The unexplained sum of squares measures variation in the dependent variable Y about the estimated Y values. The correct answer is option D.
How do we calculate unexplained variation?The unexplained variation is the sum of the squared of the differences between the y-value of each ordered pair and each corresponding predicted y-value. The sum of the explained and unexplained variations is equal to the total variation.
Unexplained variance is also known as error variation or residual variation. It refers to the random fluctuations around the regression line which show as variation. This type of variation is the sum of squared differences among each ordered pair's y-value and the predicted corresponding y-value.
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If T1(x) and T2(x) are onto linear transformations from Rn to Rm, then so is w(x) = T1(x) + T2(x) True, by the definition of linear transformation. True, by the definition of linear transformation and the definition of onto. False. Consider T2(x) = T1(x), where T1 is onto. False. Consider T2(x) =-T1(x), where T1 is one-to-one False. Consider T2(x) =-T1(x), where T1 is onto
[tex]$W(\mathbf{x})$[/tex]is a linear transformation. it is not onto .The given statement is false.
The objective is to determine whether the following statement is true or false.
"If [tex]$$T_1(\mathbf{x})$ and $T_2(\mathbf{x})$[/tex] are onto linear transformations from [tex]$\mathbf{R}^n$[/tex] to [tex]$\mathbf{R}^m$[/tex] then [tex]$W(\mathbf{x})=T_1(\mathbf{x})+T_2(\mathbf{x})$[/tex] is an onto linear transformation."
To check whether [tex]$W(\mathbf{x})$[/tex] is a linear transformation or not:
For a, b ∈ R and for x, y ∈ [tex]$\mathbf{R}^n$[/tex],
[tex]$$\begin{aligned}W(a \mathbf{x}+b \mathbf{y})= & T_1(a \mathbf{x}+b \mathbf{y})+T_2(a \mathbf{x}+b \mathbf{y}) \quad\left(\text { Since } W(\mathbf{x})=T_1(\mathbf{x})+T_2(\mathbf{x})\right) \\= & {\left[a T_1(\mathbf{x})+b T_1(\mathbf{y})\right]+\left[a T_2(\mathbf{x})+b T_2(\mathbf{y})\right] } \\& \quad\left(\text { Since } T_1(\mathbf{x}) \text { and } T_2(\mathbf{x}) \text { are onto linear transformations }\right) \\\end[/tex]
[tex]= & a\left[T_1(\mathbf{x})+T_2(\mathbf{x})\right]+b\left[T_1(\mathbf{y})+T_2(\mathbf{y})\right] \\\\= & a W(\mathbf{x})+b W(\mathbf{y})\end{aligned}$$[/tex]
Therefore, [tex]$W(\mathbf{x})$[/tex] is a linear transformation.
To check whether [tex]$W(\mathbf{x})$[/tex] is onto:
Define the linear transformations:
[tex]$$T_1: \mathbf{R} \rightarrow \mathbf{R}$ such that $T_1(\mathbf{x})=\mathbf{x}$[/tex]
[tex]$$T_2: \mathbf{R} \rightarrow \mathbf{R}$ such that $T_2(\mathbf{x})=-\mathbf{x}$[/tex]
Then, [tex]$T_2(\mathbf{x})=-\mathbf{x}=-T_1(\mathbf{x}) \Rightarrow T_2(\mathbf{x})=-T_1(\mathbf{x})$[/tex]
The range of both functions [tex]$T_1, T_2$ is $\mathbf{R}$[/tex] This is same as the co-domain of [tex]$T_1, T_2$[/tex]. So, they are onto functions.
If A and B are the two sets, if for every element of B, there is at least one or more element matching with set A, it is called the onto function.
Therefore, [tex]$T_1, T_2: \mathbf{R} \rightarrow \mathbf{R}$[/tex]are onto linear transformations.
And, [tex]$W=T_1+T_2: \mathbf{R} \rightarrow \mathbf{R}$[/tex] is a mapping.
Now, [tex]$W(\mathbf{x})=T_1(\mathbf{x})+T_2(\mathbf{x})$[/tex]
[tex]$$\begin{aligned}& =T_1(\mathbf{x})-T_1(\mathbf{x}) \\& =0\end{aligned}$$[/tex]
So, the range of [tex]$$W(\mathbf{x})$ is $\{0\} \neq \mathbf{R}($[/tex] co-domain of [tex]$W(\mathbf{x}))$[/tex]
Then, is [tex]$W(\mathbf{x})$[/tex] not onto.
So, the given statement is false.
Hence, the correct answer is 5th option
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what is the coefficient of determination; how do you interpret this number? make a comment on the strength of the regression relationship
The coefficient of determination (also known as the R-squared) is a measure of the proportion of the variance in the dependent variable (the y-variable) that is explained by the independent variable (the x-variable).
It is denoted by r-squared and typically takes values between 0 and 1. A value of 0 indicates that the independent variable does not explain any of the variance in the dependent variable, while a value of 1 indicates that the independent variable explains all of the variance in the dependent variable. The coefficient of determination (also known as the R-squared) is a measure of the proportion of the variance in the dependent variable (the y-variable) that is explained by the independent variable (the x-variable). A higher R-squared value indicates a stronger regression relationship between the two variables.
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Forum - Radicals (Moderated)
View Full Description
Which do you prefer: leaving √5 in radical form, or converting it to a decimal? Why? When would it be useful to use each?
I would prefer leaving the answer as a radical number as √5 since it is a shorter form and exact form of the answer.
How to express radical numbers?My reasons for leaving it as a radical form or a decimal approximation are;
1) If we are trying to find an exact answer, then we should leave it as √5. For example, if we are told a square has an area of 5 square units, then it means that the exact length of the side is √5 units.
2) If √5 is the length of an object that has to be made to that specific length, then we would require an approximation. For example, if you are asked to make a square out of cardboard whose area is 5 square feet, then we will definitely need an approximation of √5 ft = 2.24 ft, which would help us make each side of the cardboard square in the length of 2.24 ft.
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6x-3y= -21
4x=3y-9
Help
Answer:
The answer is x = -6 and y = -5.
Step-by-step explanation:
To solve this problem, we can use substitution. Let's first solve one of the equations in terms of the variable y, and then substitute this value into the other equation.
4x = 3y - 9
3y = 4x + 9
Since the term "3y" is present in the other equation given, we can substitute the right side of this equation (4x + 9) into the other equation for 3y. This is shown below.
6x - 3y = -21
6x - (4x + 9) = -21
6x - 4x - 9 = -21
We can simplify the left side of the equation and solve for x.
2x - 9 = -21
2x = -12
x = -6
Now, we can substitute this value for x into one of our equations to solve for y.
4x = 3y - 9
4(-6) = 3y - 9
-24 = 3y - 9
-15 = 3y
y = -5
Therefore, the correct answer is x = -6 and y = -5.
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Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. n =12, x= 5, p=0.25?
x = random variable = number of successful trials = 4
n = number of trials = 6
P = likelihood of success = 0.55
Q = likelihood of failure = 0.45
nCx = number of combinations of n objects taken x at a time
.
Binomial Distribution
b(x; n, P) = nCx * P^x * Q^(n - x)
.
b(4; 6, 0.55) = 6C4 * (0.55)^4 * (0.45)^2 = (15)(0.09150625)(0.2025) = 0.2779502
Find g(x), where g(x) is the reflection across the x-axis of f(x)=-9x+10.
8 17 26 Find the 41st term.
Answer:
368
Step-by-step explanation:
You want the 41st term of the arithmetic sequence that starts 8, 17, 26.
Arithmetic sequenceThe n-th term of an arithmetic sequence is given by ...
an = a1 +d(n -1)
for first term a1 and common difference d.
DifferenceThe difference between terms is ...
d = 17 -8 = 9
41st termThe first term is a1 = 8, so the 41st term is ...
a41 = a1 +d(41 -1) = 8 +9(41 -1) = 368
The 41st term of the sequence is 368.
<95141404393>
Bottles of water come in three sizes.
Small bottle: A 200 ml bottle costs 25p;
Medium bottle: A 750 ml bottle costs 84p;
Large bottle: A 1 litre bottle costs £1.08.
Calculate the cost of 3 litres for each bottle.
Give your answer in pence to the nearest penny.
Write the bottle that is the better value in the comments.
Small:
Р
Medium:
P
Large:
Р
Answer:
Step-by-step explanation:
Please help me!
I need to deliver it tomorrow.
i'm kind of sure it's -4.7
what is the drag force on a 1.6 m wide, 1.4 m high car traveling at 10 m/s (≈ 22 mph)?
141.472 N of drag force is applied in 1.6m wide and 1.4m high car travelling at 10m/s
What is drag force?Drag force is the net force in the direction of flow experienced by any item moving through a fluid and is caused by pressure and shear stress forces acting on the surface of the object.
Formula of drag force is given by:
[tex]F_d = \frac{1}{2}C_dAPv^2[/tex]
where
[tex]F_d[/tex] = drag force (N)
[tex]C_d[/tex] = drag coefficient (1.05 for moving car)
P = density of fluid (1.2 kg/m3 for air at NTP)
v = flow velocity (m/s)
A = characteristic frontal area of the body
A = height * width
=> 1.6*1.4
so A=2.24 [tex]m^2[/tex]
and v=10 m/s
so [tex]F_d[/tex] = 1/2* 1.05 * 2.24 *( 1.2 *10*10)
=> 0.5*1.05*2.24 *122
=> 143.472 N
so [tex]F_d[/tex] = 143.472 N
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Which represents the reflection of f(x) = startroot x endroot over the x-axis? a 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries undefined, 0, negative 1, negative 2. A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries 1, 0, undefined, undefined.
The correct option is A: A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries undefined, 0, negative 1, negative 2.
Explain the reflection along the x-axis?In order to reflect over the X axis, one must negate that value of each point's y-coordinate while maintaining its x-value.The x-coordinate remains constant when a point is reflected across the x-axis, however the y-coordinate is assumed to be an additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).The given function is;
f(x) = StartRoot x EndRoot , which is written as;
f(x) = √x
Domain for the x = [ 0 , ∞ )
x f(x)
-1 undefined
0 0
1 1
4 2
The reflection over x-axis.
f(x) ----> - f(x)
x f(x)
-1 undefined
0 0
1 -1
4 -2
Thus, the correct option is; A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries undefined, 0, negative 1, negative 2.
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The complete question is-
Which represents the reflection of f(x) = StartRoot x EndRoot over the x-axis?
A: A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries undefined, 0, negative 1, negative 2.
B: A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries 1, 0, undefined, undefined.
C: On a coordinate plane, an absolute value graph starts at (0, 0) and goes down and to the left through (negative 4, negative 2).
D: On a coordinate plane, an absolute value graph starts at (0, 0) and goes down and to the right through (2, negative 4).
Answer:
D
Step-by-step explanation:
Edge 2023
Simplify each algebraic expression. Drag the tiles to the correct boxes to complete the pairs.
Tiles
-5x - 2
Pairs
5x+2
5x-2
12z+872 - 10
z + 17-2 - 15
8- 12z 10+ 7x
-
9 - 올ㄹ - 글ㄹ - 7
-5x+2
PLEASE HELP ASAP
Answer:
.
Step-by-step explanation:
Find the area of the regular polygon.
Round to the nearest tenth.
[ ? ] yd?
Answer:
98 yd²
Step-by-step explanation:
diagonal = 7 · 2 = 14 yd
side = x² + x² = 14²
2x² = 196
x² = 196/2
x² = 98
x = √98
area = √98² = 98 yd²
HELP PLS!!These tables of values represent continuous functions. In which table do the
values represent an exponential function?
OA.Y
18
2 16
3 24
4 32
5 40
OB.y
14
28
3 16
4 32
5 64
OC.xy
1 12
2 17
3 22
4 27
5 32
OD.xy
19
2 10
3 11
4 12
5 13
The answer is A
It's multiples by 8 each time
Hello. Could someone help me to solve this question? The answer is 86.61cm.
The perimeter of the whole diagram in cm is derived as 86.6158 cm using trigonometric ratios.
Trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
Considering the angle P for right-angled triangle formed by extending the line PQ to the base of the trapezium, so that we have opposite side of 7 cm (22 cm - 15 cm)
so; sinP = 7/25.3
P = sin^(-1)(7/25.3)
P = 16.06
The isosceles triangle PQR have the angle;
Q = 180 - 2(16.06) {sum of interior angles of Isosceles triangle with two equal base angles}
Q = 147.88°
Considering the smaller right-angled triangle formed by the height of the trapezium and one side of the Isosceles triangle, we have its angle;
Q = 180° - 147.88° {sum of angles on a straight line}
Q = 32.12
also;
sin32.12 = 7/hypotenuse (one of the equal sides of the Isosceles triangle)
hypotenuse = 7/sin32.12
hypotenuse = 13.1655
The length TS is equal to the adjacent side of the smaller triangle, so;
cos32.12 = TS/13.1655
TS = 13.1655 × cos32.12
TS = 1.51503
Therefore, the perimeter of the whole diagram is;
25.3 cm + 22 cm + 15 cm + 13.1655 cm + 11.1503 cm = 86.6158 cm.
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10. jackson has 4 more cds than amal. they have a total of 18 cds. how many cds does amal have? how many cds does jackson have?
Amal has seven CDs, whereas the Jacksons have eleven, with the Jacksons owning four more than Amal. They have a total of 18 CDs.
Given that,
4 more CDs belong to Jackson than Amal. They have 18 CDs altogether.
We have to find what number of CDs does Amal own and Jackson has how many CDs.
We know that,
Let amount of CD Jackson have x.
Let Amal have CD has y.
So,
x=y+4
x-y=4 ----->equation(1)
x+y=18 ------>equation(2)
So, now we have to solve the equations.
Adding equation(1) and equation(2)
x-y=4
x+y=18
-----------
2x=22
x=22/2
x=11
So, substitute x=11 in equation(1)
11-y=4
-y=4-11
-y=-7
y=7
Therefore, Amal have 7 cd and the Jackson have 11 cd when 4 more CDs belong to Jackson than Amal. They have total 18 CDs altogether.
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the degrees of freedom for a chi-square test of independence for the following data is 5. group of answer choices true false
The number of independent pieces of information used to calculate a statistic is called the degrees of freedom, which is frequently denoted by the letters v or df. I
What is the degree of freedom?Itbis determined by subtracting the number of restrictions from the sample size. Subtract the number of relations from the number of observations to determine degrees of freedom. You need to deduct one (1) from the total number of observations, n, in order to calculate the degrees of freedom for a sample mean or average.
The degrees of freedom for the chi-square are calculated as df = (r-1)(c-1) where
r = the number of rows
c = the number of columns.
If the observed chi-square test statistic is greater than the critical value, the null hypothesis can be rejected.
Note that an overview was given as the information you gave is incomplete.
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Which ordered pair makes both inequalities true? y < –x + 1 and y > x?A.-3,5
B.-2,2
C.-1,-3
D.0,-1
The ordered pair -2,2 makes the inequalities y < –x + 1 and y > x true. Therefore, option B is true.
Inequality is the absence of an equality link between two expressions or values. An ordered pair is made up of the x and y coordinates, with two values stated in a certain order inside parenthesis.
Substitute the values from the given ordered pair one by one to check whether the given inequalities are true.
Substituting (-2,2) in y < –x + 1 and y > x,
For, y < –x + 1
2<2+1
2<3
For, y > x
2>-2
This ordered pair (-2,2) makes the given inequalities true.
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You are going send Christmas cards to 100 of your friends. Each box of
Christmas cards contains 15 cards and the cost per box is $17.00. You are going to purchase enough Forever
stamps from the post office to mail 100 cards. How much will it cost in total?
Answer:
You are going send Christmas cards to 100 of your friends. Each box of Christmas cards contains 15 cards and the cost per box is $17.00. You are going to purchase enough Forever stamps from the post office to mail 100 cards. How much will it cost in total?
1box - 15 card - $17
100/15 = 6.67 (round off to 7 box since u cant buy 6.67 box)
7 * $17 = $119
Therefore, you will spend $119 to buy 7 box with a total of 105 cards.
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-The intruction on a box of chicken pattie tate that one patty hould be cooked for 3. 5 minute in the microwave. If more than one patty i cooked, an additional 1 minute hould be added per patty. Write an equation in lope-intercept form to model the cooking time in minute, y, for x additional pattie
The equation in slope-intercept form to model the cooking time in minutes, y, for x patties is y = (3/2)x + 1.
What are lines and their slopes?
We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given, On a box of chicken patties state that one patty should be cooked for 2.5 minutes in the microwave.
If more than one patty is cooked, an additional 1.5 minutes should be added per patty.
So, The equation in slope-intercept form to model the cooking time in
minutes, y, for x patties.
If we write this as y = 1.5x + 2.5 and put x = 0 , y = 2.5 which is not satisfying the given statement.
∴ y = 1.5x + (2.5 - 1.5). (the additional patty cooking time).
y = 1.5x + 1.
y = (3/2)x + 1.
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The question is "What does the y-intercept of the line of best fit tell you about the situation below?"
Answer:
D
Step-by-step explanation:
y-intercept is when the line hits the y-axis, or when the x=0 on a line.
Look at the test below the axis.
y-axis = heartrate (resting)
for
x-axis = hrs of exercise per week
When x = 0, (0 hours of exercise,) y = 80, (average resting heart rate.)Telling us the average resting heartrate pf people who do not exercise.
A recipe for 4 people uses 250 g of flour. How much flour is needed to
make the same recipe for 8 people? Give your answer in grams (g).
Answer:
500 grams
Step-by-step explanation:
you doubled the people, so you would need to double the flour.
I need help with this image attached
Answer:
32
Step-by-step explanation:
y² + 7y-8
Please answer this and show work
The factorization of y²+7y-8 is (y+8)(y-1).
y²+7y-8
=y²+8y-y-8
=y(y+8)-1.(y+8)
=(y+8)(y-1)
The factors are (y+8), (y-1).
The method we are following here is factorize by grouping.
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The correct question is-
Factor y²+7y-8.
After solving this problem, Juan was very clever and invented the following strange question:
A building, in the shape of a rectangular prism with a square base, has on its top a radio tower. The
building is 25 times as tall as the tower, and the side-length of the base of the building is 100 feet less than
the height of the building. If the building has a volume of 2 million cubic feet, how tall is the tower?
The tower is 24 feet tall.
To solve this problem, we need to use the formula for the volume of a rectangular prism, which is V = l × w × h, where l and w are the length and width of the base and h is the height.
We are given that the side length of the base of the building is 100 feet less than the height of the building, so the height of the building is h = l + 100, where l is the side length of the base. We can substitute this expression for h into the formula for the volume of the building:
V = l × w × (l + 100) = 2 million cubic feet
Since the building is 25 times as tall as the tower, the height of the tower is h = (1/25) × h = (1/25) × (l + 100). Substituting this expression for h into the formula for the volume of the building, we get:
V = l × w × (1/25) × (l + 100) = 2 million cubic feet
Solving this equation for l, we find that l = 500 feet. This is the side length of the base of the building, so the height of the building is h = l + 100 = 500 + 100 = 600 feet. The tower is (1/25) × 600 = 24 feet tall.
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One bouquet of flower ha 7 roe for every 2 tickeed. Another bouquet ha 3 tickeed for every 4 daiie. If both bouquet have 6 tickeed, which bouquet ha more flower? LOADING. Click the icon to view the table
If both bouquets have 6 tickseeds, the first bouquet ( roses + tickseeds) has more flowers.
The problem can be solved using ratio.
Bouquet 1 :
Every 2 tickseeds there are 7 roses
Hence, the ratio
Tickseed : rose = 2 : 7
If there are 6 tickseeds, then
2 : 7 = 6 : rose
rose = (6/2) x 7 = 21
Number of flowers = 6 tickseeds + 21 roses = 27 flowers
Bouquet 2 :
Every 3 tickseeds there are 4 daisies
Hence, the ratio
Tickseed : daisy = 3 : 4
If there are 6 tickseeds, then
3 : 4 = 6 : daisy
daisy = (6/3) x 4 = 8
Number of flowers = 6 tickseeds + 4 daisies = 10 flowers
Hence, if there are 6 tickseeds in each bouquet, the first bouquet contains more flowers.
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The average age of ceo's is 56 years. Assume the random variable is normally distributed. If the standard deviation is 4 years, find the probability that the age of a ceo is between 50 and 56 years old.
There is a probability of 33.45% that the age of randomly selected CEO will be between 50 and 55 years old.
What does the math term "probability" mean?
The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.
Statistics is the study of events that follow a probability distribution.
Given that:
Mean = 56, standard deviation = 4, For 50:
z = (50 - 56) / 4 = -1.5
For 44:
z = (55 - 56) / 4 = -0.25
P(50 < x < 55) = P(z < -0.25) - P(z < -1.5) = 0.4013 - 0.0668 = 33.45
There is a probability of 33.45% that the age of randomly selected CEO will be between 50 and 55 years old.
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if the pile contains only 25 quarters and only 40 dimes but at least 50 of each other kind of coin, how many collections of 50 coins can be chosen? collections
if the pile contains only 25 quarters and only 40 dimes but at least 50 of each other kind of coin, then 20,281 collections of 50 coins can be chosen.
what are quarters?
A quarter fraction is the division of one whole into four equal parts, where one represents the referred-to part and four represents the number of parts into which the whole has been divided. It is written as 14 in numerical form.Given that:
25 quarters and only 40 dimes
No. of. Ways with at least 26 quarters and 41 dimes.
26 + 41 = 67 coins, but we have only 50 coins.
There are 0 ways to select at least 26 quarters and 41 dimes.
[tex]A_{1}[/tex] = at least 26 quarters
[tex]A_{2}[/tex] = at least 41 dimes
Using inclusion / exclusion rule for the two sets:
N([tex]A_{1} U A_{2}[/tex]) = N ( [tex]A_{1}[/tex]) + N ( [tex]A_{2}[/tex])- N ([tex]A_{1}[/tex] ∩ [tex]A_{2[/tex])
= 2925 + 220 - 0
= 3145
Therefore, no . of . ways with at most 25 quarters and at most 40 dimes are
= 23426 - 3145
= 20,281 ways
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Simplify the expression.
14+(-4)-6/7j-3/7j+7
[tex]17 - \frac{9}{7} j[/tex]
[tex]14 - 4 - \frac{6}{7} j - \frac{3}{7} j[/tex]
[tex]17 - \frac{6}{7} - \frac{3}{7}j [/tex]
[tex]17 - \frac{9}{7} j[/tex]
Lucy wants to but a new car but needs money for the down payment. Her parents agree to lend her money at an annual rate of 5%, charged as simple interest. They lend her $4000 for 2 years. She makes no payments except the one at the end of that time.
Answer the following questions:
How much total interest will Lucy have to pay?
What will the total repayment amount be (including interest)
Answer:
To calculate the total interest that Lucy will have to pay, we need to use the formula for simple interest: I = P * R * T, where I is the interest, P is the principal (the amount borrowed), R is the interest rate (as a decimal), and T is the time in years. Using this formula, we can calculate the total interest that Lucy will have to pay as follows:
I = P * R * T
I = $4000 * 0.05 * 2
I = $400
Therefore, the total interest that Lucy will have to pay is $400.
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To calculate the total repayment amount (including interest), we need to add the total interest to the original amount borrowed, which in this case is $4000. Therefore, the total repayment amount will be $4000 + $400 = $4400. This is the amount that Lucy will have to pay back to her parents at the end of the two-year period.
Step-by-step explanation:
Answer:
Total interest = $400
Total repayment (including interest) = $4,400
Step-by-step explanation:
Simple Interest Formula
[tex]\large\boxed{ \sf I = Prt}[/tex]
where:
I = Total interest.P = Principal amount.r = Interest rate (in decimal form).t = Time (in years).Given:
P = $4,000r = 5% = 0.05t = 2 yearsTo find the total interest, substitute the given values into the formula and solve for I:
[tex]\implies \sf I=4000 \cdot 0.05 \cdot 2[/tex]
[tex]\implies \sf I=200 \cdot 2[/tex]
[tex]\implies \sf I=400[/tex]
Therefore, the total interest Lucy has to pay is $400.
The total repayment amount is the sum of the principal and the interest:
[tex]\implies \sf A=P+I[/tex]
[tex]\implies \sf A=4000 +400[/tex]
[tex]\implies \sf A=4400[/tex]
Therefore, the total repayment (including interest) is $4,400.