The Boyce's house bought for $96,000 in 1995, increased approximately 4% yearly. By applying the compound interest formula, the house's value in 2007 would be approximately $139,254.09.
Explanation:We need to use the compound interest formula to calculate the value of Boyce's house in 2007 because the house price increase is compounded annually. The formula is P(1 + r/n)^(nt). Here, P is the initial amount (i.e., the original house price), r is the annual interest rate (the rate of increase in house value), and n is the number of times interest is compounded yearly. T is the number of years the money is invested.
However, as we deal with annual compounding, the formula simplifies to P(1 + r)^t. In this case, P = $96,000, r = 4% or 0.04, and t = 2007 -1995 = 12 years.
Inserting these values, we get 96000(1 + 0.04)^12 = $139,254.09 (rounded to the nearest cent).
So, according to the 4% annual increase rate, Boyce's house would be worth approximately $139,254.09 in 2007.
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the rainfalls 2 years ago was 10.2 inches.last year total was 20 percent greater. what was last years rainfalls total
Factor completely 4x2 – 8x – 60
Answer
(4x – 20)(x + 3)
4(x – 1)(x + 15)
4(x – 5)(x + 3)
(4x – 4)(x + 15) ...?
Final answer:
To factor the expression 4x² − 8x − 60 completely, factor out the greatest common factor of 4, then factor the resulting quadratic expression, which results in C. 4(x − 5)(x + 3).
Explanation:
The question asks you to factor completely the quadratic expression [tex]4x^2 - 8x - 60[/tex]To factor this expression, first, look for any common factors among the terms. Here, the common factor is 4. Factoring out the 4 gives you [tex]4(x^2 - 2x - 15).[/tex]Next, we factor the quadratic expression within the parentheses.
We look for two numbers that multiply to give − 15 (the constant term) and add to give − 2 (the coefficient of x). These numbers are − 5 and + 3, so the expression factors further into 4(x − 5)(x + 3).
The completely factored form of the quadratic expression [tex]4x^2 - 8x - 60[/tex] is C. 4(x − 5)(x + 3).
a landscaper estimates that a set of plants can be installed in six hours by 12 workers the landscaper wants to finish a set of plants in 4 hours assuming that the variables are inversely related how many workers should the landscaper bring to the job
Find the Nth term of the following sequence...
7, 27, 47, 67, .....
Find an equation of the line that satisfies the given conditions.
Through (6, 7); parallel to the line passing through
(7, 5) and (3, 1)
Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line −x+4y=20?
y=−4x−3
y=−14x+6
−x+4y=8
4x+y=−1
Lines with equations y=−4x−3 and 4x+y=−1 are neither parallel nor perpendicular to the line −x+4y=20. The line y=−14x+6 is also neither parallel nor perpendicular to the given line. The line −x+4y=8 is parallel to the given line.
Explanation:To determine whether lines are parallel, perpendicular, or neither to the given line −x+4y=20, we'll need to look at their slopes. If the slopes are the same, the lines are parallel. If the product of the slopes is -1, the lines are perpendicular.
First, we should rewrite the given equation in y = mx + b format to identify the slope. The equation becomes y = 1/4x + 5. The slope for the given line is 1/4.
The first equation, y=−4x−3, has a slope of -4. This is neither equal to 1/4 nor its negative reciprocal, so the line is neither parallel nor perpendicular. The second equation, y=−14x+6, has a slope of -14. This is not equal to 1/4 or a negative reciprocal of 1/4, so this line is also neither parallel nor perpendicular. The third equation, −x+4y=8, can be rewritten as y = 1/4x + 2, which shares a slope with the given line and is therefore parallel. The last equation, 4x+y=−1, can be rewritten as y = -4x - 1, also has a slope of -4, thus it is neither parallel nor perpendicular to the given line. Learn more about Parallel and Perpendicular Lines here:
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Solve the inequality. 2>8−43h
Final answer:
To solve the inequality 2 > 8 - 43h, subtract 8 from both sides and divide by -43, then flip the inequality sign. The solution is h > 6/43.
Explanation:
To solve the inequality 2 > 8 - 43h, we need to isolate the variable h. Let's start by subtracting 8 from both sides:
2 - 8 > 8 - 8 - 43h
-6 > -43h
Next, we divide both sides of the inequality by -43, but since we are dividing by a negative number, the inequality sign flips:
-6/-43 < -43h/-43
Simplifying the expression:
6/43 < h
The solution to the inequality is h > 6/43.
how would you write 2.04 in words
List the integers between the square root of 15 and the square root of 48 ?
For f(x) = 2x + 1 and g(x) = x2 – 7, find (f + g)(x).
A. x2 + 2x – 6
B. 2x3 – 6
C. x2 + 2x + 8
D. 2x2 – 15
A quiz consists of 4 true-false questions. What is the probability of getting 100% on the quiz by randomly guessing the answer to all 4 questions?
Answer: The probability of getting 100 % on the quiz is 0.0625.
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Step-by-step explanation:
Since we have given that
Number of true-false questions = 4
Number of chances of answer = 2
1) True,
2) False
Probability of getting correct answer is given by
[tex]\frac{1}{2}[/tex]
Probability of getting 100% on the quiz by randomly guessing the answer to all 4 questions is given by
[tex]\frac{1}{2}^4\\\\=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\\\\=\frac{1}{16}\\\\=0.0625[/tex]
Hence, The probability of getting 100 % on the quiz is 0.0625.
Emily is three years older than twice her sister Mary’s age. The sum of their ages is less than 30.
Let x represent Mary's age.
Which inequality represents Mary’s possible age?
A. 0 < x < / = 9
B. 0 < x < / = 18
C. 0 < x < 18
D. 0 < x < 9
2x+3+x<30
3x<27
x<9
The answer would be D.
What is the common difference d of the sequence?
9, −8, −25, −42, −59, ...
d =
Work for 8554 divided by 94
Mark can make 42 birdays cakes in 7 days how many birthday cakes can mark make in 5 days?
Answer:
30
Step-by-step explanation:
Nadia wants to fill her rectangular fish tank with water. The fish tank measures 2 ft x 1 ft x 1.5 ft. The water level in her fish tank needs to be at least 0.25 ft from the top. She uses a bucket that hold 1.25 ft^3 of water. How many buckets of water does Nadia need to fill the fish tank?
Nadia needs 2 buckets of water to fill the fish tank.
Explanation:To calculate the volume of water needed to fill the fish tank, we need to find the volume of the tank and subtract the volume of the empty space. The volume of the tank is 2 ft x 1 ft x 1.5 ft = 3 ft³. The volume of the empty space is 2 ft x 1 ft x 0.25 ft = 0.5 ft³. Therefore, the volume of water needed is 3 ft³ - 0.5 ft³ = 2.5 ft³.
Next, we divide the volume of water needed by the volume of water in each bucket to find the number of buckets needed. 2.5 ft³ divided by 1.25 ft³/bucket = 2 buckets. Therefore, Nadia needs 2 buckets of water to fill the fish tank.
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A cylinder is sliced by a plane that is not parallel to the base and intersects only the lateral surface. The resulting cross section is
A.circle
B.parabola
C.ellipse
D.hyperbola
Answer:
c. Ellipse
Step-by-step explanation:
Answer:
option (c)
Step-by-step explanation:
It is an ellipse.
Option (c) is correct .
3x 4-7x-6 in terms and like terms
The length of a rectangle is 6 inches longer than its width. the perimeter of the rectangle is 28 inches. if x represents the width of the rectangle, which equation can be used to find its value?
I hope choice must be given so that we can select which equation can be used to find its value.
I am showing the steps for this problem.
Given that, x represents the width of the rectangle and the perimeter of the rectangle is 28 inches.
Let's assume y represent the length of the rectangle.
Formula to find the perimeter of a rectangle is,
p= 2 * length + 2 * width.
Hence, we can set up an equation as following.
2 y + 2x = 28.
Hope this is your question, if not I think you will, still be able to
find an answer of your question based on this solution.
Hope this helps you!.
Answer: The answer is 2 × (6 + x) + 2 × x = 28.
Step-by-step explanation: Given that the length of a rectangle is 6 inches longer than its width. the perimeter of the rectangle is 28 inches. if x represents the width of the rectangle, then we are to find the equation that finds the value of 'x'.
Since width of the rectangle is 'x' inches and length is 6 inches longer than the width, so length will be (6 + x) inches.
Also, perimeter is 28 inches, therefore, we have
[tex]2\times(6+x)+2\times x=28\\\\\Rightarrow 6+x+x=14\\\\\Rightarrow 2x=8\\\\\Rightarrow x=4.[/tex]
Thus, the value of x is 4 inches, hence width = 4 inches and length = 4 + 6 = 10 inches.
A train needs 4 hours to go from the first station to the second. If the third station is 120 miles away and the total travel time must be no more than 7 hours, write an inequality that would let you find the slowest average speed, v, the train could have.
11 + (6-x/2) = 26
TIA
Answer:
X= -24
Step-by-step explanation:
What is 2x + 11y when x = 4 and y = 2?
A. 30
B. 38
C. 48
D. 136
If you invest 1,700$ at an annual interest rate of 8.9% compounded continuously. How much will you have in the account after 10 years have passed?
A: $1, 858.24
B: $20,698.60
C:$41,397.20
D$4, 139.72
A new drug has been found to be effective in treating 75% of the people afflicted by a certain disease. If the drug is administered to 400 people who have this disease, what are the mean and the standard deviation of the number of people for whom the drug can be expected to be effective? (Round your standard deviation to two decimal places.)
Answer:
The mean is 300 and the standard deviation is 8.67.
Step-by-step explanation:
It has been given that the drug has been found to be effective in treating 75% of the people afflicted by a certain disease.
Therefore, probability of success is given by p = 0.75
Now, total number of people affecting from the disease, n = 400
We know the formula for mean, which is given by
[tex]\mu=np\\\mu=400\times 0.75\\\mu=300[/tex]
And the standard deviation is
[tex]\sigma=\sqrt{np(1-p)}\\\sigma=\sqrt{400\cdot0.75(1-0.75)}\\\sigma=8.67[/tex]
Therefore, the mean is 300 and the standard deviation is 8.67.
The graph of f(x) = 6(0.25)x and its reflection across the y-axis, g(x), are shown.
What is the domain of g(x)?
all real numbers
all real numbers less than 0
all real numbers greater than 0
all real numbers greater than or equal to 0
The correct answer is:
a. all real numbers
When we reflect a function across the y-axis, the x-values change their signs. For the function [tex]\( f(x) = 6(0.25)^x \)[/tex], the domain consists of all real numbers since the function is defined for all real values of x.
When we reflect this function across the y-axis to get g(x), the domain of g(x) remains the same as the original function f(x). This is because reflecting across the y-axis does not affect the x-values for which the function is defined.
So, the correct answer is:
a. all real numbers
Solve the systems of equations 6x+3y=9 2x+3y=1
To solve the given system of linear equations, subtract one equation from the other to eliminate the y-variable, then solve for x and substitute back to find y. The solution is x = 2, y = -1.
Explanation:To solve the system of equations 6x + 3y = 9 and 2x + 3y = 1, we can use the subtraction method. We want to find the values of x and y that satisfy both equations simultaneously. Observing that both equations have the term 3y, we can subtract the second equation from the first to eliminate the y-terms:
Subtract the second equation from the first: (6x + 3y) - (2x + 3y) = 9 - 1.Simplify the subtraction: 4x = 8.Divide both sides by 4 to solve for x: x = 2.Substitute x back into one of the original equations to solve for y: 2(2) + 3y = 1.Solve for y: 4 + 3y = 1 --> 3y = -3 --> y = -1.The solution to the system of equations is x = 2, y = -1.
write 2.18 as a mixed number in simplest form
The decimal number 2.18 can be written as the mixed number 2 9/50, considering that .18 is equivalent to the fraction 18/100, which simplifies to 9/50.
Explanation:The number 2.18 is not technically a mixed number, but it can be written in a format similar to a mixed number. A mixed number is defined as a number that includes both a whole number and a proper fraction. In this case, the whole number is 2 and the decimal .18 could be viewed as a type of fraction. If we want to express .18 as a fraction, we can convert it to 18/100. This fraction, however, can be further simplified to 9/50 by dividing both the numerator and the denominator by 2. Therefore, we could write 2.18 as the mixed number 2 9/50.
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The are of a rectangle is 525 square centimeters. The ratio of the length to the width is 7: 3. Find the length and the width.
To solve for the rectangle's dimensions, the area 525 cm² is divided by the ratio of length to width (7:3), revealing a width of 15 cm and a length of 35 cm.
To find the length and width of a rectangle with an area of 525 square centimeters and a length-to-width ratio of 7:3, we can use proportions. Let's define the width as w centimeters. Then, since the ratio of the length to the width is 7:3, the length can be represented as (7/3)w centimeters.
The area of a rectangle is given by length imes width. Therefore, we can set up the equation (7/3)w × w = 525 to represent the area. To find w, we solve for w² = (525 × 3) / 7, which gives us w² = 225.
By taking the square root of both sides, we see that w = 15 centimeters. Now to find the length, we use the ratio: length = (7/3) × 15 = 35 centimeters.
justin has 6 bags of dog food his dogs eat 3/4 bag each day. how long will his dog food last
What third congruence do you need to prove that ΔADB ΔCDB by AAS?
AB (that equal sign with the ~ above it) BC
AD (that equal sign with the ~ above it) DC
∠ ABD ∠ CBD
∠ DBA ∠ CDB