Jason's trip was 9 minutes longer than his usual drive to work.
Given that,
Distance from Jason's home to office = 20 miles
Speed of driving from home to office = 50 miles/hour
Total time taken to reach from home to office = distance ÷ speed = 20/50 = 0.4 hours = 24 minutes
Thus, on a normal day, Jason takes 0.4 hours to reach his office from home.
Now, Jason drove for 12 minutes when his car broke down,
The taxi arrived 15 minutes later and drove at 40 miles/hour,
Total time spent to reach office from taxi= distance ÷ speed = 20/40 = 0.5 hours= 30 minutes
Although he already spent 12 minutes driving before the taxi arrived so,
30 - 12 = 18 minutes.
But, he waited for the taxi to arrive for 15 minutes so,
18+15 = 33 minutes.
Thus, today Jason took 33 minutes to reach the office from his home.
Therefore, Jason took (33- 24)minutes which is equal to 9 minutes longer than his usual drive to work.
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find the inequality represented by the graph
A cube with side length 5h^2 is sTacked on another cube with side length 3k . What is the total volume of the cubes in factored form?
(5h^2)^3 + (3k)^3
(5h^2 + 3k) + (25h^4 - 15 h^2k + 9k^2)
(5h^2 + 3k) + (25h^4 + 15 h^2k + 9k^2)
(5h^2 + 3k)^3
The correct option is Option A: (5h^2)^3 + (3k)^3
The total number of cubic units that the cube totally occupies is the definition of a cube's volume. A cube is a solid three-dimensional object with six square faces. Volume is simply the total amount of space an object takes up. A thing with a bigger volume would take up more room.
Total Volume = V₁ + V₂
V₁ = Volume of Cube 1
V₂ = Volume of Cube 2
Volume of Cube = (Side Length)³
V₁ = (5h²)³
V₂ = (3k)³
∴ Total Volume = (5h²)³ + (3k)³
And this cannot be simplified further.
Therefore, the correct option is Option A: (5h^2)^3 + (3k)^3
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!!! 20 POINTS !!!
It will take you t seconds to carry the water, which you will do y times a day. What is the total amount of
time you will be carrying water?
How many hours would you spend carrying water in a year?
Answer:
To find the total amount of time you will be carrying water, we can use the following formula : Total time = t x y (t represents the time taken to carry water in seconds and y represents the number of times you will carry water per day)To find how many hours you would spend carrying water in a year, we can use the following formula:Total hours = (total time in seconds) / (3600 seconds in an hour)
Note: Remember to convert the result from seconds to hours.
It's important to mention that you need to know the value of t and y to be able to calculate the total time and the total hours.
If you have the values, you can substitute them in the equations above and get the answer.
I need help bru im from Chicago need help
Answer:
3.20
Step-by-step explanation:
a ship leaves port at noon and has a bearing of the ship sails at 20 knots. how many nautical miles south and how many nautical miles west will the ship have traveled by 6:00 p.m.?
On solving the provided question we can say that the equation gives us 101.77 mi S; 63.59 mi W and S 39.4° W; 131.7 nautical miles
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence.
The ship will have traveled 120 nautical miles in the six hours between noon and six o'clock using the formula distance = speed time distance (20 nm/h) (6 h).
The location of the ship will be in (S, W) coordinates.
[tex]120(cos(32), sin(32)) ≈ 120(0.848048, 0.529919) ≈ (101.77, 63.59)[/tex]
The ship will have traveled 101.77 miles south and 63.59 miles west.
83.59). The distance from port will be ...
[tex]d = √(101.77^2 +83.59^2) = 131.7\\ arctan(83.59/101.77) ≈ 39.4[/tex]
The bearing and distance are ...
S 39.4° W
131.7 nautical miles
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Which statement is the best interpretation of the value 29,864 in the quadratic regression equation?
The company has an initial loss of about $29,864.
The company has an initial profit of about $29,864.
The company needs to sell about 29,864 units to break even.
The company needs to sell about 29,864 units to maximize its profit.
The interpretation of the value, 29,864, in the quadratic regression equation is the initial loss incurred by the company. The correct option is therefore;
The company has an initial loss of about $29,864What is a quadratic regression equation?A quadratic regression equation is the equation of the parabola that corresponds of best fits the points of the dataset on the coordinate plane.
The points on the graph of the question, obtained from a similar question, posted online are;
Number of units [tex]{}[/tex] Profits ($)
500 [tex]{}[/tex] -10000
1200 [tex]{}[/tex] 3000
2500 [tex]{}[/tex] 27000
3200 [tex]{}[/tex] 40000
3600 [tex]{}[/tex] 45000
4300 [tex]{}[/tex] 47000
5000 [tex]{}[/tex] 45000
6750 [tex]{}[/tex] 20000
The polynomial regression equation that corresponds to the points in the above table, obtained with MS Excel is presented as follows;
y = -0.004·x² + 34.637·x - 29864
Where;
y = The profit made
x = Number of units
When the company produces 0 units, x = 0, we get;
y = -0.004 × 0² + 34.637 × 0 - 29864 = -29864The 29864 is therefore the loss of $29864, of the company when the company produces zero units.
The correct option is therefore;
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For each pair of triangles below, state
whether the triangles are congruent, not
congruent or if it is impossible to tell.
a)
65°
27 cm
38 cm
19 cm
65°
27 cm
43°
43°
b)
80°
58°
42°
42°
80°
58%
C)
12 cm
82°
12 cm
37°
37%
82°
Answer: all are congruent
Step-by-step explanation:
a. The pair of triangles are not congruent.
b. It is impossible to tell about congruency.
c. The pair of triangles are congruent.
Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
These triangles can be slides, rotated, flipped and turned to be looked identical.
a. The given triangles are not congruent.
The triangle has same measures but the side lengths are different.
So the pair of triangles are not congruent.
b. The given pair of triangles are might be congruent if they have side lengths same.
But in the given triangles the side lengths are not measured.
So it is impossible to tell.
c. The given pair of triangles have same measures and same side lengths.
By AAS rule the pair of triangles are congruent.
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In the isosceles triangle has an interior angle measuring 134 degrees, what is the measure of each of the other two?.
Answer:
23°Step-by-step explanation:
In the isosceles triangle has an interior angle measuring 134 degrees, what is the measure of each of the other two?.the sum of the interior angles in a triangle is 180°, take away the know angle and divide by 2, it's an isosceles triangle so 2 side and 2 equal angles
(180 - 134) : 2 = (remember PEMDAS)
46 : 2 =
23°
----------------------------
check23 + 23 + 134 = 180°
the answer is good2.If the sum of three integers is a negative integer, we can say WITH CERTAINTY that A all the three integers are equal. B two of the three integers are positive and one is negative. C one of the three integers is positive and two are negative. D at least one of the three integers is negative.
Answer:
D)
That is the only one we can be certain with.
1st option is obviously incorrect
2nd option is wrong as it can also be two are negative one is positive
3rd option is wrong as it can also be one is negative two are positive
4th option is correct as u can't get negative values without a negative numberl.
hat is the probability that an ace appears at the 9th place, and a queen appears at the 10th place in the deck?
The probability that an ace appears at the 9th place, and a queen appears at the 10th place in the deck is 1/221.
What is Probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given:
The probability that an ace appears at the 9th place, and a queen appears at the 10th place in the deck can be calculated as:
There is a total of 52 cards in a deck and 4 aces and 4 queen cards.
So, the probability is
4/52 * 4/51 = 1/221
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3. Pencils are sold at a unit rate of 36 pencils per box.
Use the variables and number in the box to write an equation to
represent the proportional relationship. The letter b represents the
number of boxes, and p represents the total number of pencils.
Use the unit rate as the constant of proportionality.
Numbers and letters cannot be used more than once. Write
each number or letter in the appropriate box.
36
b
Р
HINT, H
The unit rates
constant of p
the equation
where m is th
proportional
The constant of proportionality for the proportional equation is 36.
Option A is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 9 is an equation.
We have,
Box = b
Number of pencils in one box.
p = 36
Now,
The proportional equation for b and p.
p ∝ b
p = mb
where m is the constant of proportionality.
Now,
b = 1
p = 36
p = mb
36 = m x 1
m = 36
Thus,
The constant of proportionality is 36.
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Merchandise inventory includes: (You may select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a wrong answer. Any boxes left with a question mark will be automatically graded as incorrect.)\
Therefore , solution of unitary method problem The cost of the items purchased, the cost of shipping and handling, the cost of transit insurance.
What exactly is a unitary method?The unitary approach is a method of problem solving that entails first calculating the percentage of a single set there is, then doubling that value to arrive at the solution. The unit technique, to put it simply, is used to extract a typical programming value from a given many. For instance, the price of 40 pens is 400 rupees ($1.01), meaning Rs. It's feasible that the method used to achieve this will be controlled in only one nation.
Here,
The finished goods kept in inventory are those that will be sold to clients.
All items that are owned by a business and kept for sale are included in the merchandise inventory.
a retail business:
purchases and sales of goods generate its net income.
It can also purchase goods from producers and market them to retailers.
It can also be a retailer or a wholesaler, purchasing goods from producers and selling them to clients.
The term "current asset" refers to merchandise inventory.
Therefore , The cost of the items purchased, the cost of shipping and handling, the cost of transit insurance, and the cost of storage are all included in the merchandise inventory account.
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How do you solve ratio word problems in 7th grade?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other
What is an equivalent ratios?
A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.
Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.
Given ratios are 2:1 and 3:1
we can write it as 2/1 and 3/1.
The lcm of 2 and 3 is 6.
Multiply denominator of both ratio with 6, we get
2/6 and 3/6 And we can see both the ratios are not equal.
Hence, there are not equivalent ratios.
4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2
11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)
3:1 and 9:3 are equivalent ratios ------> is true
because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3
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After\ flying\ at\ an\ altitude\ of\ 600\ meters,\ a\ hot\ air\ balloon\ starts\ to\ descend.\ its\ g\operatorname{round}\ \operatorname{distance}\ from\ the\ landing\ pad\ is\ 10,000\ meters.\ What\ is\ the\ angle\ of\ depression,\ in\ degrees,\ \operatorname{for}\ this\ part\ of\ the\ flight\
Using the tangent side from trigonometric ratio, the angle of depression is 86.6 degrees
What is Angle of DepressionThe angle created between the line of sight to a location below the horizontal line and the horizontal line of sight is known as the angle of depression.
The angle of depression that the balloon makes with the launch pad can be calculated using the trigonometric ratio.
Data;
Opposite = 10000madjacent = 600angle = ?Since we have the opposite and adjacent side, we can use the tangent of the angle to find the angle of depression.
tanθ = opposite / adjacent
substituting the values into the formula
tan θ = 10000 / 600
tan θ = 100 / 6
tan θ = 16.666
θ = tan⁻¹(16.666)
θ = 86.6°
The angle of depression is 86.6°
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Please assist with C ii
Solve the equation 1-2/x^2 = -x-1
x = ?
The value of x in the expression 1 - (2/x²) = - x - 1 is ± √2, 4.
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, An expression 1 - (2/x²) = - x - 1.
- (2/x²) + x = 2.
Multiplying each term by x².
- 2 + x³ = 2x².
x³ - 2x² = 2.
x²(x - 2) = 2.
x² = 2 ⇒ x = ± √2 Or x - 2 = 2 ⇒ x = 4.
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Please help, i know you have to use pythagoras and the hypotenuse is 8.44 but i dont know how to get one of the sides
======================================================
Explanation:
Check out the diagram below.
I've defined the following points:
A = center of the circle, and center of the squareB, C, D, and E = vertices of the square that are on the circleF = midpoint of segment CDNow focus on triangle ACF. This is an isosceles right triangle with legs of 0.5x each. The hypotenuse is the radius of the circle. Let R be that unknown radius.
The area of the circle is given to us. It is 56 square cm. Use this to find the value of R.
[tex]A = \pi*(\text{radius})^2\\\\56 = \pi*R^2\\\\R^2 = 56/\pi\\\\R = \sqrt{56/\pi}\\\\R = 4.22200825\\\\[/tex]
This value is approximate. I used the calculator's stored version of pi to get the most accuracy possible.
------------
We now know the hypotenuse of triangle ACF.
Use Pythagoras (aka Pythagorean Theorem) to have the following steps:
[tex]a^2+b^2 = c^2\\\\(0.5\text{x})^2+(0.5\text{x})^2 = 4.22200825^2\\\\0.25\text{x}^2+0.25\text{x}^2 = 17.82535366\\\\0.5\text{x}^2 = 17.82535366\\\\\text{x}^2 = 17.82535366/0.5\\\\\text{x}^2 = 35.65070732\\\\\text{x} = \sqrt{35.65070732}\\\\\text{x} = 5.97082132708726\\\\\text{x} = 5.97\\\\[/tex]
The final answer is 5.97With the exception of 0.5 and 0.25, each decimal value mentioned is approximate.
Keep in mind that rounding to 3 sig figs means that we're rounding to 2 decimal places. The units digit is 1 sig fig, and the 2 decimal places give a total of 1+2 = 3 sig figs.
In short, we're rounding to the nearest hundredth.
--------------------
Check:
x = 5.97 is the square's side length.
It divides in half to get x/2 = 5.97/2 = 2.985 which gives each leg of triangle ACF.
Use a = 2.985 and b = 2.985 in the Pythagorean Theorem to find that c = 4.22142748 approximately. This is the approximate radius of the circle.
Use that radius to find the area of the circle.
A = pi*r^2
A = pi*(4.22142748)^2
A = 55.984594705958
A = 56.0
I'm rounding the area to 3 sig figs to keep consistent with the rounding done to x. We arrive at the circle area of 56 square cm, which helps confirm the answer is correct.
Hey, so as you can see I know what the slope is, but i can't figure out the y intercept. Could someone please help me? Thanks!
Answer: (0, -1/3)
Step-by-step explanation: The answer is: (0, -1/3)
y=mx+b
Slope being "m"
And the y intercept being "b"
I think it's (0, -1/3)
......
..
in the hardy boys adventure while the clock ticked, the pendelum of the grandfather clock at the purdy place is 44 inches long and swings through an arc of 6. find the length of the arc taht the pendelum traces
On solving the provided question we can say that equation of pendulum traces an arc, s, that is roughly 4.61 inches long.
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
6° = 6° X [tex]\pi /180 = \pi /30[/tex]
s = r∅
s = 44 X [tex]\pi /30[/tex]
s = 4.61
Hence, The pendulum traces an arc, s, that is roughly 4.61 inches long.
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How do you know if there are no solutions?
If you attempt to solve an equation and the result is false, the problem has no solutions.
If both sides of a linear equation have unique constant values but the same variable term, then the problem has no solutions.
For instance, in the equation [tex]3x+8=1+3x[/tex],
the variable term is the same, [tex]3x[/tex], but the constant terms, 8 and 1, are on opposite sides of the equation. It, therefore, lacks solutions. Try the equation to determine why.
[tex]3x+8=1+3x\\8=1[/tex]
following mathematics, the term is not possible. so, here equation has no solutions. so how we can know that equation has no solution if mathematical inequality is wrong.
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please help me on this math question
Answer:
The formula for compound interest is: A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment (the amount Alex has at the end of 7 years)
P = the initial investment (£4000)
r = the annual interest rate (x/100)
n = the number of times interest is compounded per year (let's assume it is compounded annually)
t = the number of years invested (7)
Plugging in the given values and solving for x:
5263.73 = 4000(1 + x/100)^7
So x = ((5263.73/4000)^(1/7))-1*100
x = 6.33% (approximately)
So, the interest rate is 6.33%.
Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. Together they charged a total of $1150. What was the rate charged per hour by each mechanic if the sum of the two rates was $95 per hour?
Answer: Let's call the hourly rate of the first mechanic "r1" and the hourly rate of the second mechanic "r2".
We know that the total time they worked is 20 hours + 5 hours = 25 hours.
We also know that the sum of their hourly rates is $95 per hour, so:
r1 + r2 = $95
We can use this information along with the total amount they charged, $1150, to find out how much each mechanic charged. We know that the total amount charged is the product of the number of hours worked and the hourly rate. So we can use the following equation:
(20 hours * r1) + (5 hours * r2) = $1150
Now we can substitute the equation r1 + r2 = $95 into the above equation and solve for r1:
(20 hours * r1) + (5 hours * (95 - r1)) = $1150
20r1 + 475 - 5r1 = 1150
15r1 = 675
r1 = $45/hour
To find out the hourly rate of the second mechanic, we can use the equation r1 + r2 = $95
r2 = $95 - r1
r2 = $95 - $45
r2 = $50/hour
So the first mechanic charges $45 per hour and the second mechanic charges $50 per hour.
Step-by-step explanation:
An inurance company ell a $500,000 five-year term policy to a female. The monthly policy i m dollar. If the peron die 20 month after taking out the policy, expre the inurance company profit algebraically
The profit of the insurance company is -20x, where x is the monthly premium.
What is algebra?Algebra is a branch of mathematics that deals with the study of symbols and the rules for manipulating them. It is used to describe and analyze the relationship between numbers, variables, and operations. Algebra is used to solve equations and simplify expressions, and it is useful in a wide range of applications such as engineering, economics, and science. Algebra also helps us understand and explore abstract concepts such as equations, functions, and graphs. Algebraic thinking is a valuable skill that can help us to make sense of the world around us.
Let x = monthly premium
The insurance company's profit = (500,000 - 20x) - 500,000 = -20x
Therefore, the profit of the insurance company is -20x, where x is the monthly premium.
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angelina spent $23.65 on books and magazines when she went to chapters. She bought a total of 7 items. The books cost $5.95 each and the magazine cost $2.95 each. How many books and magazines did angelina buy
In all, she purchased 1 book and 6 periodicals, taking into account the inequality.
What is inequality?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given, Angelina spent $23.65 on books and magazines when she went to chapters. She bought a total of 7 items. The books cost $5.95 each and the magazine cost $2.95 each.
Let "b" be the number of total book and "m" be the number of magazine she bought.
Inequality from the given data
m + b = 7
since, Angelina spent $23.65 on books and magazines
thus,
5.95 * b + 2.95 * m = 23.65
from equation 1
5.95b + 2.95(7 - b) = 23.65
5.95b + 20.65 - 2.95b = 23.65
3 b = 3
b = 1
from any equation
m = 6
Therefore, she total bought 1 book and 6 magazines according the given inequality.
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Which expression is equivalent to 24(807). A 20(8)+4(8)+20(7)+
Answer:
C
Step-by-step explanation:
807 is equal to 800 + 7, and 24 is equal to 20 + 4. Using the distributive property, we get 20(800) + 4(800) + 20(7) + 20(7)
Answer:
C
Step-by-step explanation:
Because 24*807 in distributive property is C
what is the value of t? 7+8t-9=62
Answer:
t = 8
Step-by-step explanation:
8t - 2=62
8t =62+2
8t = 64
t = 64÷8
t = 8
Answer: t = 8
Step-by-step explanation:
Ekaterina’s favorite expression is 4x – 4. Alban’s favorite expression is 8x – 24. What value of x makes these two expressions equal?
Answer:
x = 5
Step-by-step explanation:
You are solving for a x that can, when plugged in, equate both given expressions. To do so, set each given expression equal to each other:
4x - 4 = 8x - 24
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& roots)
Multiplications
Divisions
Additions
Subtractions
~
First, subtract 8x and add 4 to both sides of the equation:
4x (-8x) - 4 (+4) = 8x (-8x) - 24 (+4)
4x - 8x = -24 + 4
-4x = -20
Next, divide -4 from both sides of the equation:
(-4x)/-4 = (-20)/-4
x = -20/-4
x = 5
5 is your answer.
Check:
Plug in 5 for x in both given expressions:
4x - 4
4(5) - 4
= 20 - 4
= 16
-
8x - 24
8(5) - 24
= 40 - 24
= 16
~
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A set of data with a normal distribution has a mean of 16.4 and a standard deviation of 3.2. 68% of the data falls between what two numbers?
68% of the data falls between one standard deviation from the mean which is 13.2 and 19.6
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The empirical rule states that 68% of the data falls within one standard deviation, 95% within two standard deviation from the mean and 99.7% falls within three standard deviation from the mean.
Given a mean of 16.4 and a standard deviation of 3.2.
68% of the data falls one standard deviation from the mean = 16.4 ± 3.2 = (13.2, 19.6)
68% of the data falls between 13.2 and 19.6
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use a linear approximation (or differentials) to estimate the given number. (1.999)5
The approximate value of [tex](1.999)^5[/tex] is 31.92.
Describe linear approximation :A linear approximations in maths is the use of a linear function to estimate a generic function. They are frequently used to create first order methods for solving or approximating equation solution in the method of finite difference.
To estimate [tex](1.999)^5[/tex]
we’ll find the linearization of f(x) = [tex]x^5[/tex]
at a = 2. Since
f′(x) = 5[tex]x^4[/tex]
, f(2) = 32, and
f′(2) = 80,
we have L(x) = 32+80(x−2). Thus,
[tex]x^5[/tex] ≈ 32 + 80(x − 2) when x is near 2,
so (1.999)5 ≈ 32 + 80(1.999 − 2) =
32 − 0.080 = 31.92.
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I need help with this problem ?
Answer:
398.32
Step-by-step explanation:
647.82 - 249.50 = 398.32
Jerome has $3,000 to invest in an account that yields 2.1% annual interest which is compounded quarterly. If he leaves the money untouched in the account for 4 years, how much money will he have?
Jerome will have $3261.93 after 4 years
How to calculate how much money Jerome will have?
The formula for compound interest is A = P(1 + r/n)^(nt)
where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for.
In this case, P = $3,000, n = 3, r = 2.1% = 0.021, t = 4 years. Thus:
A = P(1 + r/n)^(nt)
A = 3000(1 + 0.021/3)^(3×4)
A = 3000(1 + 0.021/3)^(12)
A = $3261.93
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