I need help with an Exponential Growth & Decay Word Problem. This is the problem: Mr. Jacobs won $1,000,000 in the lottery. He withdraws 10% of the money every year. How much money will he have left after 20 years? [Round your answer to the nearest dollar]
Answers
A=end amount
P=principal (initial) amount
R=rate
n=time (in this case, years)
For growth it is A=P(1+r/100)^n
Related Questions
Complete the equation of the line through (4,-8) and (8,5).
Use exact numbers.
y=_______ Topic:
Slope-intercept from two points.
Answers
y = mx + b
b= y - mx
b = -8 - (13/4) (4)
b = -8 -13
b = -21
equation
y = 13/4x - 21
The equation of the line that passes through (4, -8) and (8, 5) in slope intercept form is y = 13 / 4 x - 21
Slope intercept form of a lineThe slope intercept form of a line is represented as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore,
(4, -8) and (8, 5)
m = 5 + 8 / 8 - 4
m = 13 / 4
Therefore, using (8, 5)
5 = 13 / 4(8) + b
5 = 26 + b
b = 5 - 26
b = -21
Hence, the equation is as follows:
y = 13 / 4 x - 21
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A company donates 935 pencils to a shcool the pencil are divided evenly amog 9classroom the rest goes to the library how many pencil were donated to the schooland the library
Answers
Answer:
103.8
Step-by-step explanation:
calculator
Astronauts use a tool in space that weigh 5 ounces on Earth. How many grams does the tool weigh? Round your answer to the nearest hundredth.
Answers
the key here would be
1 oz. = 28.35g or 1 oz. = 28 g
Answer: 141.75
Step-by-step explanation: Yw future edge users
A rectangle has length x+9 and width 2x-1 what are the areas of the rectangle
Answers
a=(x+9)(2x-1) <--- Use FOIL
a=2x²-x+18x-9
a=2x²+17x-9
Hope I helped :)
factor the trinomial x^2 - 16x +63
Answers
x^2 - 16 x + 63
The factors of 63 that sum to -16 are -7 and -9. So, x^2 - 16 x + 63 = (x - 7) (x - 9):
Answer: (x - 7) (x - 9)
A triangle has three different integer side lengths and a perimeter of 20 units. What is the max length of any one side?
Answers
Final answer:
Using the Triangle Inequality Theorem and given a perimeter of 20 units for a triangle with integer side lengths, the maximum length of one side is found to be 15 units.
Explanation:
To determine the maximum length of one side of a triangle with integer side lengths and a perimeter of 20 units, we must apply the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Given a perimeter of 20 units, if we denote the longest side as x, and the other two sides as y and z, we must satisfy two conditions:
x + y + z = 20 (perimeter condition)
x < y + z (Triangle Inequality Theorem)
Since the triangle has different integer side lengths, the largest x can be is when y and z are consecutive integers because this allows for the largest possible x. If we try the smallest integers, 1 and 2, for y and z, their sum is 3. To satisfy the triangle inequality, the largest possible integer for x would be 20 - 1 - 2 = 17. However, this does not satisfy the inequality x < y + z, because 17 is not less than 3.
Next, we increase y and z to 2 and 3, respectively, which sums up to 5. Thus, for x, we have 20 - 2 - 3 = 15. Since 15 is less than 2 + 3, it satisfies the condition required by the Triangle Inequality Theorem. Therefore, the maximum length of any one side of the triangle is 15 units.
Emma read the statement “the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5.” She translated it as shown below.
Answers
Emma should have used division to represent the quotient of six and x, and she should have used parentheses to show that -2 is multiplied by (4.5 - x). Hence the correct options are 1 and 5.
Emma made two errors in translating the statement "the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5." First, instead of representing the quotient of six and x, she incorrectly wrote 6x, which implies multiplication rather than division. The correct representation should be 6/x.
Second, Emma failed to use parentheses to show that -2 is multiplied by the difference of x and 4.5. The correct expression should be -2(x - 4.5) to ensure proper order of operations. These errors impact the accuracy of the translated equation, and correcting them would yield a more faithful representation of the original statement. Hence the correct options are 1 and 5.
Complete question:
Emma read the statement "the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5." She translated it as shown below 6x=-2x-4.5 What errors did Emma make? Select two options
She should have used division to represent the quotient of six and x.
She should not have included an equal sign.
She should have used parentheses to show that -2 is multiplied by (x-4.5).
She should have subtracted the difference (x-4.5) from -2.
She should have used parentheses to show that -2 is multiplied by (4.5-x).
Emma made the following errors in her translation:
E. She should have used parentheses to show that -2 is multiplied by (x-4.5). Emma’s equation, 6x = -2x - 4.5, lacks parentheses around the expression (x-4.5). To correctly represent the difference of x and 4.5 being multiplied by -2, she should have written -2(x-4.5).
D. She should have subtracted the difference (x-4.5) from -2. Emma’s equation does not correctly account for the subtraction of the difference (x-4.5) from -2. The correct equation should be 6x = -2(x-4.5).
The other options are not relevant to Emma’s specific errors in translating the statement.
Emma made the following errors in her translation:
E. She should have used parentheses to show that -2 is multiplied by (x-4.5). Emma’s equation,
6x = -2x - 4.5, lacks parentheses around the expression
(x-4.5). To correctly represent the difference of x and 4.5 being multiplied by -2
, she should have written
-2(x-4.5)
.D. She should have subtracted the difference(x-4.5) from -2
. Emma’s equation does not correctly account for the subtraction of the difference
(x-4.5)
from
-2
The correct equation should be
6x = -2(x-4.5)
Complete question:
Emma read the statement "the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5." She translated it as shown below 6x=-2x-4.5 What errors did Emma make? Select two options
A. She should have used division to represent the quotient of six and x.
B. She should not have included an equal sign.
C. She should have used parentheses to show that -2 is multiplied by (x-4.5).
D. She should have subtracted the difference (x-4.5) from -2.
E. She should have used parentheses to show that -2 is multiplied by (4.5-x).
What is the length of the hypotenuse of an isosceles right triangle with an area of 32?
Answers
Which graph can be used to find the solution(s) to x2 – 1 = x + 1?
Answers
Let
[tex]f(x)=x^{2}-1[/tex]
[tex]g(x)=x+1[/tex]
we know that
The function f(x) is a vertical parabola open upward
the vertex is the point [tex](0,-1)[/tex] ------> is a minimum
The function g(x) is a linear equation
The y-intercept is the point [tex](0,1)[/tex] -----> for [tex]x=0[/tex] find the value of g(x)
therefore
the answer in the attached figure
The graph that can be used to find the solution of the given polynomial is given by option C) and this can be determined by using the given data.
Given :
Equation --- [tex]x^2 -1 = x+1[/tex]
The following steps can be used in order to determine the graph that can be used to find the solution of the given polynomial:
Step 1 - Separate LHS and RHS of the given polynomial.
[tex]\rm y = x^2-1[/tex] --- (1)
y = x + 1 --- (2)
Step 2 - Draw the graph of a line (y = x + 1) that passes through the points (-1,0) and (0,1).
Step 3 - Now, draw the graph of the equation (1). The shape of this graph is the upward parabola.
Step 4 - The two graphs intersect each other at (-1,0) and (2,3).
From the above steps, it can be concluded that the correct option is C).
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The admission fee at an amusement park is $2.00 for children and $5.60 for adults. On a certain day, 352 people entered the park, and the admission fees collected totaled 1280 dollars. How many children and how many adults were admitted?
Answers
What would '6 meters to 60 meters' be in a ratio
Answers
After 6 years, what is the total amount of a compound interest investment of $35,000 at 4% interest, compound quarterly?
Round to the nearest cent.
Answers
1.06 is the mutiplier.
A=35000(1+1/100)^4×6
A=$44440.7127
A=$44441
Consider the equation below. log4 (x+3)=log2 (2x). Which system of equations can represent the equation?
Answers
[tex]log_{4} (x+3) = \frac{log_{2} (x+3)}{log_{2}4} [/tex]
Therefore, given
log₄(x+3) = log₂(2x), obtain
[tex] \frac{log_{2}(x+3)}{log_{2}4}=log_{2} (2x) \\ log_{2}(x+3) = log_{2}4 log_{2}(2x) \\ x+3 = (2x)^{log_{2}4} [/tex]
Because
log₂4 = log₂ 2² = 2 log₂ 2 = 2, therefore
x + 3 = (2x)² = 4x²
4x² - x - 3 = 0
This factorizes into
(4x + 3)(x - 1) = 0
Answer:
4x² - x - 3 = 0
or
4x + 3 = 0, and
x - 1 = 0
How to find slope when there is the y intercept and x-intercept?
Answers
[tex] \frac{rise}{run} = \frac{y2 - y1}{x2 - x1} [/tex]
that's the equation used to find your slope
Example:
(4,2) (8,6) let's say those are the points you pick from the line
so then you subtract 6-2=4 (6 is your y2 and 2 is your y1)
then subtracts 8-4=4 (8is your x2 and 4 is your x1)
then your left with
[tex] \frac{2}{4} [/tex]
if you can reduce the reduce in this case you can which leaves you with
[tex] \frac{1}{2} [/tex]
and that's how you find the slope
Which point is an x-intercept of the quadratic function
f(x) = (x – 8)(x + 9)?
Answers
x-intercept means f(x) = 0
(x-8)(x+9) = 0 ⇒ x = 8 or x = - 9
There are two points which are x-intercepts. They are (8,0) and (-9,0).
Doris put $4000 in a 2-year CD paying 6% interest, compounded monthly. After 2 years, she withdrew all her money. What was the amount of the withdrawal?
a. 4000.00
B. $4214.41
C. $4508.64
D. $4448.13
Answers
Which inequality represents this sentence? Ten minus three is greater than one plus two.
Answers
One plus two ⇒ 1 + 2
Greater than use the symbol >
Ten minus three greater than one plus two
10 - 3 > 1 + 2
7 > 3
A game shop sells marbles in clear plastic cylinders. Four marbles fit across the diameter of the cylinder and 10 marbles fit from the base to the top of the cylinder. Each marble has a diameter of 2 cm. What is the area of the plastic that is needed to make one cylinder?
Answers
Now, to find the surface area, you first need to figure out the height of the plastic cylinder and its radius.
Since you know that the diameter (twice the radius) of the cylinder is equivalent to 4 marbles, and each marble has a diameter of 2 cm, the diameter of the cylinder would be 8 cm. Then, to find its radius, you divide by 2, so its radius is 4.
Now, since you know that the height of the cylinder is 10 marbles, you multiply 10 by 2 to get that the height is 20 cm tall.
Since you now have the values of the height and the radius, plug the values into the surface area of a cylinder formula (r is radius and h is height).
A=2π(4)(20)+2π(4)^2.
Assuming that pi is 3.14, when you simplify this using PEMDAS, you get
502.4+100.48 which then simplifies to 602.88, the area of the plastic to make one cylinder.
Please help me asap
It's due tomorrow
Answers
-15 < 3n <= 6
-5 < n <= 2
n is an integers and must be greater than -5 and can be as great as 2.
n can be -4, -3, -2, -1, 0, 1, 2
Solve the equation the square root of the quantity x minus 6 plus 2 equals 6 for the variable. Show each step please. Remember the X - 6 is under a square root sign
Answers
sqrt(x-6) = 4
sqrt(x-6) squared = 4 squared
x-6 = 16
x = 10
What is the maximum length possible for her blanket?
Answers
It looks like you are missing some information
Answer: c: 60
Step-by-step explanation:
i did the test
Which ordered pairs lie on the graph of the exponential function f(x)=4(5)2x?
Select each correct answer.
(−1,4/25)
(0,0)
(1,4)
(2,2500)
Answers
N a contest, a total of $12,000 was divided among the first, second, and third-place winners in the ratio of 3 to 2 to 1, respectively. how much did the first-place winner receive
Answers
The first Winner
3/6 × 12,000 = $6,000
The Second Winner
2/6 × 12,000 = $ 4,000
The Third Winner
1/6 × 12,000 = $2,000
A pizza parlor sold 38mc005-1.jpg pizzas during a dinner hour. If each pizza contained 8 slices, how many slices of pizza were sold?
The options are
Answers
38 pizzas times 8 slices each =
38 *8 = 304 slices total
How to find the distance between two lines in 3d?
Answers
Answer:
Step-by-step explanation:
Karen's penny bank is 1/3 full. After she removes 240 pennies, it is 1/9 full. How many pennies can Karen's bank hold?
Answers
2/9 of the capacity if 240 pennies
2/9 * x=240
x=240*(9/2)=1080
the penny bank can hold 1080 pennies
The difference between the bank being 1/3 and 1/9 full equals 240 pennies, so 1/9 of the bank's capacity equals 120 pennies. So, Karen's bank can hold a total of 1080 pennies.
Explanation:This is a mathematics problem dealing with fractions and subtraction. From the problem, we understand that after Karen removes 240 pennies, the bank is 1/9 full from previously being 1/3 full. So, the difference between 1/3 and 1/9, which is 2/9, accounts for the 240 pennies that were removed.
To find out the total capacity of the penny bank, you need to consider that 1/9 (the fraction representing the bank's fill level after removal of the 240 pennies) is equivalent to 120 pennies (half of 240, as 2/9 of the capacity is 240 pennies). This means that the total capacity of the bank (comparable to 9/9 of the fraction) is 120 pennies times 9, which equals to 1080 pennies.
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The function f(x) is graphed on the coordinate plane. What is f(−4) ?
Answers
y = 4 where x = -4.
That's the same as saying: "what is the y-value when x = -4?)
f(-4) = y = 4
Which graph represents the inequality y<−1+2x?
Answers
The ratio of computers to desk is 2 to 3. If there are 15 desk, how many computers are there?
Answers
The ratio of computers to desk is 2 to 3
2 x 3 = 6 (computers)
3 x 3 = 9 (desks)
answer
6 computers
To find the number of computers given the ratio of computers to desks and the number of desks, set up a proportion and solve for the unknown value.
Explanation:In this question, we are given the ratio of computers to desks, which is 2 to 3. We are also given the number of desks, which is 15. To find the number of computers, we can set up a proportion:
2 computers / 3 desks = x computers / 15 desks
By cross-multiplying and solving for x, we find that there are 10 computers.
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During the 2005 football season, Team Tackle beat Team Sack by 5 points. If their combined scores totaled 89, find the individual team scores.