The monthly payment of a 30-year amount $450,000 mortgage with an interest rate of 4.2% is $2,071.09.
P = 450000
r = 0.042
n = 30
M = 450000 * 0.042/12 * (1 + 0.042/12)^360 / (1 + 0.042/12)^360-1
M = $2,071.09
a) There are 26 letters in the English alphabet so the number of six-letter passwords that can be formed from letters in the English alphabet if a letter can only be used once is 26P_6 = 26!/(26 - 6)! = 26!/(20!) = 300,750,000
b) There are 10 digits (0,1,2,3,4,5,6,7,8,9) so the number of passwords that can be formed if the digits 0, 1, 2, ..., 9 can be used is 10P_6 = 10!/(10 - 6)! = 10!/(4!) = 5040.
The monthly payment of a 30-year amount $450,000 mortgage with an interest rate of 4.2% is $2,071.09. There are 300,750,000 six-letter passwords that can be formed from letters in the English alphabet if a letter can only be used once, and there are 5040 pass-words that can be formed if the digits 0, 1, 2, ..., 9 can be used.
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a car dealership sells SUVs and passenger cars for a recent year 20 more suvs were sold than passenger cars if a total of 480 were sold determine the number of each type of vehicle sold
if a total of 480 were sold then the number of each type of vehicle sold is,
250 SUVs230 passenger carsWhat is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
A car dealership sells SUVs and passenger cars
the number of each type of vehicle sold = ?
Let x be the number of passenger cars sold.
Then, the number of SUVs sold = x + 20
The combined total of the two types of vehicles sold was 480, so we can write an equation:
x + (x + 20) = 480
Expanding the right side:
2x + 20 = 480
Subtracting 20 from both sides:
2x = 460
Dividing both sides by 2:
x = 230
The number of SUVs sold = 230 + 20
= 250
So, 230 passenger cars were sold and 250 SUVs were sold.
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Curtis wears a uniform number that rounds to 50 to the nearest ten and 0 to the nearest hundred. What is the least uniform number that curtis can have
Least number of uniform = 45
What is rounding numbers?Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.
Given,
Curtis wears a uniform number that rounds to 50 to the nearest ten and 0 to the nearest hundred.
Whole numbers, that can be rounded to 50 to the nearest ten are
45, 46, 47, 48, 49, 50, 51, 52, 53, 54
Smallest number is 45
Hence, 45 is the least uniform number Curtis can have.
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Antoine is renting a car for a day to drive to his sister's college and back. He estimates that the college is about 60 miles away. Low Price Rentals charges a $49 rental fee plus $0.16 per mile driven. Easy Rental charges a $25 fee plus $0.50 per mile.
Compare the two rental options.
Which company offers a better deal? How do you know?
Select the option that correctly answers both questions.
Responses
Easy Rental, because it will charge $55.00 for the trip, while Low Price Rentals will charge $58.60 (wrong answer)
Easy Rental, because it will charge $34.60 for the trip, while Low Price Rentals will charge $79.00
Low Price Rentals, because it will charge $68.20 for the trip, while Easy Rental will charge $85.00
Low Price Rentals, because it will charge $44.20 for the trip, while Easy Rental will charge $109.00
Answer:
(c) Low Price Rentals, because it will charge $68.20 for the trip, while Easy Rental will charge $85.00.
Step-by-step explanation:
You want to compare two car rental options for a 120-mile trip. Low Price charges $49 and $0.16 per mile; Easy charges $25 and $0.50 per mile.
GraphWe find it convenient to use a graphing calculator to plot the rental charges versus mileage. We find the charges to be ...
Low Price Rentals: $68.20 . . . . better deal (lower price)Easy Rental: $85.00CalculatorYou can also evaluate the charges by adding the fixed fee to the mileage cost for each option, as in the second attachment.
characteristic of algebraic expressions
I will give you the brainliest of the brainliest. I wish I had my notes but I don't sadly
Answer:
1 4
2 c³,c²,c,-11
3 1/3
4 -1
5 3/4
A trough is made from a rectangular piece of metal by folding up the sides as shown in the figure below. What should be the value of x so that the volume is 48 m³? (Let d= 6.
Enter your answers as a comma-separated list.)
The value of x is 2 so that the volume is 48 m³
What is the Volume and Area of Rectangle?The area of a rectangle is the region occupied within the boundary of the rectangle.
The formula of the area of a rectangle is used to find the area occupied by the rectangle within its boundary. The area of a rectangle is obtained by multiplying its length and width (breadth).
Area of a Rectangle = Length × Width
Volume of a rectangular solid is the product of the length, width, and height.
Volume of a rectangular solid in terms of the area of the base. The area of the base B is equal to Length × Width
Base = Length × Width
Volume of rectangular solid = Base × Height
Given:
Length of rectangular piece of metal = 10 - 2x
Breadth of rectangular piece of metal = 8 - 2x
Area of rectangle = Length × Width
(10 - 2x) (8 - 2x) = 24
80 - 20x - 16x + 4x² = 24
4x² - 36x + 56 = 0
Divide by 4, we get,x² - 9x + 14 = 0
x² - 7x - 2x + 14 = 0
x(x - 7) -2(x - 7) = 0
(x - 2)(x - 7) = 0
x = 2 and x = 7(Not possible)
when x = 2 cm (height)
Volume = Area of Base × height
Volume = 24 × 2
Volume = 48 cm³
So, the value of x is 2.
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Brad's rectangular backyard has an area of . The white circle represents the portion of Brad's yard that water from his sprinkler reaches and has an area of . . Write an expression to represent the gray region, the area of his yard that the water from the sprinkler does not reach .
Answer: Let's call the area of Brad's rectangular backyard "A". The area of the white circle is "C". The area of the gray region, the portion of the yard that the water from the sprinkler does not reach, is "G".
We know that the sum of the areas of the white circle and the gray region is equal to the area of Brad's backyard:
C + G = A
Therefore, the expression to represent the gray region is:
G = A - C
Step-by-step explanation:
Which graph best represents the system of inequalities below?
y ≤ 1/2x+1
y > -2x+4
The correct graph is the last one (where the shaded region is on the right side)
Which graph represents the system of inequalities?Here we have the system of inequalities below:
y ≤ 1/2x+1
y > -2x+4
The first inequality is:
y ≤ 1/2x+1
Here we have a solid line with positive slope, and the shaded region is below that line.
The second inequality is:
y > -2x+4
This time we will have a dashed line with negative slope, and the shaded region must be above the line, then the correct option will be the last option.
(where the shaded region is on the right quadrant)
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30 points NEED HELP URGENTLY
Answer:
The current population in Algeria can be calculated by solving the equation P = 38(1+r)^t, where P is the population in millions after t years. Setting t = 0 gives us the current population: P = 38(1+r)^0 = 38, so the current population in Algeria is 38 million.
A least squares regression line was calculated to relate the length (cm) of newborn boys to their weight in kg. The line is . A newborn was cm long and weighed kg. According to the regression model, what was his residual? What does that say about him?
The Residual is 0.944 kg.
What is Residual ?The discrepancy between a response variable's observed value and its expected value as predicted by the regression line.
Given:
Residual is typically defined as actuals minus predicted.
The prediction is calculated from
W = −6.07 + 0.1693L
W = −6.07 + 0.1693(48)
W = 2.0564 kg
And, The actual was 3 kg
So, the residual
= 3 - 2.0564
= 0.9436
= 0.944 kg
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if P= -10, find the value of p² - 2P - 100
Answer:
solution
we assume the negative part because their is no squares of negative number.
10²-2(-10)-100
we get answer which is 20
Given (11,6)
and (x,−9)
, find all x
such that the distance between these two points is 17
. Separate multiple answers with a comma.
All possible values of 'x' such that the distance between the points is 17 is, x = 19 or x = 3.
What is the distance formula between two points?The distance formula between two points (x₁, y₁) and (x₂, y₂) is,
[tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex].
Given, (x₁, y₁) = (11, 6) and (x₂, y₂) = (x,- 9) and the distance between them
is 17 units.
Therefore, The equation can be constructed as,
[tex]17 = \sqrt{(x - 11)^2 + (- 9 - 6)^2[/tex].
[tex]17 = \sqrt{(x - 11)^2 + 225[/tex].
Taking squares on both sides to remove the square root we have,
289 = (x - 11)² + 225.
289 = x² - 22x + 121 + 225.
x² - 22x + 57 = 0.
x² - 19x - 3x + 57 = 0.
x(x - 19) - 3(x + 19) =0.
x = 19 or x = 3 are the two possible points.
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in the fall of 2014, 1 U.S. dollar was worth 1.10 canadian dollars. an automobile in toronto sells for 26,000 canadian dollars. you found the same car on sale for 23,000 U.S. dollars on the internet. Which is the better buy?
This would be in contemporary math, converting fractions.
A car is through internet is better to buy.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
In the fall of 2014,
1 U.S. dollar = 1.10 Canadian dollars.
Here, An automobile in Toronto sells for 26,000 Canadian dollars.
And, The same car on sale for 23,000 U.S. dollars on the internet.
Thus, The cost of car on internet is,
⇒ 23,000 U.S. dollars
⇒ 23,000 × 1.10 Canadian dollars.
⇒ 25,300 Canadian dollars.
Thus, A car is buy through internet is better to buy.
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If we get another sample of 100 observations from this population, find the 95% confidence interval for population mean. What can you say about the effect of the sample size on the confidence interval?
The 95% confidence interval for mean of the population is CI = (3.81,6.19).
What is confidence interval?
The confidence interval for the population mean can be found when we know the sample mean and the margin of error of the interval. This last value depends on the standard deviation, the sample size and the confidence level of the interval.
The sample size is n = 100.
The sample mean is x' = 5
The sample standard deviation is s = 6
The confidence level is 1 - α = 0.95
Find the Probability Distribution.
Let [tex]x_1,x_2,....,x_n[/tex] be a random sample of size n taken from a normal distribution with unknown mean μ and unknown variance σ².
The random variable t with formula t = (x' - μ) / (s/√n) has a t distribution with (n - 1) degrees of freedom.
[tex]t_\frac{\alpha}{2}[/tex]
1 - α = 0.95
α = 1 - 0.95
α = 0.05
α / 2 = 0.05 / 2
α / 2 = 0.025
The degree of freedom is -
d.f = n - 1
d.f = 100 - 1
d.f = 99
So, [tex]t_\frac{\alpha}{2}[/tex] using the t-distribution table is -
[tex]t_\frac{\alpha}{2} = 1.984[/tex]
To illustrate the use of the table, note that the t-value with 99 degrees of freedom having an area of 0.025 to the right is [tex]t_\frac{\alpha}{2} = 1.984[/tex].
Then the Confidence interval is -
CI = x' ± [tex]t_{\frac{\alpha}{2},n-1}[/tex] × s/√n
CI = 5 ± 1.984 × 6/√100
CI = 5 ± 1.984 × 6/10
CI = 5 ± 1.984 × 0.6
CI = (5 - 1.19) (5 + 1.19)
CI = (3.81,6.19)
Therefore, the confidence interval is CI = (3.81,6.19).
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A random sample of 100 observations from a population yields a mean equal to 5 and a standard deviation equal to 6. What is the 95% confidence interval for the mean of the population?
Andrea placed $1700 in a savings account compounded monthly at 2.5%. What is the value of her account after 8 years?
Answer:
Step-by-step explanation:
To calculate the value of Andrea's savings account after 8 years, we need to find the balance after compounding the interest for 96 months (8 years x 12 months per year). We can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
where:
A is the balance after t years,
P is the initial balance ($1700),
r is the annual interest rate (2.5%),
n is the number of times interest is compounded in a year (12),
t is the number of years (8).
Converting the interest rate to a decimal and dividing by the number of times compounded per year:
r/n = 2.5% / 12 = 0.021
Plugging in the values into the formula:
A = 1700 * (1 + 0.021)^(12 * 8) = 1700 * (1.021)^96
Calculating the value:
A = 1700 * 2.8412 = 4860.80
So, the value of Andrea's account after 8 years would be $4860.80.
Simplify: (3h^3)(6h)(h^0)
Answer:
(3^2*2h^4)
Step-by-step explanation:
A standard piano keyboard has 88 different keys. Find the probability that a cat, jumping on 7 keys in sequence and at random (possibly with repetition), will strike the first seven notes of Beethoven's Fifth Symphony. (Leave your answer as a formula.)
The probability that a cat, jumping on 7 keys in sequence and at random (possibly with repetition), will strike the first seven notes of Beethoven's Fifth Symphony is; P = 2.45 * 10⁻¹⁴
How to find the probability of selection?The parameters expressed are;
Number of Piano Keyboard keys = 88
The following steps can be used in order to determine the probability that a cat, jumping on 7 keys in sequence and at random, will strike the first four notes of Beethoven's Fifth Symphony:
Step 1 - The four notes of the piano are 3 LA's and 1 REb.
Step 2 - The probability that the first key is LA is 1/88.
Step 3 - The probability that the second key is LA is 1/88.
Step 4 - The probability that the third key is LA is 1/88.
Step 5 - The probability that the key is REb is 1/88.
Step 6 - So, the probability that a cat, jumping on 4 keys in sequence and at random, will strike the first four notes of Beethoven's Fifth Symphony is:
P = 1/88 * 1/88 * 1/88 * 1/88 * 1/88 * 1/88 * 1/88
P = 2.45 * 10⁻¹⁴
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A car can be rented for $100 per week plus $0.40 per mile. How many miles can be driven if you have at most $240 to spend for weekly transportation?
Answer:
350
Step-by-step explanation:
calculator
what is difference between centripetal and centrifugal force describe them with example
Force is required to make an object move, and force acts differently on objects depending on the type of motion it exhibits. In the case of curvilinear motion, a special force comes into the picture, i.e., centripetal force – literally meaning “centre seeking.” Centripetal force is the force acting towards the centre of the circular path. In this article, let us discuss what centripetal force is and how it is different from centrifugal force.
Pls help me figure it out
The volume of the concrete required to be poured for a rectangular prism floor slab are;
11. 5 1/3 cubic yards
12. 74 2/27 cubic yards
What is a rectangular prism?A rectangular prism is a polyhedron that consists of six rectangular faces, in which the adjacent faces are perpendicular and opposite faces are parallel.
11. The dimensions of the floor slab = 18' × 24' × 4''
Where the shape of the slab is a rectangular prism, we get;
Width of the floor slab = 24 feet
Length of the floor slab = 18 feet
Height of the floor slab = 4 inches
4 inches = (1/3) ft
The volume of the cement is therefore;
V = 24 ft × 18 ft × (1/3) ft = 144 ft³
The volume of the concrete required to pour a floor slab of the dimensions: 18' × 24' × 4'' is 144 cubic feet
1 yard = 3 feet
The dimensions of the slab are therefore;
Length = 24/3 yards = 8 yards
Width = 18/3 yards = 6 yards
Height = (1/3)/3 yards = (1/9) yards
The volume of the slab = 8 yards × 6 yards× 1/9 yard = 16/3 cubic yards
Volume of the concrete slab = 16/3 cubic yards = 5 1/3 cubic yards12. The dimensions of the slab are;
Length of the slab = 80 feet = 80/3 yards
Width of the slab = 60 feet = 60/3 yards = 20 yards
Height of the slab = 5 inches = 5/12 ft = 5/(12 × 3) yard = 5/36 yard
The volume of the concrete slab is therefore;
(80/3) yards × 20 yards × (5/36) yard = 74 2/27 cubic yards
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What decimal number do the base 10 blocks represent?
x divided by 12; x =2/3
Step-by-step explanation:
x÷12
2/3/12
2×12/3
24/3
8
Determine the monthly principal and interest payment for a 15-year mortgage when the amount financed is $75,000 and the annual percentage rate (APR) is 8.0%.
The monthly principal and interest payment is $_____?
(Round to the nearest cent as needed.)
The monthly principal and interest payment is $916.6.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
From the given information SI = (75000×8×15)/100.
SI = 750×8×15.
SI = $90000.
Therefore, A = P + SI = 75000 + 90000 = $165000.
In 15 years there is 15×12 = 180 months.
Therefore, the monthly payment is,
= $(165000/180).
= $916.6
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Shelter A has a capacity of 300 beds and is 20% occupied. Shelter B is 60% occupied. The ratio of the occupancy of Shelter A to Shelter B is 1 : 15. How many beds are in Shelter B?
Answer:
1,500 beds
Step-by-step explanation:
Occupancy rate shelter A = 300 x 20/100 = 60
Let capacity of shelter B be X
60% occupancy ==> 60/100 x X = 0.6X
Occupancy rate of A to rate of B is 1: 15 can be expressed as fraction 1/15
Therefore
60/0.6X = 1/15
1 x 0.6X = 60 x 15
0.6X = 900
X = 900/0.6 = 1,500 beds
Which of the below are equations of exponential graphs?
The equations which give exponential graphs are y = 5ˣ and y = (1/5)ˣ.
What is an exponential graph?
A curve that depicts an exponential function is known as an exponential graph. A curve with a horizontal asymptote and either an increasing slope or a decreasing slope is called an exponential graph. The graph begins as a horizontal line and then grows or decays slowly at first before accelerating.
The general formula for an exponential function is,
f(x) = aˣ
Where the input values of the function, which is x, appear as the exponent of the function.
The values x can be all real numbers.
The base of the function (a) should be a constant. It should be greater than 0 and should not be equal to 1.
Following the above prerequisites, the equations which give exponential graphs are y = 5ˣ and y = (1/5)ˣ.
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If a rock is thrown upward on the planet Mars with a velocity of 17 m/s, its height (in meters) after t seconds is given by H = 17t - 1.86t2.
The velocity of the rock after one second is v(1)=13.28 m/s.
The given equation is
H(t) = 17t - 1.86t² ------(1)
velicity=17 m/s.
(a) the velocity of the rock after one second will be:
v(t) = dH/dt = 17-3.72t
v(1) = 17 - 3.72(1)
v(1)= 13.28 m/s
(b)the velocity of the rock when t=a
v(a) = 17 - 3.72a.
(c)
The rock hits the surface when H(t) = 0
17t - 1.86t² = t(17-1.86t)=0
⇒ t= 0 or 17-1.86t = 0
The first case is launch, the second is returning to the ground.
17 - 1.86t = 0
17= 1.86t
t = 17/1.86
t ≅9.139s
(d)
v at surface = v at the time from part (c).
v(9.139) = 17- 3.72(9.139)
v(9.139) ≅ -17 m/s
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Full question:
if a rock is thrown upward on the planet mars with a velocity of 17 m/s, its height (in meters) after t seconds is given by H=17t-1.86t²
(a) find the velocity of the rock after one second
(b) find the velocity of the rock when t=a
(c) when will the rock hit the surface
(d) with what velocity will the rock hit the surface?
Aidan and Bella each plan to open a savings account. Aidan starts with $90 and plans to save $20 every month. Bella starts with $15 and plans to save $35 every month.
Aidan and Bella will have the exact same amount of savings in 5 months.
What are simultaneous equations?We know two simultaneous equations have a unique solution when they intersect at a point,
when they are parallel they have no solution and when they are coinciding they have an infinite no. of solutions.
From the given information, Let the number of months be 'm'.
And, The two equations are 90 + 20x and 15 + 35x.
Therefore, The number of months in which they will have the same amount of savings would be,
90 + 20x = 15 + 35x.
75 = 15x.
x = 5.
So, In 5 months they will have the same amount of savings.
Q. Aidan and Bella each plan to open a savings account. Aidan starts with $90 and plans to save $20 every month. Bella starts with $15 and plans to save $35 every month, in which month they will have the same amount of savings?
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A Set of 4 parallel line intersect with another 2 lines set of 5 paralel lines . how many parallelograms are formed
Write an equation for the nth term of each arithmetic sequence. Then find the 12th term of the sequence.
as = -9, d = 2
The 12th term of the sequence with a first term of -9 and common difference of 2 is 13
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
An nth term of arithmetic term is given as:
[tex]a_n=a+(n-1)d[/tex]
where a is the first term and d is the common difference and n is the term.
Given that a = -9, d = 2
The 12th term of the sequence is:
a₁₂ = -9 + (12 - 1)2
a₁₂ = -9 + 22
a₁₁ = 13
The 12th term of the sequence is 13
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what is 2 divided by 1/8
Answer:
[tex] \frac{1}{16} [/tex]
ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
Answer:
16 is correct
Step-by-step explanation:
Your welcome
question this rectangular prism was built with cubes that each have a volume of one cubic centimeter. what is the volume of the rectangular prism?'
The volume of the rectangular prism is 400 cubic centimeters which we can calculate using formula: Volume = L * W * H
The volume of rectangular prism can be computed by simply multiplying their dimensions. If the rectangular prism was built with cubes that each have a volume of one cubic centimeter, then the volume of the rectangular prism can be calculated by multiplying the number of cubes in each dimension.
Let's assume that the rectangular prism has a length of "L" cubes, a width of "W" cubes, and a height of "H" cubes. Then, the volume of the rectangular prism can be calculated as follows:
Volume = L * W * H
Each cube has a volume of one cubic centimeter, so the volume of the rectangular prism is equal to the number of cubes it contains. In other words, if the rectangular prism has 10 cubes along its length, 5 cubes along its width, and 8 cubes along its height, then its volume would be:
Volume = 10 * 5 * 8 = 400 cubic centimeters
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