Answer:
Step-by-step explanation:
FOIL
9x² -27x +27x -81 middle terms cancel
9x² - 81
David invested his profit of $50,000 from the sale of his business into an aggressive stock fund. After 15 years, the account had a total of $132,558.36 in it. A. What annual interest rate, compounded continuously, produced this return? (Enter the value of r rounded to three decimal places.). B. E termine the approximate number of years (from the original investment) it will take for the account to grow to $300,000. Round answer to the nearest tenth
Answer:
Step-by-step explanation:
A. To find the annual interest rate, compounded continuously, we can use the formula:
A = Pe^(rt)
where A is the final amount, P is the principal amount (initial investment), e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate, and t is the time in years.
We are given that P = $50,000, A = $132,558.36, and t = 15 years. We need to solve for r.
Substituting the given values into the formula, we get:
$132,558.36 = $50,000 e^(15r)
Dividing both sides by $50,000 and taking the natural logarithm of both sides, we get:
ln(2.6511672) = 15r
Solving for r, we get:
r = ln(2.6511672) / 15
r ≈ 0.045 (rounded to three decimal places)
Therefore, the annual interest rate, compounded continuously, that produced this return is approximately 0.045 or 4.5%.
B. To determine the approximate number of years it will take for the account to grow to $300,000, we can again use the formula:
A = Pe^(rt)
where A is the final amount we want to reach, P is the initial investment ($50,000), e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate we just found (0.045), and t is the time in years we want to solve for.
Substituting the given values into the formula, we get:
$300,000 = $50,000 e^(0.045t)
Dividing both sides by $50,000 and taking the natural logarithm of both sides, we get:
ln(6) = 0.045t
Solving for t, we get:
t = ln(6) / 0.045
t ≈ 27.6 years (rounded to the nearest tenth)
Therefore, it will take approximately 27.6 years from the original investment for the account to grow to $300,000.
A random sample of 10 fields of corn has a mean yield of 37.1 bushels per acre and standard deviation of 5.91 bushels per acre. Determine the 98% confidence interval for the true mean yield. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
The critical value of that used in constructing the confidence interval is (42.512 , 31.688)
We have the following information from the question:
Sample mean, x(bar) = 37.1 bushels per acre
Sample size, n = 10
Alpha, α = 0.05
Sample standard deviation, s = 5.91 bushels per acre
Degree of freedom = n - 1 = 9
We have to determine the 98% confidence interval for the true mean yield.
We use the formula:
x(bar) ± [tex]t_c_r_i_t_i_c_a_l[/tex][tex]\frac{s}{\sqrt{n} }[/tex]
Plug all the values in above formula:
37.1 ± 2.896[tex](\frac{5.91}{\sqrt{10} } )[/tex]
37.1 ± 5.412 = (42.512 , 31.688)
Hence, The critical value of that used in constructing the confidence interval is (42.512 , 31.688).
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What is the formula for the nth term of the given sequence? 48,72,108….
The explicit formula for an, the nth term of the sequence is f(n) = 48 * (3/2)ⁿ ⁻ ¹
How to determine the nth term of the sequenceFrom the question, we have the following parameters that can be used in our computation:
48, 72, 108…
The above definitions imply that the sequence is a geometric sequence with the followin features
First term, a = 48
Common ratio, r = 72/48 = 3/2
Using the above as a guide,
So, we have the following representation
f(n) = a * rⁿ ⁻ ¹
So, we have
f(n) = 48 * (3/2)ⁿ ⁻ ¹
Hence, the sequence is f(n) = 48 * (3/2)ⁿ ⁻ ¹
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what is the difference between -15-9?
Answer:
Step-by-step explanation:
-15-9 = -24
I would think about it as adding 15 and 9, but just make the answer negative.
Using the horizontal line test, which of the following can be concluded about
the inverse of the graph of the function below?
OA. It is a vertical shift.
OB. It is a function.
OC. It is not a function.
OD. It is a horizontal shift.
PLEASE HELP FAST!!
The correct answer would be option B i.e. The inverse of the function x = -y² + 4 is a function.
What is a horizontal shift?
A horizontal shift is a type of transformation in which a function is shifted left or right along the x-axis without changing its shape or orientation. If a function f(x) is shifted to the right by a distance of c units, the resulting function is denoted by f(x - c), and if it is shifted to the left by a distance of c units, the resulting function is denoted by f(x + c). Horizontal shifts are commonly used in calculus, geometry, and other branches of mathematics to analyze the behavior of functions and to solve problems related to graphs and equations.
By plotting the inverse of the function the following graph is obtained.
We know that the function is x = -y² + 4.
The inverse of the function x = -y² + 4 would be y = , which is a vertical parabola opening upwards. When we use the horizontal line test, we find that any horizontal line would intersect the once, which means that a single input (x) would have single corresponding output (y). Therefore, the inverse of the function x = -y² + 4 is a function.
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The table represents equivalent ratios. What is the missing value of x in the table
9
7
6
5
Answer:
Step-by-step explanation:
Which ordered pairs represent points on the graph of this equation? Select all that apply. 2x = -1/2y a) 4,6 b) -6,-1 c) 0,-4 d) -1,4 e) 0,0 f) 4,-2
The ordered pairs that represent points on the graph of the equation 2x = -1/2y are d) (-1,4) and e) (0,0).
What is equation?An equation is a mathematical statement that shows the equality of two expressions. It consists of two sides, a left-hand side and a right-hand side, separated by an equal sign. An equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
According to given information:The equation 2x = -1/2y can be rewritten as y = -4x. This is a linear equation in slope-intercept form, with a slope of -4 and y-intercept of 0.
To determine which ordered pairs represent points on the graph of this equation, we can substitute the x and y values into the equation and check if it satisfies the equation.
a) (4,6):
y = -4x
6 = -4(4)
6 = -16
This ordered pair does not satisfy the equation.
b) (-6,-1):
y = -4x
-1 = -4(-6)
-1 = 24
This ordered pair does not satisfy the equation.
c) (0,-4):
y = -4x
-4 = -4(0)
-4 = 0
This ordered pair does not satisfy the equation.
d) (-1,4):
y = -4x
4 = -4(-1)
4 = 4
This ordered pair satisfies the equation.
e) (0,0):
y = -4x
0 = -4(0)
0 = 0
This ordered pair satisfies the equation.
f) (4,-2):
y = -4x
-2 = -4(4)
-2 = -16
This ordered pair does not satisfy the equation.
Therefore, the ordered pairs that represent points on the graph of the equation 2x = -1/2y are d) (-1,4) and e) (0,0).
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Jayden is packing for college.If each of his boxes are 4.5 ft x 2 ft x 4 ft.,how many boxes can he fit in his 185ft^3 closet?
Volume is Length x width x height
1 box = 4.5 x 2 x 4 = 36
Each box is 36 cubic feet. Now divide the closet size by box size
185 cubic feet/36 cubic feet per box = 5.138
Since you can't have .138 of a box, and rounding up to 6 boxes is too much, the closet will hold 5 boxes (with .138 cubic feet left over).
solve 732.178+167-542.137
Answer:
357.041 is the answer first add then subtract
Which expression has an aproxímate value be between 6 and 7 select all that apply
The expression which has an approximate value be between the numbers 6 and 7 are (a) π + 3 and (b) √39.
In order to determine which expression has an approximate value between the numbers, 6 and 7, we can estimate the value of each expression and compare them to 6 and 7.
Option(a) π + 3 ;
We know that the approximate value of "π" is 3.14,
So, 3.14 + 3 = 6.14 (it is between 6 and 7)
Option(b) : √39 ≈ 6.24 (it is between 6 and 7)
Option (c) : 6π , We substitute, π ≈ 3.14,
We get, ≈ 18.85 (it is not between 6 and 7)
Option (d) : √35 ≈ 5.92 (it is not in between 6 and 7)
Therefore, the correct options are (a) and (b).
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The given question is incomplete, the complete question is
Which expression has an approximate value be between 6 and 7?
Select all that apply
(a) π + 3
(b) √39
(c) 6π
(d) √35
Which of the following is best described as a line segment that has both
endpoints on a circle?
O A. Center
OB. Radius
O C. Chord
O D. Tangent
SUBMIT
Answer:
C. Chord
Step-by-step explanation:
Chord: Any segment whose endpoints lie on the circle is a chord.
For the given triangle, find the missing length(s). Give an exact answer and, where appropriate, an approximation to three
decimal places.
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
A. Using radicals, the shorter leg is exactly The shorter leg, up to three decimal places, is approximately
B. The shorter leg is exactly No approximation is necessary.
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
OA. Using radicals, the hypotenuse is exactly The hypotenuse up to three decimal places, is approximately
B. The hypotenuse is exactly No approximation is necessary.
This question: 1 point(s) poss
15
The missing length of the triangle above would be =
A.Using radicals, the shorter leg is exactly 9. The shorter leg, up to three decimal places, is approximately 8.660.
How to calculate the missing length of the given triangle?To calculate the missing length of the given triangle, the sine formula is used such as;
a/sinA = c/sinC
where;
a = 15
A = 60°
c= ?
V= 90°
15/sin60° = b/sin90°
Make be the subject of formula;
c = 15× 1/0.866025403
c = 17.32
Using the Pythagorean formula;
c² = a² + b²
17.32² = 15² + b²
b² = 300 - 225
b² = 75
b = √75
b = 8.660.
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can someone help me on number 2
Answer:
P=32 yards, A=64 yards^2
Step-by-step explanation:
We know that P = 4 x s, where s is the side length. In this case, we know that s=8. So, the perimeter is 32 yards. We know that A= s^2. Substituting for s=8 makes the area 64 yards^2. Thus, the perimeter of this square is 32 yards, while the area is 64 yards squared.
La suma de las edades de 3 hermanos es de 36. La edad del mayor es igual a la suma de los dos hermanos menores, dentro de 8 años el menor doblará la edad del mayor¿cuál es la edad de los hermanos?
The age of oldest is 44 and age of youngest is 18.
We have,
Sum of age of 3 brother = 36
let the age of three brother be x, y and z.
so, x + y + z = 36
x = y + z
After 8 year, (z+ 8) = 2(x+8)
z+ 8 = 2x+ 16
2x - z +8=0
Thus, the age of oldest is 44 and age of youngest is 18.
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The Translation of the given question is:
The sum of the ages of 3 brothers is 36. The age of the eldest is equal to the sum of the two younger brothers, within 8 years the younger will double the age of the older, what is the age of the brothers?
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options
Answer:
-6x + 15 < 10 - 5x or 11x > 5
Step-by-step explanation:
Given 3 positive intergers a, b, and c. Knowing a < b < c. If 42ª + 2² +2²=2336, what is the value of a?
Answer: We are given that:
42^a + 2^2 + 2^2 = 2336
Simplifying the expression on the left-hand side, we get:
42^a + 4 = 2336
Subtracting 4 from both sides, we get:
42^a = 2332
Taking the logarithm of both sides with base 42, we get:
a = log₄₂₂₋₃₂ ≈ 1.417
Since a is a positive integer, the closest integer to 1.417 is 1. Therefore, the value of a is 1.
Step-by-step explanation:
A 3cm by 3cm by 3cm cube has three holes, each with a 1cm by 1cm cross section
running from the centre of each face to the centre of the opposite face. What is
the total surface area of the resulting solid (including the internal surfaces)
The total surface area of the resulting solid is [tex]54 cm^2 + 9 cm^2 = 63 cm^2.[/tex]
What is area of solid?
The area of a solid refers to the total amount of surface space that the solid occupies. This can be measured in square units, such as square centimeters or square meters, depending on the unit of measurement being used.
To calculate the surface area of the resulting solid, we need to consider the surface area of each of the six faces of the cube, as well as the surface area of the three internal hole walls.
The surface area of each face of the cube is 3 cm x 3 cm = [tex]9 cm^2[/tex]. Since there are six faces, the total surface area of the cube is 6 x 9 [tex]cm^2[/tex] = 54 [tex]cm^2[/tex].
Each hole has a length of 3 cm, so the surface area of the internal walls of each hole is 3 cm x 1 cm = 3 [tex]cm^2[/tex]. Since there are three holes, the total surface area of the internal walls is 3 x 3 [tex]cm^2[/tex] = 9 [tex]cm^2[/tex].
Therefore, the total surface area of the resulting solid is 54 [tex]cm^2[/tex] + 9 [tex]cm^2[/tex] = 63 [tex]cm^2[/tex].
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Please help! What is slope of the line? y+6=1/3(x−4) will give you brainlist and good ratings plus 70 points.
Answer:
The slope is 1/3
Step-by-step explanation:
y+6=1/3(x-4)
-6 -6
-----------------
y = 1/3 * x + 1/3 * (-4) - 6
y = 1/3x -7 1/3
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
First, start by simplifying the right side of the equation, [tex]y+6=\frac{1}{3}(x-4)[/tex].
When we simplify the right side using distributive property, we will get:
[tex]y+6=\frac{1}{3}x-\frac{4}{3}[/tex]
Subtract 6 from both sides to get:
[tex]y=\frac{1}{3}x-\frac{4}{3}-6[/tex]
Simplify further and get:
[tex]y=\frac{1}{3}x-\frac{22}{3}[/tex]
By viewing the equation, we can tell the slope is 1/3.
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Question content area top
Part 1
In a different plan for area codes, the first digit could be any number from 0 through 6, the second digit was either 2,3, or,4 and the third digit could be any number except 0 or 3. With this plan, how many different area codes are possible?
There are 168 different area codes possible with this plan by using the multiplication principle of counting.
What is multiplication principle ?
The multiplication principle of counting, also known as the rule of product, is a counting principle in combinatorics that states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.
There are 7 possible choices for the first digit (0 through 6), 3 possible choices for the second digit (2, 3, or 4), and 8 possible choices for the third digit (any digit except 0 or 3). To find the total number of possible area codes, we can use the multiplication principle of counting:
Total number of area codes = Number of choices for first digit x Number of choices for second digit x Number of choices for third digit
Total number of area codes = 7 x 3 x 8
Total number of area codes = 168
Therefore, there are 168 different area codes possible with this plan.
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(2x+6yx)-(12ay+-6y) pls helpp pls
The required, simplified expression is 2x - 6y(2a - x) + 6y.
To simplify the expression (2x+6yx)-(12ay+-6y), we need to distribute the negative sign to the second term.
2x - 6y(2a - x) + 6y.
Now we can combine like terms, which means adding up any terms that have the same variables raised to the same powers. In this case, we have two terms with "x" and two terms with "y". Combining them, we get:
2x+6yx-12ay+6y = 2x - 12ay + 6yx + 6y
= 2x - 6y(2a - x) + 6y
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The number of bats in a colony is growing exponentially. After 1 year, there were 130 bats. After 4 years, there were 1040 bats. If the colony continues to grow at the same rate, how many bats are expected to be in the colony after 7 years? Do not include units in your answer.
Answer:
1,040 ÷ 130 = 8
After 7 years: 1,040 × 8 = 8,320
Which ordered pair represents the point labeled C?
The x axis starts at negative 3, with tick marks every one unit up to positive 3. The y-axis starts at negative 3, with tick marks every one unit up to three. Point A is left two units and up one unit from the origin. Point B is right two units and up one unit from the origin. Point C is down two units from the origin. Point D is left one unit and down one unit from the origin.
(−2, 1)
(−1, −1)
(0, −2)
(2, 2)
The ordered pair that represents the point labeled C is (0, -2). Option (C) is the correct answer.
We can start by considering the given information about the coordinate axes. The x-axis starts at negative 3 with tick marks every one unit up to positive 3, and the y-axis starts at negative 3 with tick marks every one unit up to 3. The origin is the point where the x-axis and y-axis intersect, and it has coordinates (0, 0).
Next, we are given information about four points labeled A, B, C, and D. Points A and B are both one unit up and two units to the left or right of the origin, respectively. Point D is one unit to the left and one unit down from the origin.
Finally, we are asked to determine the coordinates of point C. We know that point C is labeled as being two units down from the origin, which means that it has a y-coordinate of -2.
To determine the x-coordinate of point C, we can observe that it lies on the y-axis, which means that it has an x-coordinate of 0 (since the y-axis intersects the x-axis at x = 0). Therefore, the ordered pair that represents point C is (0, -2), which matches option (C).
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Write the following statements as P^Q, PVQ, -P, P then Q, P <-> Q State what P and Q are.
a) If it is a rock, then it contains magnesium.
b) The weather is nice or I am chilly
c) x ∈ A ∩ B
In statement c), A and B are sets, and x is an element that belongs to both sets A and B.
What is equation?
An equation is a mathematical statement that shows the equality between two expressions, often denoted by placing an equals sign (=) between the two expressions. The expressions on either side of the equals sign are typically composed of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and so on.
An equation is said to be true if the expressions on both sides of the equals sign represent the same quantity or value. Equations are often used in mathematics and science to model real-world phenomena, to make predictions, and to solve problems.
a) P: It is a rock.
Q: It contains magnesium.
P → Q
b) P: The weather is nice.
Q: I am chilly.
P ∨ Q
c) P: x belongs to set A.
Q: x belongs to set B.
P ∧ Q
d) P: It is raining.
Q: The ground is wet.
P → Q
e) P: The food is hot.
Q: I will blow on it.
P → Q
f) P: The car is red.
Q: It is a convertible.
P ↔ Q
Note: In statement c), A and B are sets, and x is an element that belongs to both sets A and B.
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Pls help me (its in the png below)
The number of pieces of mail that the United States Postal Service delivers in 6 days would be 2 ¹⁶ . 3 ⁴ . 5 ⁴ mail
How to find the number of mail ?The number of mail delivered in 6 days by the United States Postal Service would be:
= Number of mail delivered in a second x Number of seconds in 6 days
= (2⁸ . 5² ) x ( 2⁸.3⁴.5² )
The properties of exponents, which state that when multiplying two powers with the same base, we can add their exponents, allow us to simplify the expression:
= 2⁸ ⁺ ⁸ . 5 ² ⁺ ² x 3 ⁴
= 2 ¹⁶ . 3 ⁴ . 5 ⁴ mail
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Find the area of the shape below. Give your answer in cm².
9 cm
4 cm
12 cm
Not to scale
The area of the shape is equal to 60 square centimeters
How to calculate for the area of the shapeThe shape is observed to be made up of a triangle and a rectangle, so we shall calculate for each area and sum the results to get the total area of the shape as follows:
area of triangle = 1/2 × 4 cm × 12 cm
area of the triangle = 24 cm²
area of the rectangle = 9 cm × 4 cm
area of the rectangle = 36 cm²
total area of the shape = 24 cm² + 36 cm²
total area of the shape = 60 cm²
Therefore, the area of the shape is equal to 60 square centimeters
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1. The cost of the three lightest packages is ($8.80 / $9.60 / $10.45 / $11.40)
2. The cost of the remaining packages is ($20.35 / $22.20 / $30.80 / $33.60)
The cost of the three lightest packages is $8.80.
The cost of the remaining packages is $33.60.
The total cost of all packages is $42.40.
What is a line plot?In Mathematics and Statistics, a line plot can be defined as a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.
By critically observing the line plot that represents the weight of meat, we have the following weights:
Three lightest weights = 5/8 pounds + 5/8 pounds + 6/8 pounds
Cost of three lightest weights = (5/8 + 5/8 + 6/8) × $4.40
Cost of three lightest weights = $8.80.
Cost of remaining package = (1 + 1 1/8 + 1 1/8 + 1 1/8 + 1 2/8 + 1 3/8) × $4.80
Cost of remaining package = $33.60
Total cost of all packages = $8.80 + $33.60 = $42.40.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
What are the coordinates of the reflection of point R across the x-axis?
(-2, -3)
(-3, 2)
(-2, 3)
(2, -3)
The radius of a cylindrical pipe is 2 ft. If the pipe is 19 ft long, what is its volume
Answer: The volume of the cylindrical pipe is 76pi cubic feet.
Step-by-step explanation: Sincerely, answered by Lizzy ♡ :: as an A+ student, I want to make sure other students can succeed as well, so in my free time: i answer questions like yours on Brainly! if you could click the thanks heart, give me brainliest by clicking the crown, and rate my answer 5 stars, it would be appreciated! have a lovely day! (ᵔᴥᵔ)
Answer:
Step-by-step explanation:
239 cubic feet
i asked my math teacher
Use a calculator to approximate √13. Round your answer to 4 decimal places.
Answer:
3.6056
Step-by-step explanation:
An office supply company is shipping a case of
wooden pencils to a store. There are 64 boxes of
pencils in the case. If each box of pencils weighs
2.5 ounces, what is the weight, in pounds, of the
case of wooden pencils?
Answer:
10 pounds
Step-by-step explanation:
First, we need to determine the total weight of the pencils in ounces:
64 boxes x 2.5 ounces per box = 160 ounces
To convert this weight to pounds, we need to divide by the number of ounces in a pound:
160 ounces / 16 ounces per pound = 10 pounds
Therefore, the case of wooden pencils weighs 10 pounds.
