Madeline is financing $321,800 to purchase a house. How much money will she save over the life of a 20 year fixed rate loan by buying five points with the rate of 4.23% instead of not buying points with the rate of 5.18%? Round to the nearest dollar. (show work)
A= $39,984
B= $23,894
C= $36,697
D= $36,766
Suppose you want to organize a community watch, one from each street. you have 5 volunteers from maple street and 3 volunteers from elm street. how many permutations do you get?
tom has twice as much as peter. peter has half as much as Mary. together they all have a total of $15.00. how much money did each have?
Below is the graph of y=b^x. Find b.
Functions can be represented as equations, and equations can be represented as functions.
The value of b is 1/2
The graph is given as:
[tex]\mathbf{y = b^x}[/tex]
From the graph, we have the following point:
(x,y) = (-1,2)
Substitute these values in the function
[tex]\mathbf{2 = b^{-1}}[/tex]
Rewrite as:
[tex]\mathbf{2 = \frac{1}{b}}[/tex]
Multiply both sides by b
[tex]\mathbf{2b = 1}[/tex]
Divide both sides by 2
[tex]\mathbf{b = \frac{1}2}[/tex]
Hence, the value of b is 1/2
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5 plus 5 divided by 2 times 300032 plus 6
Find the first derivative?
y = 1/(x - 2) - 3
y' = d(x - 2)^-1 / dx The three is a constant and will disappear.
y' = d(x - 2)^-1 -1 d(x - 2)/dx
y' = -1*(x - 2)^-2 * 1
The minus comes from bringing down the original power down and reducing the power by one of the question. The 1 at the end comes from differentiating what is inside the brackets. It is called the chain rule
d(x - 2) / dx = d(x) / dx which is 1. The two, being a constant, disappears. The final answer is
y' = - (x - 2)^-2
Answer:
[tex]\displaystyle y' = \frac{-1}{(x - 2)^2}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \frac{1}{x - 2} - 2[/tex]
Step 2: Differentiate
Derivative Rule [Quotient Rule]: [tex]\displaystyle y' = \frac{1'(x - 2) - 1(x - 2)'}{(x - 2)^2}[/tex]Basic Power Rule [Derivative Property - Addition/Subtraction]: [tex]\displaystyle y' = \frac{-1(1)}{(x - 2)^2}[/tex]Simplify: [tex]\displaystyle y' = \frac{-1}{(x - 2)^2}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
An electrician can wire a house in 20 hours. if she works with an apprentice, the same job can be completed in 12 hours. how long would it take the apprentice, working alone, to wire the house?
It would take the apprentice 30 hours to wire the house alone.
Explanation:Let's assume that the work done by the electrician alone in 1 hour is represented by E, and the work done by the apprentice alone in 1 hour is represented by A. According to the given information, the electrician can wire the house in 20 hours, so E = 1/20. When the electrician and the apprentice work together, they can wire the house in 12 hours, so their combined work in 1 hour is represented by (E + A) = 1/12.
To find out how long it would take the apprentice to wire the house alone, we can subtract the work done by the electrician in 1 hour (E) from the combined work done by both the electrician and the apprentice in 1 hour (E + A), which gives us A = (E + A) - E. Substitute the values:
A = (1/12) - (1/20) = (20 - 12) / (12 x 20) = 8 / 240 = 1/30.
So, the apprentice can wire the house alone in 30 hours.
In this figure, angle 3 = (2x+15) and angle 6 = (3x+10)
What value of x makes a || b?
A ball is thrown into the air with an upward velocity of 32 ft/s. Its height (h) in feet after t seconds is given by the function h= -16t^2 + 32t + 6. How long does it take the ball to reach its maximum height? What is the ball’s maximum height? Roun
helppp how do u do 12
1)
At 1 pm the shadow of a tree is 14 feet long. At the same time the shadow of a 18 foot telephone pole is 21 feet long. What is the height of the tree?
A) 9 feet
B) 12 feet
C) 18 feet
D) 22 feet
Using 125 words or more, write a short paragraph discussing the reasons why someone should make a wil
A will tells everyone what will happen to your money, possessions, and property when you die. There are many reasons to make a will. First, it will be easier for your family and friends to sort everything out. Without a will, it can be very stressful and time consuming to figure out how to allocate everything. Plus, if you don't have a will the law will decide how to allocate it and this might not be the way you want it. It can be especially important to write a will if you have children or other family that depend on you financially. This way, you can leave them the most possible to help them even when you are no longer alive. By writing a will, you can decrease the amount of inheritance tax that might need to be paid on any property and money that you will leave behind. Ultimately, by writing a will you will be able to decide who you leave your money, possessions, and property to when you die which can be very important to some individuals.
Joy started with 2.75 gallons of milk. She used 1.5 pints to make mashed potatoes and another cup to make cookies. How much milk does joy have left?
A newly hatched channel catfish typically weighs 0.3 grams. During the first 6 weeks of life, its growth is approximately exponential, increasing by about 10% each day. Find the weight at the end of four weeks. (Hint: Be sure to change the number of weeks to days before plugging into the formula!) Formula: A=C(1+r)t
0.53g
4.33g
16.43g
1.14g
The weight of a newly hatched channel catfish after four weeks of exponential growth is approximately 1.14 grams.
Explanation:To find the weight at the end of four weeks, we need to convert the number of weeks to days since the growth rate is given in terms of daily percentage increase. The formula to calculate exponential growth is A = C(1 + r)^t, where A is the final weight, C is the initial weight, r is the growth rate, and t is the number of periods. In this case, C = 0.3 grams, r = 0.10 (10% daily increase), and t = 4 weeks x 7 days/week = 28 days. Plugging in these values, we get A = 0.3(1 + 0.10)^28. Evaluating the expression, the weight at the end of four weeks is approximately 1.14 grams.
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A class's test scores are normally distributed. If the average score is 60 and the standard deviation is 7, choose the spots where the students scoring below 46 and above 74 lie.
Answer with Step-by-step explanation:
We are given that a class's test scores are normally distributed with the average score 60.
We know that the curve of a normal distribution is symmetric about its mean.
60-14=46
60+14=74
Hence, the point 46 lies to the left of the mean and 74 lies to the right of mean and the two points have the same function value
(since the graph is symmetric to the left and right of mean i.e. points which are equidistant from the mean have same values)
Answer:
One of the answers I got that was correct was the box on the furthest left.
Step-by-step explanation:
There are 5 cars to be displayed in 5 parking spaces, with all the cars facing the same direction. of the 5 cars, 3 are red, 1 is blue, and 1 is yellow. if the cars are identical except for color, how many different display arrangements of the 5 cars are possible?
The question relates to combinatorial mathematics and asks for possible arrangements of 5 cars of three different colors. Treating identical colors as one entity, we find that there are 6 ways to arrange the color groups and another 6 ways to arrange the red cars among themselves, resulting in 36 possible arrangements.
Explanation:The subject of this question is combinatorial mathematics. We're asked how many different arrangements there are if we have 5 cars to be displayed in 5 parking spaces, with the condition that the cars are identical besides their color; 3 of them are red, 1 is blue, and 1 is yellow.
Since three cars are identical (red ones), we treat them as one. So initially, we have three 'entities' to arrange: the red group (of 3 cars), the blue car, and the yellow car. These can be arranged in 3! (which means 3 factorial, or 3 * 2 * 1) = 6 ways.
However, within the red group, those 3 red cars can be arranged amongst themselves in 3! = 6 ways.
Therefore, to get the total number of arrangements, we multiply these results together, giving us: 6 * 6 = 36 different arrangements.
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find two consecutive even integers such that twice the smaller is 16 more than the larger
A plane is flying at an altitude of 32,000 feet. The distance between the plane and a radio tower on the ground is 50,000 feet. What is the angle of depression between the plane and radio tower (round to 1 decimal place)?
An irregularly shaped stone was lowered into a graduated cylinder holding a volume of water equal to 20mL. The height of the water rose to 30.2mL. If the mass of the stone was 25g what was its density?
To find the density of the stone, subtract the initial volume of water from the final volume, then divide the mass of the stone by the volume. The density of the stone is 2.45 g/cm³.
Explanation:In order to find the density of the stone, we first need to calculate its volume. The volume can be determined by subtracting the initial volume of water in the graduated cylinder from the final volume with the stone submerged. In this case, the volume of the stone is 30.2 mL - 20 mL = 10.2 mL.
Next, we can use the formula for density: density = mass/volume. Plugging in the given values, we have density = 25 g/10.2 mL.
Since density is mass divided by volume, we need to convert mL to g/cm³. 1 mL is equal to 1 g/cm³. Therefore, the density of the stone is 25 g/10.2 mL = 2.45 g/cm³.
A 4-foot tall person standing with her back to the sun casts an 6-foot long shadow. To the nearest degree, what angle does the sun make with the ground?
Find the absolute maximum value of the function
How do you find the lateral area of the prism
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Choose the equation that represents the graph below:
Answers:
y = −2x − 6
y = 2/3x + 6
y = −2/3x + 6
y = 2x + 6
When a parabola represented by the equation y - 2x 2 = 8 x + 5 is translated 3 units to the left and 2 units up, the new parabola has its vertex at
Brian wants to build a ramp that leads to a storeroom 5 meters above the ground. He wants the ramp to be 10 meters long. What should the angle of elevation of the ramp be?
15°
30°
45°
60°
Answer:
It would be 30
Step-by-step explanation:
I did it on plato
width = (b - a)/n = (8 - 0)/4 = 2
2(f(0) + f(2) + f(4) + f(6))
2(-1 - 2.5 - 1.5 - 0.5)
2(-5.5)
-11
Is my answer C, -11? The question says four subintervals, so I used f(0), f(2), f(4), and f(6). I want to make sure that I am NOT supposed to be using f(8), because f(8) would give me a final answer of D. -13.5
Nearly 90 percent of the people of indonesia are _______.
Answer: Muslims
Total Muslims in Indonesia is approximately 207.2 million or 87.2 (90%) of the total population. Other religions recognized by the Indonesian government aside from Islam are Protestant, Catholic, Hindu, Buddhism, and Confucian which accounts for 6.9,2.9,1.7,.7 and .05% of the total population, respectively.
Religion is a mandatory personal data to the Indonesians.
Answer:
MUSLIMS
Step-by-step explanation:
PLEASE HELP!! SO CONFUSED... WILL GIVE BRAINLIEST!!!
Amy owns a graphic design store. She purchases a new printer to use in her store.
The printer depreciates by a fixed rate of 14% per year. The function
V = 2,400(1 – 0.14)t can be used to model the value of the printer in dollars after
t years.
Question:
Part A: Explain what the parameter 2,400 represents in the equation of the function.
Part B: What is the factor by which the printer depreciates each year?
Part C: Amy also considered purchasing a printer that costs $4,000 and depreciates by 25% each year. Which printer will have more value in 5 years? Justify your answer by showing/explaining your work.
If 6 is 30% of a value,
a.what is 70% of that value? b8 is omlwhat is 10%of the value?
What does the underlined conjunction connect in the sentence? The family enjoyed fishing, but they loved hiking during their trip. A. sentences B. predicates C. subjects D. direct objects