Mr. Yang invested the $1000 approximately 8.55 years ago
To calculate the time that Mr. Yang invested the money, you can use the formula for compound interest: A=P(1+r/n)^nt where A is the amount of money after t years, P is the initial principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years. We are given A= $1435.77, P=$1000, r=0.06, and n=2 (since interest is compounded twice per year). We want to solve for t, so we will rearrange the formula to solve for t:t=ln(A/P)/(n ln(1+r/n))Plugging in the values, we have: t= ln(1435.77/1000)/(2 ln(1+0.06/2)) ≈ 8.55 years, rounded to two decimal places.Therefore, Mr. Yang invested the $1000 approximately 8.55 years ago.
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suppose we draw 2500 samples of size 100 from a population and compute a 97% confidence interval for each sample. approximately how many of those intervals will contain the population mean?
There are approximately 2425 of those intervals that will contain the population means.
What is a confidence interval?A confidence interval is a range of values that includes a parameter estimate with a certain degree of certainty. A confidence interval is a measure of uncertainty about an estimation procedure, rather than a statement about a parameter. A confidence interval is a specific value or a range of values in statistics that is used to estimate population characteristics.
This is because a 97% confidence interval means that if we were to repeat the sampling process many times, about 97% of the resulting intervals would contain the population mean. In other words, we would expect 97% of the intervals to be "correct" in the long run, while about 3% of them would not contain the population mean.
Therefore, out of the 2500 intervals we compute, we would expect approximately 0.97 x 2500 = 2425 intervals to contain the population mean, and about 0.03 x 2500 = 75 intervals not to contain the population mean. However, it's important to note that the actual number of intervals that contain the population means may vary from this expected value due to random sampling variability.
Where, [tex]\[\bar{x}\][/tex] is the sample mean
[tex]\[\frac{s}{\sqrt{n}}\][/tex] is the standard error of the mean
zα/2 is the z-score that covers α/2 in the tails of a normal distribution.
As we draw 2500 samples of size 100 from a population and compute a 97% confidence interval for each sample, the proportion of the sample will contain the population means.
Therefore, the number of intervals that will contain the population mean is approximately 2425.
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the area of rectangular surface of a triangular prism having base sides 9 CM 10 cm and 17 cm is 864 CM square calculate the height of the prism
Answer:
The formula for the volume of a triangular prism is given by:
V = (1/2)bhL
where b is the base length of the triangle, h is the height of the triangle, and L is the length of the prism (i.e., the distance between the two triangular faces).
We are given the area of the rectangular surface of the prism, which is the product of the lengths of two adjacent sides of the rectangle, and we know that this area is equal to 864 cm^2. Therefore, we can use the Pythagorean theorem to find the length of the third side of the rectangle, which is also the base length of the triangular face:
17^2 = 9^2 + 10^2
289 = 81 + 100
289 = 181
So, the base length of the triangular face is 8 cm. Now we can plug in the known values into the formula for the volume of the prism:
864 = (1/2)(8 cm)(h)(L)
We are not given the length of the prism, L, but we know that it is equal to the base length of the triangle, which is 8 cm. Therefore, we can simplify the equation to:
864 = 32h
Solving for h, we get:
h = 864/32
h = 27
So the height of the prism is 27 cm.
A plane can fly 340 mph in still air. If it can fly 200 miles downwind in the same amount of time it can fly 140 miles upwind, find the velocity of the wind.
By using the speed fοrmula, the velοcity οf the wind is apprοximately 66.23 mph.
What is speed?Speed is defined as the distance travelled by an οbject in a given amοunt οf time. Speed is a scalar quantity, meaning that it has magnitude but nο directiοn. Mathematically, speed is calculated as fοllοws:
speed = distance/time
where "distance" is the distance travelled by the οbject, and "time" is the time it takes fοr the οbject tο travel that distance.
Let's assume that the speed οf the wind is represented by the variable "v" (in mph). When the plane flies dοwnwind, the speed οf the plane relative tο the grοund is the sum οf its airspeed and the wind speed, οr (340 + v) mph. Similarly, when the plane flies upwind, the speed οf the plane relative tο the grοund is the difference between its airspeed and the wind speed, οr (340 - v) mph.
Nοw, lets use the fοrmula:
time = distance / speed
tο set up twο equatiοns and sοlve fοr the wind speed "v".
First, fοr the dοwnwind flight:
time = distance / speed
200 / (340 + v) = t
Secοnd, fοr the upwind flight:
time = distance / speed
140 / (340 - v) = t
Since the time taken fοr bοth flights is the same, we can equate the twο equatiοns:
200 / (340 + v) = 140 / (340 - v)
Nοw, we can sοlve fοr "v":
200(340 - v) = 140(340 + v)
68,000 - 200v = 47,600 + 140v
308v = 20,400
v ≈ 66.23
Therefοre, the velοcity οf the wind is apprοximately 66.23 mph.
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A couple has $5,000 to invest and has to choose between three investment options.
• Option A: 2.25% interest applied each quarter
• Option B: 3% interest applied every 4 months
• Option C: 4.5% interest applied twice each year
If they plan on no deposits and no withdrawals for 5 years, which option will give them the largest
balance after 5 years? Use a mathematical model for each option to explain your choice. Share the
value of each investment.
Make sure you use the formula from the lesson for each option then compare. As an investment, you
want the option with the most money!
nt
A = P(1 +r )"nt
—
n
Use this tax table to find how much tax you need to pay on a taxable income of $25,000.
If taxable income is over-- But not over-- The tax is:
$0 $7,825 10 percent of the amount over $0
$7,825 $31,850 $782. 50 plus 15 percent of the amount over 7,825
$31,850 $77,100 $4,386. 25 plus 25 percent of the amount over 31,850
$77,100 $160,850 $15,698. 75 plus 28 percent of the amount over 77,100
$160,850 $349,700 $39,148. 75 plus 33 percent of the amount over 160,850
$349,700 no limit $101,469. 25 plus 35 percent of the amount over 349,700
On a taxable income of $25,000, you must pay $3,358.75 in taxes.
To find how much tax you need to pay on a taxable income of $25,000, you will need to use the tax table given.
Since $25,000 falls in the third row of the table, which is for taxable income over $7,825 but not over $31,850, we will need to use the formula for this row:
Tax = $782.50 + 15% of the amount over $7,825
To calculate the tax, we need to first find the amount over $7,825, which is:
25,000 - 7,825 = 17,175
Now we can substitute this into the formula to get:
Tax = 782.50 + 0.15 x 17,175
Tax = 782.50 + 2,576.25
Tax = 3,358.75
Therefore, the amount of tax you need to pay on a taxable income of $25,000 is $3,358.75.
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Find the value of $x$ . Write your answer in simplest form.
A right triangle is shown. The measure of one of the interior angles is 45 degrees. The length of one of the legs is 1 unit. The length of the hypotenuse is x units.
$x=$
Answer:
The length of the hypotenuse is $x=\sqrt{2}$ units. ($x=\√2$)
Explanation:
If one of the angles of a right triangle is 45 degrees, then the other acute angle is also 45 degrees. Let's label the other leg of the triangle as $y$ units.
Using the Pythagorean Theorem, we have:
$1^2 + y^2 = x^2$
Simplifying:
$1 + y^2 = x^2$
We can also use the fact that the ratio of the sides of a 45-45-90 triangle is $1:1:\sqrt{2}$ to write:
$\frac{x}{1}=\sqrt{2}$
Simplifying:
$x=\sqrt{2}$
Now, substituting this value of $x$ into our equation $1 + y^2 = x^2$, we have:
$1 + y^2 = (\sqrt{2})^2$
Simplifying:
$1 + y^2 = 2$
$y^2 = 1$
$y = 1$ (since we're looking for a positive length)
Therefore, the length of the hypotenuse is $x=\sqrt{2}$ units.
Hope this helps you, if not I'm sorry. If you need more help, ask me! :]
Is 14x + 2 equivalent to 16x?
Answer:
No
Step-by-step explanation:
14x + 2 ≠ 16x
Because 2 doesn't have an x variable, it can't be added with 14x!
Jessica earns 52 dollars per week working part- time at a book store she makes one dollar more for each book sells the amount,A(in dollars), that Jessica earns in a week if she sells b books is given by the following
The amount that Jessica will earns if she sells 34 books is 86 dollars.
How much will Jessica earns?An earning refers to the income that a person get from wages and salaries, security and other government benefits, dividends and interest, business ownership, other sources etc.
Our Equation to solve for earnings is:
A = 52 + (1)B
A = 52 + B
A(34) = 52 +34
A(34) = $86
Therefore, the total earned in one week if she sold 34 books is $86.
Missing words' Write an equation relating A to B. Then use this equation to find the amount of money Lena earns if she sells 34 books. Equation: Amount Jessica earns is she sells 34 books: ____ dollars".
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1)Sketch the function f(x)=1 /(x−2)^3 −8.
Calculate and show the x-intercepts and y-intercepts, as well as
the horizontal and vertical asymptotes. Must show all the steps in
the calculations in order to receive credit.
2) Calculate the average rate of change of f(x)=2x^3−3x^2−4x
from x=1 to x=3. Must show all the steps in the calculations in order to receive credit.
1) f(x) = 1/(x - 2)^3 - 8
2)f(x) from x = 1 to x = 3 is 15.5.
1) Sketch the function f(x) = 1/(x - 2)^3 - 8 and calculate its x-intercepts, y-intercepts, horizontal and vertical asymptotes.To sketch the function f(x) = 1/(x - 2)^3 - 8, we need to find the x-intercepts, y-intercepts, horizontal and vertical asymptotes. First, let's find the x-intercept. It's a point on the graph where the function intersects the x-axis, so y-coordinate should be zero.f(x) = 1/(x - 2)^3 - 8y = 0 = 1/(x - 2)^3 - 8⇒ 1/(x - 2)^3 = 8⇒ (x - 2)^3 = 1/8⇒ x - 2 = 1/2⇒ x = 2 + 1/2 = 5/2So, the x-intercept is (5/2, 0).Next, let's find the y-intercept. It's a point on the graph where the function intersects the y-axis, so x-coordinate should be zero.f(x) = 1/(x - 2)^3 - 8x = 0 = 1/(0 - 2)^3 - 8⇒ 1/(-2)^3 - 8 = -1/8 - 8 = -8 1/8So, the y-intercept is (0, -8 1/8).Next, let's find the horizontal asymptote. As x approaches infinity or negative infinity, the function approaches a certain value, which is the horizontal asymptote.To find the horizontal asymptote, we need to find the limit of f(x) as x approaches infinity.f(x) = 1/(x - 2)^3 - 8∴ as x → ∞, (x - 2)^3 → ∞⇒ 1/(x - 2)^3 → 0So, the horizontal asymptote is y = -8. To find the vertical asymptotes, we need to find the values of x that make the denominator of the fraction zero.f(x) = 1/(x - 2)^3 - 8x - 2 = 0 = (x - 2)^3⇒ x = 2So, the vertical asymptote is x = 2.Now, we can sketch the function as shown below. f(x) = 1/(x - 2)^3 - 8Answer:2) Calculate the average rate of change of f(x) = 2x^3 - 3x^2 - 4x from x = 1 to x = 3.To find the average rate of change of a function, we need to divide the change in the function by the change in the variable. In this case, the change in the variable is Δx = 3 - 1 = 2.f(x) = 2x^3 - 3x^2 - 4xf(1) = 2(1)^3 - 3(1)^2 - 4(1) = -5f(3) = 2(3)^3 - 3(3)^2 - 4(3) = 26So, the change in the function is Δf = f(3) - f(1) = 26 - (-5) = 31.Now, the average rate of change is given by,Δf/Δx = 31/2 = 15.5Therefore, the average rate of change of f(x) from x = 1 to x = 3 is 15.5.
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i dont know how to do this
the answer isnt 4
pls answer if u know with simple working
Answer:
13 matches
Step-by-step explanation:
Notice 1st have 4 matches
then 2nd have 7 matches (since one is shared), this is 8-1
then 3rd have 10 matches (since two are shared) this is 12-2
Notice the pattern 4 matches per square minus one per aditional square from the first.
This give an equation
4n-1(n-1)= 3n+1
lets check
For n=1 matches= 3(1)+1=4
For n=2 matches= 3(2)+1=7
For n=3 matches= 3(3)+1=10
It works.
so
For n=4 matches= 3(4)+1=13
Write the first 5 terms of a sequence whose general term, An, is given as an =-9n-9
The first 5 terms of the sequence, whose general term is an = -9n - 9, would be the following: -18, -27, -36, -45, -54.
How to Calculate the Terms of a Sequence?In mathematics, a sequence is an ordered list of numbers, called terms, that follow a particular pattern or rule. Each term in a sequence is identified by its position in the sequence, which is usually represented by an integer index or subscript.
To find the first 5 terms of the sequence with the general term an = -9n - 9, we can simply substitute the values of n from 1 to 5 into the formula and simplify:
a1 = -9(1) - 9 = -18
a2 = -9(2) - 9 = -27
a3 = -9(3) - 9 = -36
a4 = -9(4) - 9 = -45
a5 = -9(5) - 9 = -54
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Because of your amazing work maximizing the revenue for the math club, the basketball team wants you to help them. They want to know how much admission they should charge for their games to make the most money. The team manager tells you that when they charged $5 per ticket, they sold 600 tickets, but when they tried to charge $20 per ticket, they sold no tickets.
1. You can assume the relationship between the price of the ticket and the number of tickets sold is linear. Write a linear function “n” that models the number of tickets sold “n(p),” as a function of the price of a ticket, “p.”
2. To calculate revenue, you multiply the price of the ticket by the number of tickets sold. Write a function “r” that models the revenue generated by selling tickets, “r(p),” as a function of the price of the ticket, “p.”
3. Use your function “r” from question 2 to recommend a ticket price to the basketball team. Support your recommendation by explaining how much revenue they could generate from your ticket price versus a higher or lower price.
1. Linear function: n(p) = -40p + 800
2. r(p) = P. n(p)
3. Total revenue = $4000
What is the slope of a linear function?There are numerous formulas for deriving a line's equation using linear functions, depending on the available data.
With the exception of vertical lines, which are not functions, any line may have its equation found using a formula for a linear function.
In the question,
We can assume, we have two points:
(5, 600) and (20,0)
The slope:
0-600/20-5
= -40
So, n(p) = -40 (p-20)
n(p) = -40p +800
Now solving,
r(p) = P. n(p)
= -40p² + 800p
Now to calculate the revenue,
r'(p) = -2 × 40p + 800
= -80p + 800
Order r'(p) = 0
⇒ P = 10
The highest price is: $10.
Revenue = -40 × ($10) ² + 800 × $10 = $4000
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If the total surface area of a cube is 302.46 in², which best describes the length of an edge of the cube?
The length of the edge of the cube with the given total surface area is 7.1 inches.
What is total surface area?The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a form with a curved base and surface is equal to the sum of the two areas.
Let us suppose the length of an edge of the cube = l.
The total surface are of the cube is given as:
TSA = 6l²
Substituting TSA = 302.46 we have:
302.46 = 6l²
l² = 50.41
l = 7.1 in.
Hence, the length of the edge of the cube with the given total surface area is 7.1 inches.
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5.8 Khomo and Peter bought a house for R575 000 as an investment. Khomo payed R245 000 and Peter payed the rest. They sold the house 5 years later and made a profit of R234 500.if they share the profit in the same ratio as their respective investments,how much profit will peter recieve
Answer:
133,380
Step-by-step explanation:
Cost of house 575,000
Khomo paid 245,000
Peter paid 575,000 - 245,000 = 330,000
Ratio of Khomo to Peter = 245,000 : 330,000 = 49:66
Profit made = 234,500
Khomos share is 49/ 115 x 234,00 = 0.43 x 234,000 = 100,620
Peters share is 66/115 x 234,000 = =0.57 x 234,000 = 133,380
(-7+3)4 with work shown
Answer: -16
Step-by-step explanation:
First, we need to solve the parentheses by performing the operation inside them. (-7 + 3) equals -4, so we can substitute that in the expression to get:
(-7 + 3)4 = -4 × 4
Next, we can perform the multiplication operation:
-4 × 4 = -16
Therefore, (-7 + 3)4 = -16.
Answer:
-16
Step-by-step explanation:
First, you distribute 4 into the equation, basically multiplying, so 4 * 3 is 12, then 4 * -7 is -28. Add them together so -28 + 12 is -16
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During gym class, there were 7 teams in the four-square match. Each team was made of 5 third-graders.
Which shows how many students were in the four-square match in all?
1. 5 times 5
2. 5 minus 7
3. 7 times 5
4. 7 plus 5
7 times 5 shows the number of students in the four-square match. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
It is stated that the four fundamental operations, often known as "arithmetic operations," can explain all real numbers. Quotient, product, sum, and difference are the next four mathematical operations after division, multiplication, addition, and subtraction.
We are given that there were 7 teams in the four-square match and each team was made of 5 third-graders.
Now, in order to find the total students, we will use the multiplication operation.
From this, we get 7 times 5 which represents the total students.
Hence, 7 times 5 shows the number of students in the four-square match.
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A cylinder has a height of 30 ft and a volume of 63,679 ft³. what is the radius of the cylinder? round your answer to the nearest whole number. responses 676 ft 676 ft 338 ft 338 ft 52 ft 52 ft 26 ft
The correct response is (f) 26 ft. The radius of the cylinder is approximately 26 ft.
To solve for the radius, we can use the formula for the volume of a cylinder, V = πr²h, where V is the volume, r is the radius, and h is the height. We can plug in the given values to get:
63,679 = πr²(30)
Dividing both sides by 30π gives:
r² = 676
Taking the square root of both sides gives:
r ≈ 26
Rounding to the nearest whole number gives the answer of 26 ft. Therefore, the correct response is (f) 26 ft.
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Complete Question:
A cylinder has a height of 30 ft and a volume of 63,679 ft³. what is the radius of the cylinder? round your answer to the nearest whole number. responses
a) 676 ft
b) 676 ft
c)338 ft
d) 338 ft
e) 52 ft
f) 26 ft.
What is the equation for part a?
The rectangle shown has a perimeter of 52 inches.
a. Write an equation describing the possible values of x and y.
Using the perimeter formula of a rectangle we can write an equation describing the values of x and y is as follows:
2y + 2x = 52 inches
Define perimeter?The perimeter of a rectangle is the total length of its edges. It is expressed in linear units like centimetres, inches, and the like and can be taken to mean the total measurement of the rectangle's length and width. For instance, you may rapidly calculate how much ribbon you'd need if you needed to decorate the edge of your rectangular notebook. Similar to how calculating the perimeter will help you determine how much wire you'll need to erect a fence around your garden.
The formula P = 2(l + w), where l is the length and w is the width, determines the perimeter of a rectangle. Since we are aware that this rectangle's perimeter is 52 inches, we can write the following equation: 2l + 2w = 52 inches.
We can express the equation in terms of x and y to discover the potential values for x and y. We may substitute the width (x) and the length (y) into the equation to get 52 inches: 2y + 2x.
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I need some help with it
The Answer is approximately equal to 942.48 or 300π
(π=pi)
Geometry: Find the unknown lengths of these isosceles right triangles (ASAP!!)
22=4 square root 2
Step-by-step explanation:
Using Pythagorean Theory
Solve for a.
18= a/2
In the figure below, quadrilateral UVWX is a parallelogram.
Part a) What are the values of p, UV, and VW?
Part b) What property of a parallelogram did you use to solve?
For the given quadrilateral the value of p is 8, UV = 70 and VW = 34. The property of parallelogram used is the opposite sides are parallel and equal.
What is parallelogram and its properties?A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Also, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.
The opposing sides are equal and parallel. Angles on either side are equal. The subsequent or neighbouring angles are additional. All of the angles will be at right angles if any one of them is a right angle.
We know that the opposite sides of a parallelogram are parallel and equal thus,
8p + 6 = 9p – 2
6 + 2 = 9p – 8p
8 = p
Now, the value of side is:
UV = 8(8) + 6 = 70
The value of side VW is:
VW = 5(8) – 6 = 34
Hence, for the given quadrilateral the value of p is 8, UV = 70 and VW = 34. The property of parallelogram used is the opposite sides are parallel and equal.
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I Need help with this
Consider drawing four cards without replacement from a standard deck of cards. What is the conditional probability of drawing a heart on the fourth draw, given that the first three cards are not hearts?
Group of answer choices:
13/52 or 1/4
10/49
10/52 or 5/26
13/49
The conditional probability of drawing a heart on the fourth draw given that the first three cards are not hearts is 13/49.. The correct answer is D.
After drawing three cards without replacement, there are 52 - 3 = 49 cards remaining in the deck, of which 13 are hearts and 36 are not hearts.
If the first three cards are not hearts, then there are 36 cards remaining in the deck for the fourth draw, of which 13 are hearts and 23 are not hearts.
The conditional probability of drawing a heart on the fourth draw, given that the first three cards are not hearts, can be calculated using Bayes' theorem:
P(heart on 4th draw | first 3 not hearts) = P(heart on 4th draw and first 3 not hearts) / P(first 3 not hearts)
The probability of drawing a heart on the fourth draw and the first three not being hearts is:
P(heart on 4th draw and first 3 not hearts) = (36/52) * (35/51) * (34/50) * (13/49) = 0.0334
The probability of the first three cards not being hearts is:
P(first 3 not hearts) = (36/52) * (35/51) * (34/50) = 0.5764
Therefore, the conditional probability of drawing a heart on the fourth draw, given that the first three cards are not hearts, is:
P(heart on 4th draw | first 3 not hearts) = 0.0334 / 0.5764 ≈ 0.058 or approximately 5.8%.
Therefore, the answer is 13/49. The correct answer is D.
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Find an equation of the line with gradient 1/3 and passes through the point (5,-1)
Answer:
y = x/3 - 8/3 (OR) 3y = x - 8
Both of the above solutions are the same
Step-by-step explanation:
Using the form 'y=mx+c',
Since m = 1/3,
y = 1/3x + c
Substituting (5, -1) into the above equation:
-1 = 5/3 + c
c = -1 - 5/3
= -8/3
Hence,
y = x/3 - 8/3
(which is also the same as)
3y = x - 8
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13. (6 pts) Jasmine has a cube with an edge length of 4 inches. How would the volume of the cube change if the edge length were doubled?
A) The volume is multiplied by 2
B) The volume is multiplied by 6.
C) The volume is multiplied by 4.
D) The volume is multiplied by 8.
Answer: The volume of a cube is calculated by multiplying the edge length by itself three times, or V = l^3.
If the edge length of Jasmine's cube is doubled, the new edge length will be 4 inches x 2 = 8 inches.
Thus, the new volume of the cube would be V = 8^3 = 512 cubic inches.
Comparing this new volume to the original volume of the cube, V = 4^3 = 64 cubic inches, we can see that the new volume is multiplied by 8.
Therefore, the correct answer is D) The volume is multiplied by 8.
Step-by-step explanation:
Deandre wants to measure the height of a tree. He sights the top of the tree, using a mirror that is lying flat on the ground. The mirror is 33 ft from the tree, and Deandre is standing 10.2 ft from the mirror, as shown in the figure. His eyes are 6 ft above the ground. How tall is the tree? Round your answer to the nearest foot.
A car dealership uses the linear model y= -1100x + 25,000 to predict the depreciation of car values as time progresses. If x is how old the vehicle is in years and y is the current value of the vehicle,
what will the value of the vehicle be 5 years after purchase?
The value of the vehicle 5 years after purchase will be $12,500. After we predict the depreciation of car values as time progresses.
Due to use, wear, and tear, or becoming obsolete, an asset loses value over time. Depreciation is the measurement of this decrease.
Using the given linear model y = -1100x + 25,000, we can substitute x = 5 (since we want to find the value after 5 years of purchase) and solve for y:
y = -1100(5) + 25,000
y = -5500 + 25,000
y = 19,500
Therefore, the value of the vehicle 5 years after purchase will be $19,500.
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Surface area of the prism
Answer: 450
Step-by-step explanation:
9x10x5
→Be sure to use three to six complete sentences in your response.
Answer:
1. To expand the polynomial f(x) = (x-3)(x+2)(x+3), we can use the FOIL method twice, where we first multiply (x-3) and (x+2) using FOIL, then multiply the resulting binomial by (x+3) using FOIL again.
2. To expand the polynomial g(x) = (x-3)(x+2)(x-2), we can also use the FOIL method twice, where we first multiply (x-3) and (x+2) using FOIL, then multiply the resulting binomial by (x-2) using FOIL again.
3. The polynomial f(x) has three linear factors, and so the degree of the polynomial will be 3, since we will have to multiply three binomials together. The polynomial g(x) has four linear factors, and so the degree of the polynomial will be 4.
If we were to expand a polynomial with five linear factors, the degree of the polynomial would be 5, since we would have to multiply five binomials together.
4. The degree of a polynomial is determined by the highest power of x in the polynomial, which is determined by the number of terms in the expanded polynomial expression.
(6 sentences to use):
1. To expand the polynomial (x-3)(x+2)(x+3), we use the distributive property and multiply each term of the first binomial by each term of the second binomial, then multiply the resulting trinomial by the third binomial.
2. To expand the polynomial (x-3)(x+2)(x-2), we use the same strategy as in the previous example, multiplying each term of the first binomial by each term of the second binomial, and then multiplying the resulting trinomial by the third binomial.
3. The polynomial f(x) has three linear factors, so its degree is 3, which means the highest exponent in the polynomial is 3.
4. The polynomial g(x) has four linear factors, so its degree is 4, which means the highest exponent in the polynomial is 4.
5. If we were to expand a polynomial using five linear factors, we would again use the distributive property to multiply each term of each binomial together, resulting in a polynomial with a degree of 5, which means the highest exponent in the polynomial would be 5.
6. This strategy for multiplying three binomials is a useful tool in algebraic manipulation, allowing us to expand and simplify polynomial expressions.
Hope this helped! Sorry if it didn't. If you need more help, ask me! :]