Answer:
[tex]\displaystyle d = 2\sqrt{10}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point (-5, -2) → x₁ = -5, y₁ = -2
Point (-3, 4) → x₂ = -3, y₂ = 4
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(-3+5)^2+(4+2)^2}[/tex][√Radical] (Parenthesis) Add: [tex]\displaystyle d = \sqrt{(2)^2+(6)^2}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{4+36}[/tex][√Radical] Add: [tex]\displaystyle d = \sqrt{40}[/tex][√Radical] Simplify: [tex]\displaystyle d = 2\sqrt{10}[/tex]The graph shows an exponential function relating the balance in
an investment account to the time in years.
What does the y-intercept represent?
O
the time it takes the account to reach its maximum
value
O the maximum value of the account
O the initial balance of the account
O the amount the account increases by each year
Account balance (5)
1600
1400
1200
1000
800
600
The value of the y-intercept represent,
⇒ the amount of the account increases by each year.
We have to given that;
The graph shows an exponential function relating the balance in an investment account to the time in years.
Now, From graph we have;
The value of the y-intercept represent,
⇒ the amount of the account increases by each year.
Thus, value of the y-intercept represent,
⇒ the amount of the account increases by each year.
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Vanessa makes 7 identical flower arrangements for the tables at a banquet. Each arrangement contains some roses and 9 tulips. Vanessa uses a total of 147 flowers to make the arrangements. How many roses are in each arrangement?
Tanya flew 2,299 miles the first year on the job. She flew 3,831 miles the second year. Tanya flew 1,510 more miles the third year than the first and second years combined. How many miles did Tanya fly the third year?
Please help me!!
Answer: 7,640
Step-by-step explanation: Because we know that she flew 2,299 the first year and 3,831 the second, we can add them together to get: 6,130. It says that she flew 1,510 more miles the third year than the first and second combined. Therefore: 6,130 + 1,510 = 7,640
Which graph has the same end behavior as f (x) = StartFraction 10 x cubed + x squared + 3 Over 2 x squared + 1 EndFraction?
On a coordinate plane, a line goes through (negative 2, negative 10), (0, 0), and (2, 10).
On a coordinate plane, a graph approaches the x-axis in quadrant 2, increases up to (0, 10), and then curves down and approaches the x-axis in quadrant 1.
On a coordinate plane, a parabola opens up. It goes through (negative 2, 8), has vertex (0, 1), and goes through (2, 8).
The function with the same end behavior as f(x) = (10x³ + x² + 3)/(2x² + 1) is given as follows:
On a coordinate plane, a line goes through (-2, -10), (0, 0), and (2, 10).
What is the end behavior of a function?The end behavior of a function refers to how the function behaves as the input variable approaches positive or negative infinity.
The function for this problem is given as follows:
f(x) = (10x³ + x² + 3)/(2x² + 1)
As we are looking for the end behavior, we look at the terms with the highest exponent, hence:
f(x) = 10x³.
Then the end behavior is given as follows:
As x -> - ∞, 10(-∞)³ -> -∞.As x -> ∞, 10(∞)³ -> ∞.Hence the function with the same end behavior is the increasing line, which is given by the first option.
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Can someone answer this question
The equations and their graphs are:
Graph 4: I(x)=P(x)−4
Graph 2: I(x)=P(x+4)
Graph 1: I(x)=P(x)+4
Graph 3: I(x)=P(x−4)
Here we have,
to match the equations and their graphs:
The parent function is given as:
P(x) = x^2
As a general rule of function transformation, we have:
Vertical translation up: I(x) = P(x) + k
Vertical translation down: I(x) = P(x) - k
Horizontal translation left: I(x) = P(x + k)
Horizontal translation right : I(x) = P(x - k)
Using the above rules and the assumption that k is 4;
We have:
Vertical translation up: I(x) = P(x) + 4
Vertical translation down: I(x) = P(x) - 4
Horizontal translation left: I(x) = P(x + 4)
Horizontal translation right : I(x) = P(x - 4)
Hence, the graphs of the equations are:
Graph 4: I(x)=P(x)−4
Graph 2: I(x)=P(x+4)
Graph 1: I(x)=P(x)+4
Graph 3: I(x)=P(x−4)
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complete question;
Consider the function P(x)=x2, which is a parabola that opens upward, with a vertex at (0,0).
It undergoes four separate transformations as indicated by the graphs that follow.
P(x) represents the preimage and is placed correctly on all images. I(x) represents the image after the transformation.
Match each transformation indicated by I(x) to the correct graph.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
I(x)=P(x)−4
I(x)=P(x+4)
I(x)=P(x)+4
I(x)=P(x−4)
What is the period of this function?
a.2
b.1
c.4
d.-1.15
The value of period of function is,
Period = 2
Since, A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
We have to given that;
The graph of function is shown in figure.
Since, The distance between the repetition of any function is called the period of the function.
And, For a trigonometric function, the length of one complete cycle is called a period.
Hence, By definition of period, we get;
The value of period of function is,
Period = 3 - 1
Period = 2
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Can someone help me please
(a) The given system of equation as an augmented matrix is [tex]\left[\begin{array}{cccc}1&3&0&150\\0&1&0&250\\-1&-1&1&400\end{array}\right][/tex];
(b) For the given augmented matrix, the system of equations is
-5x-6y-4z=400;
y+z=100;
-3x-3y-2z=150;
A "system-of-equations" is a set of two or more equations which contain multiple variables. The solution to the system of equations is the set of values for the variables that satisfy all the equations in the system.
An "Augmented-Matrix" is a way to represent a system of linear equations in a concise and organized manner. It is obtained by writing the coefficients of the variables and the constants in each equation in a rectangular array, with each row representing an equation.
Part(a) : The system-of-equations is given as :
x + 3r +0m = 150
0x + r + 0m = 250
-x - r + m = 400,
We see that the first column of the matrix will have 1, 0, -1,
the second-column will have 3, 1, -1 ;
the third-column will have 0, 0, 1.
So, the Augmented Matrix is represented as : [tex]\left[\begin{array}{cccc}1&3&0&150\\0&1&0&250\\-1&-1&1&400\end{array}\right][/tex].
Part(b) :
The augmented-matrix is given as : [tex]\left[\begin{array}{cccc}-5&-6&-4&400\\0&1&1&100\\-3&-3&-2&150\end{array}\right][/tex],
In this matrix, the terms in the "first-column" will be multiplied by variable"x";
the terms in the "second-column" will be multiplied by variable"y"; and
the terms in the "third-column" will be multiplied by variable"z";
The term sin the "fourth-column" represents the output value.
So, "system-of-equation" will be represented as : -5x - 6y - 4z = 400;
0x + y + z = 100;
-3x - 3y - 2z = 150.
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9.7/0.0268
need help please
This is a basic arithmetic problem and the solution to 9.7/0.0268 is equal to 361.94
Understanding Basic Arithmetic OperationBasic Arithmetic Operations are fundamental to solving mathematical problems and they are addition (+), subtraction (-), multiplication (×) and division (÷).
1. Addition:
Addition is the process of combining two or more numbers to find their total or sum. The symbol used for addition is "+". For example, to add the numbers 3 and 5, you write it as:
3 + 5 = 8
Here, 3 and 5 are added together to get the sum, which is 8.
2. Subtraction:
Subtraction is the process of finding the difference between two numbers. The symbol used for subtraction is "-". For example, to subtract 5 from 8, you write it as:
8 - 5 = 3
Here, 5 is subtracted from 8 to get the difference, which is 3.
3. Multiplication:
Multiplication is the process of repeated addition or combining equal groups. The symbol used for multiplication is "×" or "*". For example, to multiply 4 and 6, you write it as:
4 × 6 = 24
Here, 4 is multiplied by 6 to get the product, which is 24.
4. Division:
Division is the process of dividing a number into equal parts or finding how many times one number is contained within another. The symbol used for division is "÷" or "/". For example, to divide 20 by 5, you write it as:
20 ÷ 5 = 4
Here, 20 is divided by 5 to get the quotient, which is 4.
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how do I change 1/4 to a percentage .
Answer: You divide it, get your answer, move the decimal point to the right twice, and that's you're percent.
Step-by-step explanation:
1/4=.25
.25 > 25%
Answer:
The answer is 25%
Step-by-step explanation:
To change decimal to percentage multiply by 100
1/4×100%
=25%
Part 1 An aquarium in Watertown, USA needs to confirm their measurements to be sure there is enough room for incoming injured whales coming from another aquarium on the coast.
Main Show Tank Calculation:The main tank has a radius of 95 feet. What is the volume of the quarter-sphere sized tank? Round your answer to the nearest whole number. You must explain your answer using words, and you must show all work and calculations to receive credit.
Holding Tank Calculations: The holding tanks are congruent in size, and both are in the shape of a cylinder that has been cut in half vertically. The bottom of the tank is a curved surface. What is the volume of both tanks if the radius of tank #1 is 15 feet and the height of tank #2 is 120 feet? You must explain your answer using words, and you must show all work and calculations to receive credit.
Density Calculation: Using the calculations for the main and holding tanks above, what is the maximum number of killer whales allowed in the main show tank at any given time? The maximum density of killer whales per cubic foot is 0.000021142, You must explain your answer using words, and you must show all work and calculations to receive credit.
The volume of the quarter-sphere tank is approximately 1,387,244 cubic feet.
The volume of tank 1 is 353h cubic feet, and the volume of tank 2 is 31,416 cubic feet.
The main tank is in the shape of a quarter-sphere, which means it is a quarter of a full sphere.
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.
Given that the radius of the main tank is 95 feet
we can substitute this value into the formula to calculate the volume:
V = (4/3)π(95³) = 1,387,244 cubic feet.
The holding tanks are in the shape of cylinders that have been cut in half vertically.
The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height.
For tank 1, the radius is given as 15 feet. Since it is a half-cylinder, we divide the volume by 2:
V1 = (1/2)π(15²)h = 353h cubic feet.
For tank 2, the height is given as 120 feet.
V2 = (1/2)π(15²)(120) = 31,416 cubic feet.
The maximum density is 0.000021142 killer whales per cubic foot
we can calculate the maximum number of killer whales as follows:
Number of killer whales = (Volume of main show tank) / (Density of killer whales)
Number of killer whales = 1,387,244 / 0.000021142 ≈ 65,606,197.
Therefore, the maximum number of killer whales allowed in the main show tank at any given time is 65,606,197
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Triangle ABC is the preimage of a transformation that consists of a reflection across x -axis followed by a reflection across the y -axis. Which of the triangles is the image of △ABC under this transformation? Select the triangle that corresponds to the image △A′B′C′ .
The image triangle △A'B'C' is formed by reflecting triangle ABC across the origin, resulting in each point's coordinates being negated.
The preimage triangle ABC undergoes a reflection across the x-axis followed by a reflection across the y-axis.
To determine the image triangle △A'B'C', we need to understand the effects of these transformations.
Reflection across the x-axis flips the points of the preimage vertically, while reflection across the y-axis flips the points horizontally.
When both reflections are applied successively, the resulting image will be a reflection across the origin (0,0).
Given that, the image triangle △A'B'C' will be the reflection of triangle ABC across the origin.
In this case, the x-coordinate and y-coordinate of each point in triangle ABC will be negated to obtain the corresponding point in △A'B'C'.
Let's consider the points of triangle ABC:
A(x₁, y₁), B(x₂, y₂), C(x₃, y₃)
To obtain the corresponding points in △A'B'C', we negate the x and y coordinates:
A'(-x₁, -y₁), B'(-x₂, -y₂), C'(-x₃, -y₃)
Therefore, the image triangle △A'B'C' is formed by reflecting triangle ABC across the origin, resulting in each point's coordinates being negated.
Note: It's important to note that without the actual coordinates of triangle ABC, it's not possible to determine the specific shape or size of the image triangle △A'B'C'.
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Solve for y
Finally, solve the proportion for y.
y/8 = 10/y
y = √ [?]
M
Enter the square root NOT simplified.
=
The square root of y is not simplified and can be represented as:
y = √([tex]2^4 \times[/tex] 5) or y = 4√5.
To solve the proportion y/8 = 10/y for y, we can cross-multiply:
y [tex]\times[/tex] y = 8 [tex]\times[/tex]10
This simplifies to:
[tex]y^2[/tex] = 80
To solve for y, we can take the square root of both sides of the equation:
[tex]\sqrt{y^2[/tex] = √80
Since the square root of [tex]y^2[/tex] is simply y, we have:
y = √80
The square root of 80 can be further simplified by breaking it down into its prime factors. Since 80 can be expressed as 2 [tex]\times[/tex]2 [tex]\times[/tex]2 [tex]\times[/tex]2 [tex]\times[/tex]5, we can simplify the square root:
y = [tex]\sqrt(2 \times 2 \times 2 \times 2 \times 5)[/tex]
Therefore, the square root of y is not simplified and can be represented as:
y = [tex]\sqrt{(2^4 \times 5)[/tex] or y = 4√5.
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Answer:
[tex]y = \sqrt{80\\} =4\sqrt{5}[/tex]
Step-by-step explanation:
2
Select the correct answer from each drop-down menu.
Triangle ABC is shown in the coordinate plane. It is translated 6 units left and 4 units down. Then it is dilated by a scale factor of 3 centered about the
origin. Complete the statements.
-6 -4
v.
6
4-
2-
lo
-2-
-4-
-6-
The translation of triangle ABC
A
2
с
6
B
Reset
The dilation of triangle ABC
Next
For the transformations of the triangle, we have that:
1. The translation of triangle ABC preserves side lengths and angles.
2. The dilation of triangle ABC preserves angles but not side lengths.
Hence the correct options are, respectively, C and B.
A translation involves shift left, shift right, shift down, or shift up, meaning that just the coordinates of the figure change, not the angles or the side lengths,
1. The translation of triangle ABC preserves side lengths and angles.
For a dilation, the coordinates of the vertices are multiplied by a constant, hence the side lengths change while the angles remain constant, thus:
2. The dilation of triangle ABC preserves angles but not side lengths.
Hence the correct options are, respectively, C and B.
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hey here is my algebra 13 homework, can someone please help! heres screenshot. QUICK PLSS
The graph of the given exponential function f(x) = 4(0.5)ˣ + 2 is g(x) = 5(1/6)ˣ + 2
Hence, the correct option is A.
An exponential function is a mathematical function of the form f(x) = aˣ, where "a" is a positive constant known as the base, and "x" is the independent variable. The exponential function is defined for all real values of x, and the output values of the function are always positive.
The exponential function is characterized by its unique property of having a constant rate of change with respect to its own value. This means that the function increases (or decreases) by a constant factor each time the independent variable is increased by a fixed amount.
For the given exponential function g(x) = 5(1/6)ˣ + 2 as the graph of f(x) and g(x) are same.
Hence, the correct option is A.
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find the area of each figure pls
Answer:
Step-by-step explanation:
1 = 20cm
2 = 0.56cm^2
3 = 77.5m2
ANSWER ASAP!! (GIVING BRAINLIEST IF CORRECT!!)
A scale has a percent error of 5%. The actual mass of a rock is 30 g.
The scale is likely to show the mass as either;
A: 25 g. or 30 g.
B: 25.5 g. or 30.5 g.
C: 28 g or 31.5 g.
D: 28.5 g. or 31.5 g.
Answer:
ans d
Step-by-step explanation:
5 percent of 30 is 1.5 so d
What is the period of this function?
Calculus Integral Questions Unit 2 Lesson 5 Fundamental Theorem of Calculus
Answer: b and c
Step-by-step explanation:
Answer:
The first question is 3 and the third question is the one with = 20
I have no answer for the second
The other answer left by farrelljacob646 is incorrect
who can help me solve this pls need help
Answer:
Step-by-step explanation:
1+3=4
4x4=16
10/2=5
16-5=11
answer is 11
i need serious help someone pleaseeeee
The value of c in the polynomial is - 7.
How to solve polynomials?The polynomial is given as follows:
p(x) = 2x³ - x² + cx + 2 . The value of c if x - 2 is a factor of p(x) can be computed as follows:
Therefore,
p(x) = 2x³ - x² + cx + 2
when x - 2 is a factor, p(x) = 0
Therefore,
0 = 2x³ - x² + cx + 2
Hence,
2(2)³ - (2)² + 2c + 2 = 0
16 - 4 + 2c + 2 = 0
12 + 2 + 2c = 0
2c = - 14
divide both sides by 2
c = - 14 / 2
c = - 7
Therefore,
c = -7
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If someone can explain this to me that would be amazing, I have a college algebra final tomorrow and I am rly confused. I don’t know how wide to make it, if someone can explain this I will give 100 points and brainliest
You have $400,000 saved for retirement. Your account earns 10% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 20 years?
You will be able to withdraw $3,548.50 per month for 20 years if you have $400,000 saved for retirement and earn 10% interest.
To calculate the monthly withdrawals for a given time period, we can use the present value annuity formula. This formula allows us to calculate the fixed monthly withdrawal amount needed to deplete a given initial amount (in this case, $400,000) over a specified time period (20 years) at a given interest rate (10%).
The formula for present value annuity is:
PMT = PV * r / (1 - (1 + r)⁻ⁿ)
Where:
PMT = the fixed monthly withdrawal amount
PV = the present value of the initial investment ($400,000)
r = the interest rate per month (10%/12 = 0.00833)
n = the total number of monthly withdrawals (20 years * 12 months per year = 240)
Plugging in the values, we get:
PMT = 400,000 * 0.00833 / (1 - (1 + 0.00833)⁻²⁴⁰) = $3,548.50 (rounded to the nearest cent)
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A given triangle has vertices at (-3, 1) (2, 4) and (5, -3). If the triangle were rotated 360 degrees clockwise, the new coordinates would be:
The following table displays the number of sofas sold in a furniture store during certain months of the year.
Based on these data, the correct statement is B. The mean best describes the data.
What is the mean?The mean is one of the measures of central tendency.
The mean is also described as the average.
The average or mean is the quotient of the total data value divided by the number of data items.
Furniture Store Sofa Sales
January 255
February 234
March 263
April 229
May 248
Total sales = 1,229
The number of months of sales = 5
Mean = 245.8 (1,229 ÷ 5)
Thus, using the mean, we can conclude that the average sales from Januar to May were 245.8.
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Question Completion:The following table displays the number of sofas sold in a furniture store during certain months of the year.
Furniture Store Sofa Sales
January 255
February 234
March 263
April 229
May 248
Based on these data, which statement is correct?
A. There are outliers.
B. The mean best describes the data.
C. The median best describes the data.
D. The measure of variability that best describes the data is the IQR, 27.5.
What is the apparent solution set for the system of equations:
x ^ 2 + 3x - 2;
- x ^ 2 + 2x + 4
A) {(- 3.5, 0) , (-1.2, 0), (0.5, 0), (3.3, 0)}
B) {(0, 2), (1.5, - 4.25)}
C) {(- 2, - 4), (1.5, 4.75)}
D) {(0, 4), (1, 5)}
There are no apparent solutions that satisfy both equations.
We have,
The system of equations is:
x² + 3x - 2 = 0
-x² + 2x + 4 = 0
To find the solutions, we can solve each equation separately:
x² + 3x - 2 = 0
This equation can be factored as:
(x + 2)(x - 1) = 0
Setting each factor equal to zero gives:
x + 2 = 0
x = -2
And,
x - 1 = 0
x = 1
-x² + 2x + 4 = 0
This equation does not factor easily, so we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
For this equation, a = -1, b = 2, and c = 4.
Plugging in the values into the quadratic formula:
x = (-2 ± √(2² - 4(-1)(4))) / (2(-1))
x = (-2 ± √(4 + 16)) / (-2)
x = (-2 ± √20) / (-2)
Simplifying further:
x = (-2 ± 2√5) / (-2)
x = 1 ± √5
Now,
let's check which of these solutions satisfies both equations:
For x = -2:
(-2)² + 3(-2) - 2 = 4 - 6 - 2 = -4 ≠ 0
-(-2)² + 2(-2) + 4 = -4 - 4 + 4 = -4 ≠ 0
x = -2 does not satisfy both equations.
For x = 1:
1² + 3(1) - 2 = 1 + 3 - 2 = 2 ≠ 0
-(1)² + 2(1) + 4 = -1 + 2 + 4 = 5 ≠ 0
x = 1 does not satisfy both equations.
For x = 1 ± √5:
We can substitute these values into the equations, but it can be seen that they will not satisfy both equations either.
Therefore,
There are no apparent solutions that satisfy both equations.
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need help on this math question
The expression which gives the number of months passed in terms of p is √300 -0.5p
Subject of formulaWe make t the subject of the formula in the expression
p = 600 - 2t²
subtract 600 from both sides in other to isolate 2t²
p - 600 = 600 - 2t² - 600
p - 600 = -2t²
Rearrange the equation
2t² = 600 - p
Divide both sides by 2 in other to isolate t²
2t²/2 = 600/2 - p/2
t² = 300 - 0.5p
Take the Square root of both sides in other to isolate t
√t² = √300 - 0.5p
t = √300 - 0.5p
Hence, the correct expression which gives the number of months t in terms of price p is t = √300 - 0.5p
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what is an equation in point-slope form of the line shown in the graph, using the point (-2,-1)
The equation of the line in point-slope form, using the point (-2, -1), is: y + 1 = -2(x + 2)
How to Write the Equation of a Line in Point-slope Form?The equation of a line in point-slope form is given by y - y₁ = m(x - x₁), where (x₁, y₁) represents a point on the line and m represents the slope.
Given:
Slope (m) = rise/run = -2
Point (-2, -1)
Substituting the given slope and point into the equation, we have:
y - (-1) = -2(x - (-2))
y + 1 = -2(x + 2)
Therefore, the equation of the line is: y + 1 = -2(x + 2).
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John borrowed $4,300.00 for 8 days at an annual simple interest rate of 13.75%. What is the amount of interest will John have to pay at the end of the loan?
John will have to pay $12.24 in interest at the end of the loan.
To calculate the amount of interest John will have to pay at the end of the loan, we can use the formula for simple interest:
Interest = Principal * Rate * Time
Given:
Principal (P) = $4,300.00
Rate (R) = 13.75% per annum
Time (T) = 8 days
First, we need to convert the rate from an annual percentage to a daily rate. Since there are 365 days in a year:
Daily Rate = (Rate / 100) / 365 = (13.75 / 100) / 365 = 0.0003767
Now we can calculate the interest:
Interest = Principal * Rate * Time
= $4,300.00 * 0.0003767 * 8
= $12.24
Therefore, John will have to pay $12.24 in interest at the end of the loan.
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what gives the response the sequare of the highwr common fact of 30 and 50
Answer:
GCF of 30 and 50 is 10 :}
Raina wants to buy a new house but needs money for the down payment. Her parents agree to lend her money at an annual rate of 6%, charged as simple
interest. They lend her $7000 for 5 years. She makes no payments except the one at the end of that time.
Answer the following questions. If necessary, refer to the list of financial formulas.
(a) How much total interest will Raina have to pay?
(b) What will the total repayment amount be (including interest)?
$
X
a. Raina will have to pay a total of $2100 in interest.
b. The total repayment amount, including interest, will be $9100.
How to Calculate Total Interest?To calculate the total interest and total repayment amount, we can use the formula for simple interest:
Simple Interest = Principal * Rate * Time
(a) Total interest:
Principal = $7000
Rate = 6% per year
Time = 5 years
Total Interest = Principal * Rate * Time
= $7000 * 0.06 * 5
= $2100
(b) Total Repayment Amount = Principal + Total Interest
= $7000 + $2100
= $9100
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