ≈ 2.77 - 2.91
≈ -0.14
So, the imaginary part of (A - B) is approximately -0.14.
To learn more about complex numbers visit:
https://brainly.com/question/27940074
#SPJ4
You used a student deck of 52 cards and selected a card at random find (c) 2 of heart
Answers
Definition
Theoretical Probability is the ratio of the number of favorable outcomes to the total possible outcomes of an event.
Expressing probability as a formula:
\(\text{probability = }\frac{Number\text{ of favorable outcomes}}{Total\text{ possible outcomes of an event}}\)Information about a standard deck of cards:
A standard deck of cards has four suits: hearts, clubs, spades, diamonds. Each suit has thirteen cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. Thus the entire deck has 52 cards total.
(a) Picture card (J, Q, and K)
In a standard deck, there are 4 Jacks, Queens, and Kings. Hence, the probability of J, Q, and K are:
\(\begin{gathered} \text{Number of picture cards = 4 }\times\text{ 3} \\ =\text{ 12} \end{gathered}\)Probability as a fraction:
\(=\text{ }\frac{12}{52}\)In decimal:
\(=\text{ }0.23\)Percent:
\(\begin{gathered} =\text{ 0.23 }\times\text{ 100} \\ =\text{ 23\%} \end{gathered}\)(b) 9 or 10
There are 4 cards labeled 9 and 10 each.
Probability as a fraction:
\(\begin{gathered} P(9or10)=\text{ P(9) + P(10)} \\ =\text{ }\frac{4}{52}\text{ + }\frac{4}{52} \\ =\text{ }\frac{8}{52} \end{gathered}\)In decimal:
\(=\text{ 0.15}\)In percent:
\(\begin{gathered} =\text{ 0.15 }\times\text{ 100} \\ =\text{ 15\%} \end{gathered}\)(c) 2 of heart
In a standard deck of cards, there are only one 2 of hearts.
Probability as a fraction:
\(=\text{ }\frac{1}{52}\)In decimal:
\(=\text{ 0.02}\)In percent:
\(\begin{gathered} =\text{ 0.02 }\times\text{ 100} \\ =\text{ 2\%} \end{gathered}\)If 2(x+y)^2=116, and xy= 24, find the value of x^2+y^2.
Answers
Answer:
10
Step-by-step explanation:
\(2(x + y)^{2} = 116 \\ {(x + y)}^{2} = \frac{116}{2} \\ {(x + y)}^{2} = 58....(1) \\ xy = 24.....(2) \\ \because \: {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ \therefore \: 58 = {x}^{2} + {y}^{2} + 2 \times 24 \\ \therefore \: 58 = {x}^{2} + {y}^{2} + 48 \\ \therefore \: {x}^{2} + {y}^{2} = 58 - 48 \\ \huge \purple{ \boxed{\therefore \: {x}^{2} + {y}^{2} = 10}}\)
Answer:
10
Step-by-step explanation:
2(x+y)^2=116
xy= 24
x^2+y^2 =?
---------------
x^2+y^2= (x+y)^2- 2xy
(x+y)^2 = 116/2 = 58x^2+y^2 = 58- 2*24 = 58 - 40= 10Nick's mark on a test was 39.
This mark was 60%.
What was the total possible mark?
Answers
Answer:
65
Step-by-step explanation:
Since 39 is 60%, 100/60= 1 2/3
39*1 2/3 is 65
Find the measure of the exterior angle.
Answers
By exterior angle property
\(j = 90 + 40\)
\(j = 130\)
Help please urgent i will give 10 pint
Answers
Answer:
Median=Middle Number
Range=Difference of Min and Max number
Step-by-step explanation:
Dalmation
124,126,134,136,138,140,140,141,142
Median=138
Range=18
Golden Retriever
124,132,134,136,138,140,140,145,145,145,146,147,150
Median=140
Range=26
Sry if this was a little late
Find the x-intercept(s) of the following equation.
Answers
Answer:
The first answer
Step-by-step explanation:
Looking at the graph we can see that the line crosses the x-axis (horizontal line) at (-2,0) and (0,0) so those are the two x intercepts because that is where the line intercepts the x axis
I hope this helps!
Determine the equation of the parabola whose graph is given below. Enter your answer in general form. A parabola graphed on a coordinate plane.
Answers
The equation of a parabola can be determined by analyzing its graph. The equation of a parabola can have various forms, so the general form allows for flexibility in its representation.
y = ax^2 + bx + c
To find the values of a, b, and c, we need to use the information provided by the graph of the parabola. Let's break down the steps:
1. Determine the vertex of the parabola:
- The vertex is the lowest or highest point on the graph, depending on the orientation of the parabola.
- Identify the coordinates of the vertex. Let's say it is (h, k).
2. Substitute the vertex coordinates into the equation:
- Replace x with h and y with k in the equation: k = ah^2 + bh + c.
3. Use another point on the graph to find the equation:
- Choose any other point (x1, y1) on the parabola.
- Substitute the coordinates into the equation: y1 = ax1^2 + bx1 + c.
4. Solve the system of equations:
- Set up a system of equations using the information from step 2 and step 3.
- For example, if the vertex coordinates are (h, k) and the other point is (x1, y1), the system of equations would be:
k = ah^2 + bh + c (equation 1)
y1 = ax1^2 + bx1 + c (equation 2)
5. Solve the system of equations for a, b, and c:
- Use any method (substitution, elimination) to solve the system and find the values of a, b, and c.
6. Write the equation in general form:
- Once you have the values of a, b, and c, substitute them into the equation y = ax^2 + bx + c to obtain the final equation of the parabola.
Remember, the equation of a parabola can have various forms, so the general form allows for flexibility in its representation.
To know more about parabola refer here:
https://brainly.com/question/11911877#
#SPJ11
Solve for x please!
No links or trolls.
Answers
Answer:
help me
Step-by-step explanation:
If 12(x -7) = -11 then x =?
Answers
Answer:
x = 73/12
Step-by-step explanation:
Given:
\(\displaystyle \large{12(x-7)=-11}\)
Distribute 12 in x-7:
\(\displaystyle \large{12x-84=-11}\)
Add both sides by 84:
\(\displaystyle \large{12x-84+84=-11+84}\\\displaystyle \large{12x=73}\)
Divide both sides by 12:
\(\displaystyle \large{\dfrac{12x}{12}=\dfrac{73}{12}}\\\displaystyle \large{x=\dfrac{73}{12}}\)
Therefore, the solution is x = 73/12
Answer:
\(\large\boxed{\bf\:x = \frac{73}{12} = 6\frac{1}{12} \approx 6.083}\)
Step-by-step explanation:
\(12(x - 7) = -11\)
Multiply 12 by x & 7 (distributive property) in the left hand side of the equation .
\(12(x-7)=-11\\(12*x)-(12*7)=-11\\12x - 84 =-11\)
Bring -84 to the right hand side of the equation. Then,
\(12x = -11 + 84\\12x = 73\\x=\frac{73}{12} \\\\\boxed{\bf\:x = \frac{73}{12} = 6\frac{1}{12} \approx 6.083}\)
\(\rule{150pt}{2pt}\)
In which situation may the sample proportion safely be assumed to follow a normal distribution?
Select one:
a. 8 successes in a sample of 72 items.
b. 5 successes in a sample of 20 items.
c. 9 successes in a sample of 200 items.
d. 12 successes in a sample of 500 items.
Answers
What is the sum of this infinite geometric series?
-5+4-16/5+64/25-256/125-
Enter your answer in the box. Enter any fraction as a simplified fraction.
...
Answers
The sum of this infinite geometric series is -25/9.
What is a geometric sequence?A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.
The given geometric series is -5+4-16/5+64/25-256/125
The general formula for finding the sum of an infinite geometric series is S= a/1-r, where s is the sum, a is the first term of the series, and r is the common ratio.
Here, a=-5 and r= -4/5
Now, S = -5/(1+4/5)
= -5/(9/5)
= -25/9
Therefore, the sum of the series is -25/9.
To learn more about the geometric sequence visit:
https://brainly.com/question/11266123.
#SPJ1
Vibrations of harmonic motion can be represented in a vectorial form. Analyze the values of displacement, velocity, and acceleration if the amplitude, A=2+T, angular velocity, ω=4+U rad/s and time, t=1 s. The values of T and U depend on the respective 5th and 6th digits of your matric number. For example, if your matric number is AD201414, it gives the value of T=1 and U=4.
Answers
The values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.
We know that the amplitude, A = 2 + T; the angular velocity, ω = 4 + U rad/s; and time, t = 1s. Here, the value of T = 1 and the value of U = 4 (as mentioned in the question).
Harmonic motion is a motion that repeats itself after a certain period of time.
Harmonic motion is caused by the restoring force that is proportional to the displacement from equilibrium.
The three types of harmonic motions are as follows: Free harmonic motion: When an object is set to oscillate, and there is no external force acting on it, the motion is known as free harmonic motion.
Damped harmonic motion: When an external force is acting on a system, and that force opposes the system's motion, it is called damped harmonic motion.
Forced harmonic motion: When an external periodic force is applied to a system, it is known as forced harmonic motion.Vectorial formVibrations of harmonic motion can be represented in a vectorial form.
A simple harmonic motion is a projection of uniform circular motion in a straight line.
The displacement, velocity, and acceleration of a particle in simple harmonic motion are all vector quantities, and their magnitudes and directions can be determined using a coordinate system.
Let's now calculate the values of displacement, velocity, and acceleration.
Displacement, s = A sin (ωt)
Here, A = 2 + 1 = 3 (since T = 1)and, ω = 4 + 4 = 8 (since U = 4)
So, s = 3 sin (8 x 1) = 2.68 m (approx)
Velocity, v = Aω cos(ωt)
Here, v = 3 x 8 cos (8 x 1) = 2.24 m/s (approx)
Acceleration, a = -Aω2 sin(ωt)
Here, a = -3 x 82 sin(8 x 1) = -18.07 m/s2 (approx)
Thus, the values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.
Learn more about acceleration
brainly.com/question/12550364
#SPJ11
Find all the real zeros of the function. y=-3(x+4/5)³+8/9.
Answers
The real zeros of the function y = -3(x + 4/5)³ + 8/9 are x = -8/15.
To find the real zeros of the function, we set y equal to zero and solve for x. In this case, the function is given as y = -3(x + 4/5)³ + 8/9.
Setting y = 0, we have:
0 = -3(x + 4/5)³ + 8/9.
Next, we can simplify the equation:
3(x + 4/5)³ = 8/9.
Now, we can isolate the term with the cube:
(x + 4/5)³ = (8/9) / 3.
Simplifying further:
(x + 4/5)³ = 8/27.
To find the real zeros, we take the cube root of both sides:
x + 4/5 = ∛(8/27).
Taking the cube root of 8/27 gives us 2/3:
x + 4/5 = 2/3.
Finally, we solve for x by subtracting 4/5 from both sides:
x = 2/3 - 4/5.
Finding a common denominator and simplifying, we get:
x = -20/15 + 12/15.
Combining the fractions, we find:
x = -8/15.
Therefore, the real zero of the function is x = -8/15.
Learn more about denominator here:
https://brainly.com/question/32621096
#SPJ11
Edwin wrote the word MATHEMATICS on separate index cards. What is the probability of pulling out a “M” and then an “A”, If you do not replace the first letter?
Show all work.
Answers
A motorboat travels kilometers in hours going upstream and kilometers in hours going downstream. What is the rate of the boat in still water and what is the rate of the current
Answers
The rate of the motorboat in still water is 49 km/hr. The rate of the current is 6 km/hr.
We have, A motorboat travels 258 km in 6 hours going upstream. It travels 330 km going downstream in the same amount of time. We have to calculate the rate of the boat in still water and the rate of the current. Let the speed of the boat in still water and rate of stream be "B" and "S" respectively.
Using the relative speed formula , the speed upstream is B - S and the speed downstream is B + S.
Use the distance , in speed/rate formula ,
Rate × Time = Distance
Upstream : (B-S)6 = 258
=> B - S = 43 --(1)
Downstream: (B+S)6 = 330
=> B + S = 55 --(2)
Solve the linear equations by elimination method. Add the two equations.
=> 2B = 98
=> B = 49 km/hr
Substitute this value of B in equation(2) and solve for S, B+S = 55
=> 49+S = 55
=> S = 6 km/hr
So, the rate of the current is 6 km/hr.
To learn more about Relative speed, visit :
https://brainly.com/question/28330915
#SPJ4
Complete question:
A motorboat travels 258 km in 6 hours going upstream. It travels 330 km going downstream in same amount of time. What is the rate of the boat in still water and what is the rate of the current.
verbal scale uses a representative fraction to describe the ratio between the map and the real world
Answers
Verbal scale uses a representative fraction to describe the ratio between the map and the real world is a "true" statement.
What is verbal scale/expression?A verbal scale is also known as a "word statement" or a "scale expression," and it is one of the possibilities for entering "scale text" in the ArcGIS software.
It is presented as a relationship between map distance and ground distance that is stated in common units that both parties can agree upon.
Uses of the verbal scale:
Verbal scales are widely employed on large-scale maps and planning documents, most frequently by civil engineers, just like representative fractions. On some smaller-scale maps, you can discover them, although not as frequently as you can with representative fractions. The verbal scales have already been calculated in some common map scales, so you might utilize those. The best treatment of verbal scales and the other scale indications may be found in Map Use by Kimerling, Muehrcke, and Muehrcke.To know more about the verbal expression(scale), here
https://brainly.com/question/95862
#SPJ4
The complete question is-
Verbal scale uses a representative fraction to describe the ratio between the map and the real world.(True/False).
how to divide polynomials using synthetic division
Answers
Polynomials are divided using synthetic division by the simplified form of long division.
Polynomials are divided using a technique called synthetic division, which uses a condensed version of long division. The procedures listed below can be used to divide a polynomial P(x) by a binomial of the form x - c (where c is a constant):
The first step is to write the divisor x-c and the dividend P(x).Second, the dividend's first term is to be written next to the divisor after bringing it down.The third step is to divide the divisor by the dividend's first term, and then put the result down below.The outcome of step 3 should be added to the dividend's subsequent period.Repetition of steps 3 and 4 with the prior step's outcome serving as the new dividend.The quotient and the remainder will be the outcome once all of the terms of the dividend have been applied (if any)Read more about polynomials on:
https://brainly.com/question/4142886
#SPJ4
Connor has made deposits of $125.00 into his savings account at the end of every three months for 15 years. If interest is 10% per annum compounded monthly and he leaves the accumulated balance for another 5 years, what would be the balance in his account then?
Answers
You can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.
To calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation with 10% interest compounded monthly, we can break down the problem into two parts:
Calculate the accumulated balance after 15 years of regular deposits:
We can use the formula for the future value of a regular deposit:
FV = P * ((1 + r/n)^(nt) - 1) / (r/n)
where:
FV is the future value (accumulated balance)
P is the regular deposit amount
r is the interest rate per period (10% per annum in this case)
n is the number of compounding periods per year (12 for monthly compounding)
t is the number of years
P = $125.00 (regular deposit amount)
r = 10% = 0.10 (interest rate per period)
n = 12 (number of compounding periods per year)
t = 15 (number of years)
Plugging the values into the formula:
FV = $125 * ((1 + 0.10/12)^(12*15) - 1) / (0.10/12)
Calculating the expression on the right-hand side gives us the accumulated balance after 15 years of regular deposits.
Calculate the balance after an additional 5 years of accumulation:
To calculate the balance after 5 years of accumulation with monthly compounding, we can use the compound interest formula:
FV = P * (1 + r/n)^(nt)
where:
FV is the future value (balance after accumulation)
P is the initial principal (accumulated balance after 15 years)
r is the interest rate per period (10% per annum in this case)
n is the number of compounding periods per year (12 for monthly compounding)
t is the number of years
Given the accumulated balance after 15 years from the previous calculation, we can plug in the values:
P = (accumulated balance after 15 years)
r = 10% = 0.10 (interest rate per period)
n = 12 (number of compounding periods per year)
t = 5 (number of years)
Plugging the values into the formula, we can calculate the balance after an additional 5 years of accumulation.
By following these steps, you can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.
Learn more about balance from
https://brainly.com/question/28767731
#SPJ11
Assume you call a customer who has a balance of $3585.26. They are required to pay 20% down and 6 equal payments of remainder amount. What should the 20% down and remainder payment amounts be?
Answers
To compute for the 20% down,
\(\text{ }\frac{\text{Balance x \% of Down to pay}}{100\text{\%}}\)\(\frac{\text{ (\$3,585.25)}(20\text{ \%)}}{100\text{ \%}}\text{ = (\$3,585.26)}(0.20)\text{ = \$ 717.05}2\text{ }\cong\text{ \$ 717.05}\)To solve for the remaining payment,
\(\text{Balance - 20\% Down = Remaining Payment}\)\(\text{ \$3,585.26 - \$717.05 = Remaining Payment}\)\(\text{ Remaining Payment = \$ 2,868.21}\)When divided into 6 equal payments,
\(\frac{\text{Remainder }Payment\text{ }}{6}\text{ =}\frac{\text{ \$ 2,868.21}}{6}\text{ = \$478.035}\)