The answer would be ≈60mph, hence the answer is B.
helppppppppppppppppppppp
Danielle poured 3/4 gallon of water from a 7/8 gallon bucket. How much water is left in the bucket?
Which expression represents the number of sides in the polygon for the nth member of the pattern? A) n + 3 B) n3 C) n + 2 D) 3n
Ben and Marge are purchasing a house with a 20-year, 5/1 ARM for $265,000 at 5.25% with a 3/12 cap structure. What will the difference in payments be from year 5 to year 6?
A. $925.81
B. $880.29
C. $369.32
D. $234.39
The difference in payments from year 5 to year 6 is approximately $369.32 for the 5/1 ARM mortgage.
To calculate the payment difference from year 5 to year 6 for a 5/1 ARM (Adjustable Rate Mortgage) with a 3/12 cap structure, we need to understand how the ARM works and how the caps affect the adjustment.
1. Initial Mortgage Parameters :
- Loan Amount: $265,000
- Interest Rate: 5.25%
- Term: 20 years
2. Adjustment Frequency : The 5/1 ARM adjusts after the initial 5-year fixed period, then annually.
3. Cap Structure :
- Initial Adjustment Cap: 3%
- Subsequent Adjustment Cap: Each year after the initial adjustment, the rate can adjust up to 3% from the previous rate.
4. Calculation Steps :
a. Calculate the initial monthly payment using the loan amount, interest rate, and term.
b. Determine the new interest rate for year 6 based on the cap structure.
c. Calculate the monthly payment for year 6 with the new interest rate.
d. Find the difference between the payments from year 5 to year 6.
Let's start the calculations:
a. Calculate the initial monthly payment using the loan amount, interest rate, and term. We'll use the formula for a fixed-rate mortgage:
[tex]\[ P = \frac{P_r \cdot A}{1 - (1 + r)^{-n}} \][/tex]
Where:
- [tex]\( P \)[/tex] = Monthly Payment
- [tex]\( P_r \)[/tex] = Periodic Interest Rate (annual rate divided by 12)
- [tex]\( A \)[/tex] = Loan Amount
- [tex]\( r \)[/tex] = Periodic Interest Rate
- [tex]\( n \)[/tex] = Total number of payments (loan term in years multiplied by 12)
For the initial fixed period of 5 years:
[tex]\[ P_r = \frac{5.25\%}{12} = 0.004375 \][/tex]
[tex]\[ n = 20 \times 12 = 240 \][/tex]
Plugging these values into the formula:
[tex]\[ P = \frac{0.004375 \cdot 265000}{1 - (1 + 0.004375)^{-240}} \][/tex]
[tex]\[ P \approx 1645.80 \][/tex]
So, the initial monthly payment is approximately $1,645.80.
b. Determine the new interest rate for year 6 :
- The initial rate can adjust up to 3% in year 6.
- So, the new interest rate could be up to \( 5.25\% + 3\% = 8.25\% \).
c. Calculate the monthly payment for year 6 :
- Use the formula for the monthly payment again with the new interest rate:
[tex]\[ P_r = \frac{8.25\%}{12} = 0.006875 \][/tex]
Plugging into the formula:
[tex]\[ P = \frac{0.006875 \cdot 265000}{1 - (1 + 0.006875)^{-240}} \][/tex]
[tex]\[ P \approx 1985.09 \][/tex]
So, the monthly payment for year 6 is approximately $1,985.09.
d. Find the difference in payments from year 5 to year 6:
[tex]\[ Difference = Payment_{Year6} - Payment_{Year5} \][/tex]
[tex]\[ Difference = 1985.09 - 1645.80 \][/tex]
[tex]\[ Difference \approx 339.29 \][/tex]
So, the difference in payments from year 5 to year 6 is approximately $339.29.
Therefore, the closest answer is C. $369.32 .
Joan has 45 marbles . MARY HAS m marbles if Joan has 15 times as many marbles , write an equation that shows how many marbles mary has
Mary has 3 marbles.
Explanation:To find out how many marbles Mary has, we can use the information that Joan has 45 marbles and Joan has 15 times as many marbles as Mary. So, we can set up an equation:
45 = 15m
To solve for m, we divide both sides of the equation by 15:
m = 45/15
Simplifying the expression, we get:
m = 3
Therefore, Mary has 3 marbles.
The formula used to find the length of a line segment in space.
if youre doing the vocab thing -- Distance
Which is the ratio for sin a written as a fraction in simplest form
your Answer issss:
√3/2
An inscribed angle has a measure of 48°. Determine the measure of the intercepted arc.
24° 48° 72° 96°
An ellipse has vertices along the major axis at (0, 1) and (0, −9). The foci of the ellipse are located at (0, −1) and (0, −7). The equation of the ellipse is in the form below.
The equation of the ellipse is required.
The required equation is [tex]\dfrac{x^2}{16}+\dfrac{(y+4)^2}{25}=1[/tex]
It can be see that the major axis is parallel to the y axis.
The major axis points are
[tex](h,k+a)=(0,1)[/tex]
[tex](h,k-a)=(0,-9)[/tex]
[tex]k+a=1[/tex]
[tex]k-a=-9[/tex]
Subtracting the equations
[tex]2a=10\\\Rightarrow a=5[/tex]
The foci are
[tex](h,k+c)=(0,-1)[/tex]
[tex](h,k-c)=(0,-7)[/tex]
[tex]k+c=-1[/tex]
[tex]k-c=-7[/tex]
Subtracting the equations
[tex]2c=6\\\Rightarrow c=3[/tex]
[tex]k+c=-1\\\Rightarrow k=-1-c\\\Rightarrow k=-1-3\\\Rightarrow k=-4[/tex]
Foci is given by
[tex]c^2=a^2-b^2\\\Rightarrow b=\sqrt{a^2-c^2}\\\Rightarrow b=\sqrt{5^2-3^2}=4[/tex]
The equation is
[tex]\dfrac{(x-h)^2}{b^2}+\dfrac{(x-k)^2}{a^2}=1\\\Rightarrow \dfrac{(x-0)^2}{4^2}+\dfrac{(y+4)^2}{5^2}=1\\\Rightarrow \dfrac{x^2}{16}+\dfrac{(y+4)^2}{25}=1[/tex]
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Is .8/100 equal to .8%
Would be glad if you answer my question!
Which linear inequality is represented by the graph? y > 2/3x – 1/5 y ≥ 3/2x + 1/5 y ≤ 2/3x + 1/5 y < 3/2x – 1/5
Answer: The correct option is third, i.e., [tex]y\geq \frac{3}{2} x+\frac{1}{5}[/tex].
Explanation:
From the figure it is noticed that the line passing through the points (0,0.2) and (3,2.2).
The equation of line passing through two points is,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
[tex]y-0.2=\frac{2.2-0.2}{3-0}(x-0)[/tex]
[tex]y-\frac{1}{5} =\frac{2}{3} x[/tex]
[tex]y =\frac{2}{3} x+\frac{1}{5}[/tex]
The equation of the line is [tex]y =\frac{2}{3} x+\frac{1}{5}[/tex].
From the figure it is noticed that as the value of x increases the value of y is less.
he point (1,0) lies on the shaded reason it means this point must satisfy the equation.
[tex](0)=\frac{2}{3} (1)+\frac{1}{5}[/tex]
[tex](0)=\frac{2}{3} +\frac{1}{5}[/tex]
[tex](0)=\frac{10+3}{15}[/tex]
[tex](0)=\frac{13}{15}[/tex]
It is true of the sign is less than or equal to instead of equal.
[tex]y \leq \frac{2}{3} x+\frac{1}{5}[/tex]
Therefore, option third is correct.
PLEASE HELP
Is this A, B, or C?
if the remainder on division of x^3+2x^2+kx+3 by x-3 is 21,find the quotient and the value of k. Hence,find the zeroes of the cubic polynomial x^3+2x^2+kx-18.
A group of college students are volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Irina can paint a certain room in 9 hours. Paulo can paint the same room in 8 hours. Write an equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room? If necessary, round your answer to the nearest hundredth
The combined work rate can be found by using the equation for combined rate.
The correct responses;The time it will take them working together is; [tex]\displaystyle \underline{\frac{1}{t_b} = \frac{1}{t_1} + \frac{1}{t_2} }[/tex]The number of hours it will take them working together to paint the room is approximately 4.24 hours. The method by which the above responses are obtained:The time it takes Irina to paint the room alone, t₁ = 9 hours
Time it takes Paulo to paint the room, t₂ = 8 hours
Required:
To write the equation for the combined rate of Irina and Paulo
Solution:The equation that gives the time, [tex]\mathbf{t_b}[/tex], it will take both Irina and Paulo to paint the room together is given by the combined rate formula, as follows;
[tex]\displaystyle \underline{ \frac{1}{t_b} = \frac{1}{t_1} + \frac{1}{t_2}}[/tex]Required:The duration it will take them to paint the room when working together.
Solution:The time it will take them to paint the room together is found as follows;
[tex]\displaystyle \frac{1}{t_b} = \mathbf{\frac{1}{9} + \frac{1}{8}}[/tex]
Which gives;
[tex]\displaystyle \frac{1}{t_b} = \frac{8 + 9}{9 \times 8} = \mathbf{\frac{17}{72}}[/tex]
Therefore;
[tex]\displaystyle t_b = \frac{72}{17} \approx \mathbf{4.24}[/tex]
The time it takes Irina and Paulo to paint together, [tex]t_b[/tex] ≈ 4.24 hrs.Learn more about combined rate of work here:
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Can someone help me please!!!
in a given circuit, the supplied voltage is 1.5 volts, and the resistor value is 3 ohms. use ohm's law to determine the current in the circuit
Final answer:
The current in a circuit with a supplied voltage of 1.5 volts and a resistance of 3 ohms is calculated using Ohm's Law (I = V/R), resulting in a current of 0.5 amperes.
Explanation:
Using Ohm's Law to Calculate Current
To determine the current in a circuit with a supplied voltage of 1.5 volts and a resistor value of 3 ohms, we can use Ohm's Law, which is stated as I = V/R, where I is the current, V is the voltage, and R is the resistance. Plugging in the values, we have I = 1.5 volts / 3 ohms. Therefore, I = 0.5 amperes or 500 milliamperes. This is the current flowing through the circuit.
Ohm's Law is a fundamental principle in physics used for analyzing simple circuits where the relationship between voltage, current, and resistance is linear. Remember that this law holds true for ohmic materials where the resistance remains constant over a range of voltages and temperatures.
A small plane leaves an airport at a speed of 252 miles per hour. A jet leaves the airport 2 hours later traveling at 672 miles per hour. How long will the small plane be flying before the jet catches up to it? What unit will you use for your answer?
No, thanks to you, I got the question wrong it was hours.
Use the Remainder Theorem to find the remainder: (–6x3 + 3x2 – 4) ÷ (2x – 3).
23
-17.5
-4.4444444...
-0.8888888...
The remainder obtained when we carry out the operation (-6x³ + 3x² - 4) ÷ (2x - 3) is -17.5 (2nd option)
How do i determine the remainder?The following data were obtained from the question:
Expression = (-6x³ + 3x² - 4) ÷ (2x - 3)Remainder =?Using the remainder theorem, we can obtain the remainder as illustrated below:
Let
f(x) = -6x³ + 3x² - 4
2x - 3 = 0
From 2x - 3 = 0, make x the subject as shown below:
2x - 3 = 0
x = 3/2
Substitute the value of x into f(x). We have:
f(x) = -6x³ + 3x² - 4
f(3/2) = -6(3/2)³ + 3(3/2)² - 4
= -6(27/8) + 3(9/4) - 4
= -20.25 + 6.75 - 4
= -17.5
Thus, we can conclude that the remainder obtained when (-6x³ + 3x² - 4) is divided by (2x - 3) is -17.5 (2nd option)
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Which list shows all the factors of 18?
1, 2, 3, 4, 6, 9, 18
1, 2, 3, 6, 9, 18
2, 3, 4, 6, 9
2, 3, 6, 9
In a Quadratic Regression problem, a graph is a perfect fit for the data when r = ? a. 1 c. 2 b. 0 d. 100 Please select the best answer from the choices provided A B C D
Answer:
the answer is A on edge :)
Step-by-step explanation:
The graph that is a perfect fit for the given data in a quadratic regression problem is when r is; A: 1
What is a quadratic regression?Quadratic regression is defined as a statistical technique that is used to find the equation of the parabola that best fits a set of data.
Now, this type of regression is an extension of simple linear regression that is used to find the equation of the straight line that best fits a set of data.
Thus, in this type of regression, we say a graph is a perfect fit when r = 1.
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Which graph represents the function over the interval [−3, 3]?
Third graphrepresents the function [tex]f\left( x \right) = \left\lfloor x \right\rfloor-2[/tex] over the interval [tex]\left[ { - 3,3} \right].[/tex]
Further explanation:
Given:
The function is [tex]f\left( x \right) = \left\lfloor x \right\rfloor- 2.[/tex]
The function is defined in the interval [tex]\left[ {-3,3}\right].[/tex]
Explanation:
The greatest integer function is represented [tex]y = \left\lfloor x \right\rfloor.[/tex]
The greatest integer can also be known as floor function. The function is integral part of real numbers.
The values of greatest function [tex]f\left( x \right)= \left\lfloorx \right\rfloor- 2[/tex] in interval [tex]\left[{ - 3,3}\right][/tex] can be obtained as follows,
Substitute [tex]-3[/tex] for [tex]x[/tex] in the function [tex]f\left( x \right)= \left\lfloor x \right\rfloor- 2.[/tex]
[tex]\begin{aligned}f\left({- 3} \right)&=\left\lfloor{ - 3} \right\rfloor- 2\\&=- 3- 2\\&=- 5\\\end{aligned}[/tex]
Substitute [tex]3[/tex] for [tex]x[/tex] in the function [tex]f\left( x \right)=\left\lfloor x \right\rfloor- 2.[/tex]
[tex]\begin{aligned}f\left( 3 \right)&= \left\lfloor3\right\rfloor- 2\\&=3- 2\\&=1\\\end{aligned}[/tex]
The minimum value of the function in [tex]\left[ { - 3,3} \right] {\text{is}\: \boxed{ - 5}.[/tex]
The maximum value of the function in [tex]\left[ { - 3,3} \right] {\text{is}\: \boxed{1}.[/tex]
Third graphrepresents the function [tex]f\left( x \right)=\left\lfloor x\right\rfloor- 2[/tex] over the interval [tex]\left[{ - 3,3}\right].[/tex]
Kindly refer to the image attached.
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Number system
Keywords: factor, factorization, polynomial, quadratic, cubic, greatest common factor, groups, multiplication, product, identities, common factor, expression, terms, grouping.
At a furniture manufacturer, worker A can assemble a shelving unit in 5 hours. Worker B can assemble the same shelving unit in 3 hours. Which equation can be used to find t, the time it takes for worker A and worker B to assemble a shelving unit together?
The equation 1/t = 1/5 + 1/3 can be used to find the time it takes for worker A and worker B to assemble a shelving unit together.
To find the time t it takes for worker A and worker B to assemble a shelving unit together, we need to add their work rates.
Worker A's work rate is 1 unit per 5 hours (or 1/5 units per hour), and worker B's work rate is 1 unit per 3 hours (or 1/3 units per hour).
The combined work rate is the sum of their individual work rates:
1/5 + 1/3 = (3 + 5) / 15 = 8 / 15 units per hour
If t is the time they take together to complete one shelving unit, then their combined work rate is 1 unit per t hours. Setting this equal to their combined rate, we get:
1/t = 8/15
Solving for t gives:
t = 15/8 hours
Therefore, the equation 1/t = 1/5 + 1/3 can be used to find the time it takes for worker A and worker B to assemble a shelving unit together.
The city of Beijing has a population of more than 10 to the 7th power people. Write 10 to the 7th power without using an exponent
Answer:
[tex]10\times 10\times 10\times 10\times 10\times 10 \times 10[/tex]
Step-by-step explanation:
Exponentiation is the operation used to write the product of two or more equal factors. This expression can written as follows:
[tex]a^n\\\\Where:\\\\a=Base\\n=Exponent[/tex]
That is, [tex]a^n[/tex] is the product of multiplying n bases:
[tex]a^n=a\times...\times...\times a[/tex]
In this sense:
[tex]10^7=10\times 10\times 10\times 10\times 10\times 10 \times 10[/tex]
Instructions:Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
is parallel to . and are perpendicular to and .
The ratio of the lengths of and is
:
.
Answer:
The ratio of the lengths of PR and QS is 1 : 1
Step-by-step explanation:
If your question is based on this exercise:
PQ Is parallel to RS. PR and QS are perpendicular to PQ and RS
Here is why
A rectangle is 2 times as long as it is wide. if the area is 18 square feet, find its perimeter.
What is the circumference of a circle with a radius of 6.1 centimeters? Enter your answer as a decimal in the box. Use 3.14 for pi. Round your answer to the nearest tenth. cm
If a 10. m3 volume of air (acting as an ideal gas) is at a pressure of 760 mm and a temperature of 27 degrees Celsius is taken to a high altitude where the pressure is 400. mm Hg and a temperature of -23 degrees Celsius, what volume will it occupy? (Hint: remember the temperature must be in Kelvin)
Answer:
16. m3
Step-by-step explanation:
27 degrees Celsius= 27+273= 300 kelvin
23 degrees Celsius= -23+273=250 kelvin
Combined Gas Law: P1V1/T1 = P2V2/T2
(760mm*10 m3)/300 K=(400mm*x m3)/250 K x= 16. m3
The volume that it will occupy is 16. m3.
(Don't forget the sig fig, 15.83--->16. because the question said 10.)
If a < 0 and b > 0, then the point (a, b) is in Quadrant A) I. B) II. C) III. D) IV.
Answer:
The actual answer is D
The point (a, b) lies in the second quadrant. Then the correct option is B.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
If a < 0 and b > 0.
Then the point (a, b) is in Quadrant will be given as,
If a > 0 and b > 0, then the points is in first quadrant.If a < 0 and b > 0, then the points is in second quadrant.If a < 0 and b < 0, then the points is in third quadrant.If a > 0 and b < 0, then the points is in fourth quadrant.Thus, the point (a, b) lies in the second quadrant.
Then the correct option is B.
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Tickets for the school play cost $17 each. Gary wrote the expression n X 17 to find the cost of n tickets to the play. He used the Distributive Property to find the product. Use the Distributive Property to write Gary's expression another way.