Answer:
To calculate the amount in the IRA at retirement, we can use the formula for the future value of an annuity:
S = PMT * (((1 + r)^n - 1) / r)
Where:
PMT = the monthly payment (in dollars)
r = the monthly interest rate (APR/12)
n = the number of months (45 years * 12 months/year)
Substituting the given values, we get:
PMT = $50
r = 0.06/12 = 0.005
n = 45 * 12 = 540
S = $50 * (((1 + 0.005)^540 - 1) / 0.005) = $204,055.57
So the IRA will contain $204,055.57 at retirement.
The total deposits made over the time period is:
Total deposits = 540 * $50 = $27,000
Therefore, the amount in the IRA at retirement ($204,055.57) is significantly higher than the total deposits made over the time period ($27,000). This demonstrates the power of compound interest over a long time horizon
Step-by-step explanation:
If u have other qstns too, feel free to ask me on my sn ap
To the nearest whole number, what is the mean of the
number of stamps for these four friends?
F. 92
G. 124
H. 203
J. 217
K. 234
To find the mean of the number of stamps for these four friends, we need to add up the total number of stamps and divide by 4 (the number of friends).
Samir has 60 stamps. Lisa has 2 1/2 times as many stamps as Samir, which can be calculated as follows: 2 1/2 * 60 = 150
Kwame has 443 stamps.
Jake has 159 fewer stamps than Kwame, which can be calculated as follows: 443 - 159 = 284 To find the total number of stamps, we add up the number of stamps each friend has: 60 + 150 + 443 + 284 = 937
To find the mean, we divide by 4: 937 / 4 = 234.25
Therefore, to the nearest whole number, the mean of the number of stamps for these four friends is 234.
Therefore, the answer is K. 234.
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ASAAPP ONE QUESTION ONLY
Answer:
mWX = 106°-------------------------------
Angles at vertex V and Y are of same measure since they intercept same arc WX:
6x - 7 = 10x - 4710x - 6x = 47 - 74x = 40x = 10Angle measure of V and Y is:
6*10 - 7 = 60 - 7 = 53°Arc measure of WX is double the inscribed angle:
mWX = 2*53° = 106°The average retail price of gasoline (all types) for the first half of 2005 was 212.2 cents. What would the standard deviation have to be in order for a 11% probability that a gallon of gas costs less than $1.80? Round z-value calculations to two decimal places and final answer to the nearest cent.
how many degrees is a obtuce angel
A, B & C form the vertices of a triangle.
∠
CAB = 90°,
∠
ABC = 59° and AC = 9.3.
Calculate the length of AB rounded to 3 SF.
what function is equivalent to the following:
the cofunction of sin
Trigonometric ratios connect angles and sides of right triangle. The cofunction of sinθ = cosecθ.
What is trigonometric ratios?Trigonometric ratios are mathematical proportions that connect the angles and sides of a right triangle. The hypotenuse, adjacent, and opposing sides are the three sides of a right triangle, which is a triangle having one angle of 90 degrees.
For example, imagine a triangle made up of wires of length L.
The same wire can be used to create a square if all sides are the same length.
The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.
As we can say, the surroundings are one-dimensinal. As a result, you can measure in meters, kilometers, millimeters, etc.
Inches, feet, yards, and miles are other globally recognized units of circumference measurement.
Hence, The function equivalent to sinθ = cosecθ.
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CAN SOMEONE HELP PLEASE!!!
What is the circumference of a circle with a diameter of 21 cm? Approximate using pi equals 22 over 7.
7 cm
33 cm
66 cm
132 cm
Answer:
The formula gives the circumference of a circle:
C = πd
Where d is the diameter of the circle.
Substituting the given values, we get:
C = (22/7) x 21 cm
C = 66 cm (approx)
Therefore, the circle's circumference with a diameter of 21 cm, approximated using π equals 22/7, is 66 cm.
So, the correct option is (C) 66 cm.
The ratio of the width to the length of a flower bed is 10:19. How long is the flower bed if it's width is 6feet
Answer:
The length of the flower bed is 11.4 feet.
Step-by-step explanation:
If the ratio of width to length of the flower bed is 10:19, this means that for every 10 units of width, there are 19 units of length.
Let's call the width of the flower bed "W" and the length "L". We know that W is 6 feet, so we can write:
W:L = 10:19
Substituting the value of W, we get:
6:L = 10:19
To solve for L, we can cross-multiply to get:
10L = 6 x 19
10L = 114
L = 11.4
Therefore, the length of the flower bed is 11.4 feet.
I NEED THIS ANSWER TO THIS QUESTION
You should invest $139.07 each month to end up with $17,000 in 8 years, assuming a guaranteed APR of 4.5%.
What is annual interest rate?The annual interest rate (also known as the annual percentage rate or APR) is the amount of interest that is charged on a loan or investment over the course of one year.
According to question:To calculate the monthly deposit needed to reach the target amount of $17,000 in 8 years at a guaranteed APR of 4.5%, we can use the formula for future value of an annuity:
FV = P * ([tex](1 + r/n)^(n*t)[/tex] - 1) / (r/n)
where FV is the future value, P is the monthly payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.
In this case, we want to find the monthly payment (P), and we know that:
FV = $17,000
r = 4.5% = 0.045 (decimal)
n = 12 (since we are making monthly deposits)
t = 8
When these values are added to the formula, we obtain:
$17,000 = P * ([tex](1 + 0.045/12)^(12*8)[/tex] - 1) / (0.045/12)
Simplifying and solving for P, we get:
P = $139.07
Therefore, you should invest $139.07 each month to end up with $17,000 in 8 years, assuming a guaranteed APR of 4.5%.
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HELP PLS THIS IS DUE TOMORROW PLSSSSSSSS
Are ARST and ANSP similar? Use pencil and paper. Find the
measure of the angles in each triangle.
Which two angles must be congruent? What type of angles are they? (1 point)
The measure of the angles in triangle ARST are: 28 degrees, 28 degrees, 124 degrees, 124 degrees. The measure of the angles in triangle ANSP are: 28 degrees, 51 degrees, 101 degrees, 129 degrees.
What is angle?An angle is a geοmetric figure fοrmed by twο rays οr lines with a cοmmοn endpοint, called the vertex. Angles are typically measured in degrees οr radians and are used tο describe the amοunt οf turn οr rοtatiοn between twο intersecting lines οr οbjects. Angles can be acute (less than 90 degrees), right (exactly 90 degrees), οbtuse (greater than 90 degrees), straight (exactly 180 degrees), οr reflex (greater than 180 degrees).
Here,
To find the measure of the angles in each triangle, we need to solve for the value of x in both equations.
For the first equation, we can simplify it as follows:
x + 14 = 2x
Subtracting x from both sides, we get:
14 = x
For the second equation, we can simplify it as follows:
3x + 9 = 2x + 23
Subtracting 2x and 9 from both sides, we get:
x = 14
Now that we know x = 14, we can find the measure of the angles in each triangle.
In triangle ARST, we have:
angle A = x + 14
= 14 + 14
= 28 degrees
angle R = 2x
= 2(14)
= 28 degrees
angle S = 180 - (angle A + angle R)
= 180 - (28 + 28)
= 124 degrees
angle T = 180 - (angle A + angle R)
= 180 - (28 + 28)
= 124 degrees
In triangle ANSP, we have:
angle A = x + 14
= 14 + 14
= 28 degrees
angle N = 3x + 9
= 3(14) + 9
= 51 degrees
angle S = 180 - (angle A + angle N)
= 180 - (28 + 51)
= 101 degrees
angle P = 180 - (angle N)
= 180 - 51 = 129 degrees
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What was the age distribution of prehistoric Native Americans? Suppose an extensive anthropological studies in the southwestern United States gave the following information about a prehistoric extended family group of 84 members on what is now a Native American reservation.
Age range (years) 1-10 11-20 21-30 31 and over
Number of individuals 35 22 20 7
For this community, estimate the mean age expressed in years, the sample variance, and the sample standard deviation. For the class 31 and over, use 35.5 as the class midpoint. (Round your answers to one decimal place.)
x =
years
s2 =
s =
years
Mean age: 16.1 years, Sample variance: 50.47 square years and Sample standard deviation: 7.10 years for the given problem.
To estimate the mean age, we need to find the midpoint of each age range and multiply it by the number of individuals in that range. Then we add up these products and divide by the total number of individuals:
Mean age = [(1+10)/2 x 35 + (11+20)/2 x 22 + (21+30)/2 x 20 + 35.5 x 7] / 84
= (5.5 x 35 + 15.5 x 22 + 25.5 x 20 + 35.5 x 7) / 84
= 16.1
Therefore, the estimated mean age of this extended family group is 16.1 years.
To calculate the sample variance, we need to find the deviation of each age from the mean, square each deviation, and add up these squared deviations. Then we divide this sum by the total number of individuals minus one:
s2 = [(1-16.1)2 x 35 + (11-16.1)2 x 22 + (21-16.1)2 x 20 + (35.5-16.1)2 x 7] / (84-1)
= (2254.05 + 537.08 + 220.89 + 253.68) / 83
= 50.47
Therefore, the estimated sample variance is 50.47 square years.
We simply take the square root of the sample variance to calculate the sample standard deviation:
s = [tex]\sqrt{s2}[/tex]
= s[tex]\sqrt{50.47}[/tex]
= 7.10
Therefore, the estimated sample standard deviation is 7.10 years.
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cadens savings account had $70 in its first year. each year since the , his account accumulated interest amounting to 10% of the valance in the previous year.
let f(n) be cadens account balance at the nth year of the saving
f is a sequence what kind of sequence is it
The supplied question's response based on the savings account is A geometric sequence is the sequence f.
What is Geometric sequence?A geometric sequence is a set of numbers where each term is obtained by multiplying the one before it by a predetermined quantity known as the common ratio. The following is the generic formula for a geometric sequence:
[tex]a, ar, ar^2,ar^3,ar^4,...[/tex]
There are two types of geometric sequences: finite and endless. While an infinite geometric sequence has no end, a finite geometric sequence has a set number of terms.
Because each term is created by multiplying the term that came before by a constant ratio of 1.1, the sequence f is a geometric sequence. (which accounts for the interest that has accrued on the preceding balance using the formula 1 + 0.1).
The first term is for $70, and each succeeding term is equal to the first term times 1.1. As a result, the nth term of the series can be
written as: [tex]f(n)=\$ \times 1.1^{n-1}[/tex]
where n is how long it has been since the first year of saving.
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Pls help, Micheal tracked the value of his boat each year after he purchased it. Determine whether the data are linear, quadratic, or exponential. Use regression to the function that models the data.
This means that after two years since the purchase, the boat was worth $24.57.
What is worth?In general, worth refers to the value or monetary equivalent of something. It can be used to describe the financial value of assets such as property, stocks, or commodities, or to describe the value of something in terms of its usefulness, importance, or significance.
Michael tracked the value of his boat each year after he purchased it. Determine whether the data are linear, quadratic, or exponential. Use regression to find the function that models the data.
16.75
19.5
4
3
22.9
27.25
2
1
32
0
Years Since Purchase
To better understand the exponential function that models the data, let's break it down:
y = 10.92 * 1.50ˣ
The constant "10.92" represents the initial value of the boat when it was purchased. This means that the boat was worth $10.92 when Michael first bought it.
The constant "1.50" represents the growth factor of the boat's value. This means that each year, the value of the boat increases by a factor of 1.50.
The variable "x" represents the number of years since the boat was purchased. The function takes this input and returns the value of the boat at that time.
For example, if we plug in x=1 into the function, we get:
y = 10.92 * 1.50¹
y = 16.38
This means that after one year since the purchase, the boat was worth $16.38. Similarly, if we plug in x=2 into the function, we get:
y = 10.92 * 1.50²
y = 24.57
This means that after two years since the purchase, the boat was worth $24.57.
It's important to note that the exponential function assumes that the growth rate remains constant over time. In reality, the value of the boat may be affected by other factors such as wear and tear, maintenance, and market fluctuations. Nevertheless, the exponential function provides a useful model for understanding the trend in the data and making predictions about the future value of the boat.
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How do you solve this?
Answer:
[tex]100\pi \text{ in}^3[/tex]
Step-by-step explanation:
Volume of a Cone Equation:
[tex]v = \frac{1}{3}\times \pi \times r^2 \times h[/tex]
1) Find h
Use the Pythagorean Theorem to find h
[tex]a^2 \times b^2 = c^2[/tex]
Change diameter to radius. (10 in ---> 5in)
a = 5
[tex]1) 5^2 + b^2 = 13^2\\\\2) 25 + b^2 = 169\\\\3) b^2 =144\\\\4) 12[/tex]
Step 2) Subtract 25 on both sides so [tex]b^2[/tex] is alone
Step 3) Square root both sides
Step 4) h = 12
2) Plug in known variables:
h = 12 in
r = 5 in;
Equation now:
[tex]v = \frac{1}{3} \times \pi \times 5^2 \times 12[/tex]
3) Solve:
[tex]1) \frac{1}{3} \times \pi \times 5^2 \times 12\\\\2) \frac{\pi}{3} \times 5^2 \times 12\\\\3) \frac{\pi}{3} \times 25 \times 12 \\\\4) \frac{\pi}{3} \times 300\\\\5) \frac{300\pi}{3} \\\\\text{Simplify:}\\100\pi[/tex]
At the start of a game of marbles, Peter and Jack had 160 marbles in all. In the first round, Peter lost 3/5 of his marbles to Jack. In the second round, James lost 3/7 of his marbles to Peter. At the end of the second round of the game, they had the same number of marbles. How many marbles did each of them have at first?
Answer: Therefore, at the start of the game, Peter had 80 marbles and Jack had 80 marbles.
Step-by-step explanation:
Find the two -intercepts of the function and
show that at some point between the two -intercepts.
The x intercept of the function f(x) = x√(x + 4) is at
(-4, 0) and (0, 0)
What is x-intercept?The x-intercept is the point where a graph or a line crosses the x-axis. In other words, it is the point where the value of the dependent variable (usually represented on the y-axis) is zero.
In an equation, the x-intercept is the value of x when y is equal to zero. It is often denoted by the point (x, 0) on a graph.
The plotted graph shows that the x intercept is at
(-4, 0) and (0, 0)
Graph is attached
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can someone give me the answers in order please
A car was valued at $45,000 in the year 1991. The value depreciated to $12,000 by the year 2000.
A) What was the annual rate of change between 1991 and 2000?
r=-------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2003 ?
value = $----------------Round to the nearest 50 dollars.
The total change in value is $45,000 - $12,000 = $33,000. The annual rate of change is 0.0495. Converting the rate of change to a percentage is 4.95%. Assuming the car value continues to drop by the same percentage, the value of the car in 2003 is $10,850.
What is a percentage?A percentage is a way of expressing a number as a fraction of 100. Percentages are typically expressed using the symbol "%".
In the given question,
A) The total change in value is $45,000 - $12,000 = $33,000. The time period is 9 years (2000 - 1991). Therefore, the annual rate of change is:
r = [tex](Change in value / Initial value) ^ (1/Time period)[/tex] - 1
r = [tex]($33,000 / $45,000) ^ (1/9)[/tex] - 1
r = 0.0495
Rounding this to 4 decimal places, the annual rate of change is 0.0495.
B) Converting the rate of change to a percentage:
r = 0.0495 * 100
r = 4.95%
Therefore, the answer to part A in percentage form is 4.95%.
C) Assuming the car value continues to drop by the same percentage, we need to calculate the value of the car in the year 2003. The time period from 2000 to 2003 is 3 years. Therefore, the value of the car in 2003 can be calculated as follows:
Value in 2003 = $12,000 * [tex](1 - r) ^ 3[/tex]
Value in 2003 = $12,000 * [tex](1 - 0.0495) ^ 3[/tex]
Value in 2003 = $10,840.09
Rounding this to the nearest 50 dollars, the value of the car in 2003 is $10,850.
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A furniture company is introducing a new line of lounge chairs next quarter. These are the cost and revenue functions, where x represents the number of chairs to be manufactured and sold: R(x) = 1,248x – 8.32x2 C(x) = 36,400 – 83.2x
The profit function for a furniture company introducing a new line of lounge chairs is P(x) =[tex]-8.32x^2 + 1,248x - 36,400[/tex], where x represents the number of chairs to be manufactured and sold.
The problem provides the revenue function and cost function for a furniture company introducing a new line of lounge chairs. To find the profit function, we need to subtract the cost function from the revenue function.
The revenue function R(x) is given as 1,248x - [tex]8.32x^2[/tex], where x represents the number of chairs manufactured and sold. This function calculates the total revenue obtained by the company by multiplying the number of chairs sold (x) by the price of each chair (1,248 - 8.32x).
The cost function C(x) is given as 36,400 - 83.2x. This function calculates the total cost incurred by the company to manufacture x chairs, which includes both fixed and variable costs.
To find the profit function for the furniture company, we need to subtract the cost function C(x) from the revenue function R(x):
P(x) = R(x) - C(x) = (1,248x - [tex]8.32x^2[/tex]) - (36,400 - 83.2x)
Simplifying this expression, we get:
P(x) =[tex]-8.32x^2[/tex] + 1,248x - 36,400
Therefore, the profit function for the furniture company is P(x) = [tex]-8.32x^2[/tex] [tex]+ 1,248x - 36,400[/tex].
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Harper is deep-sea diving with two friends. Toby is floating on the surface 57 feet above
Harper, and Meg is exploring a coral reef 76 feet in front of Harper. How far apart are Toby
and Meg?
The distance between Toby and Meg are approximately 95 feet apart.
How to solve for the distanceWe can solve this problem using the Pythagorean theorem, which relates the lengths of the sides of a right triangle.
The distance between Toby and Meg is the hypotenuse of a right triangle with legs 57 feet and 76 feet.
So we can use the Pythagorean theorem to find this distance:
distance^2 = 57^2 + 76^2
distance^2 = 3249 + 5776
distance^2 = 9025
distance = sqrt(9025)
distance = 95
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2. You check 50 cartons of eggs. Eight of the cartons have at least one
cracked egg. What is the experimental probability that a carton of ega
has no cracked eggs?
Answer: 3/20 and 15%
Step-by-step explanation:
Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number.
the product of 6 less than a number and 2 more than the number
The complete verbal phrase translates to
(Do not perform the calculation.)
The expression represents the product of two terms = (x - 6) × (x + 2)
What do you mean by Linear Equation ?An equation in mathematics that is linear has a variable whose maximum power is 1. Alternatively said, it is an algebraic equation of the following form:
ax+ b = 0
where an is a constant that cannot equal zero, b is a constant, and x is a variable. Another way to express a linear equation in its general form is as follows:
y = mx + b
where the y variable is the dependent variable, the independent variable is x, the slope is m, and the y-intercept is b.
The product of 6 less than a number and 2 more than the number can be translated into the mathematical expression:
(x - 6) × (x + 2)
Here, x represents the unknown number, and the expression represents the product of two terms: "6 less than a number" (x - 6) and "2 more than the number" (x + 2).
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Use substitution to determine whether the given number is a zero of the given
polynomial.
3; f(x) = -x^4 -8x²-x-5
also
As f(3) is not equal to zero, 3 is not a zero of the polynomial f(x) = -x⁴ -8x²-x-5.
How to determine whether a given number is a zero of the a polynomial?Given the polynomial in the question;
f(x) = -x⁴ -8x²-x-5
Given number: 3
To check if 3 is a zero of the polynomial f(x) = -x⁴ -8x²-x-5, we need to substitute x = 3 into the polynomial and see if the result will give zero.
f(x) = -x⁴ -8x²-x-5
plug i x = 3
f(3) = -3⁴ - 8(3)² - 3 - 5
= -81 - 72 - 3 - 5
= -161
Therefore, 3 is not a zero of the polynomial f(x) = -x⁴ -8x²-x-5.
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According to the line plot, what is the total weight of the dog toys that weighed
1
8
of a pound or
3
8
of a pound?
3
4
of a pound
1
1
2
pounds
3 pounds
7
8
of a pound
The total weight of the dog toys that weighed 1/8 of a pound or 3/8 of a pound is 1 3/8 pounds.
What is line plot?A line plot is a graphical representation of data that involves placing X's or other symbols above a number line to show the frequency of each value in a data set.
Each X represents one occurrence of the data value on the number line. Line plots are useful for quickly visualizing the distribution of a data set, especially when there are only a few unique values in the data set.
Based on the line plot, we can see that there are 2 dog toys that weigh 1/8 of a pound and 3 dog toys that weigh 3/8 of a pound.
To find the total weight of the dog toys that weigh 1/8 of a pound or 3/8 of a pound, we need to add the weights of these toys.
The total weight of the dog toys that weigh 1/8 of a pound is 2/8 of a pound, which simplifies to 1/4 of a pound.
The total weight of the dog toys that weigh 3/8 of a pound is 3 x 3/8 = 9/8 of a pound.
Adding these weights together, we get:
1/4 + 9/8 = 11/8 of a pound
This simplifies to 1 3/8 pounds.
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If you divide a positive number that is larger than 36 by a positive number that is less than 9, what can you definitely say about the relative value of the quotient?
It must be equal to 5
It must be greater than 4
It must be between 9 and 36
It must be less than 4
Answer:
It must be greater than 4
Step-by-step explanation:
We know that 36 ÷ 9 = 4.
Therefore, if the denominator is less than 9 and the numerator is greater than 36, the quotient would only increase since the numerator increases while the denominator decreases.
Therefore, it must be greater than 4.
By what number must row 2 in the matrix be multiplied for the matrix to be change to ___
The number that must row 2 in the matrix be multiplied for the matrix to be changed to B. -2.
What are row operations?
Row operations are mathematical operations that can be performed on the rows of a matrix to manipulate its properties or solve systems of linear equations.
To solve this problem, we need to perform row operations on the matrix until row 2 is transformed into the desired row. Each row operation involves multiplying a row by a scalar, adding or subtracting one row from another, or swapping two rows.
Starting with the given matrix:
20 -2
1 1 1 1 1 6 -14
We can perform the following row operations:
Subtract row 1 from row 2:
20 -2
1 1 1 -19 -19 4 -6
Multiply row 2 by -3:
20 -2
-3 -3 -3 57 57 -12 18
Subtract 2 times row 2 from row 1:
26 4
-3 -3 -3 57 57 -12 18
Divide row 1 by 13:
2 4/13
-3 -3 -3 57 57 -12 18
Therefore, we see that row 2 in the matrix must be multiplied by -3 to transform it into the desired row.
So the answer is: B. -2
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Estimate the cost of painting a concrete patio if it is a 12 foot by 14 foot rectangle, and a quart of paint that covers 53 square feet costs $10.99
Answer:
$43.96
Step-by-step explanation:
We first need to find the area of the patio which is 12-foot by 14-foot
12 ft * 14 ft = 168 sq ft
next, we need to know how many quarts are needed to cover the entire area of the patio, and we know a quart cover 53 square feet, so we divide the total area of the patio by 53:
168 sq ft ÷ 53 sq ft/quart ≈ 3.17 quarts
We'll need to buy 4 quarts of paint to cover the entire patio.
The cost of 1 quart of paint is $10.99, so the total cost of 4 quarts will be:
4 quarts x $10.99/quart = $43.96
Therefore, the estimated cost of painting the concrete patio will be around $43.96.
Select "Growth" or "Decay" to classify each function.
y=200(0.5)2t = DECAY
y=12(2.5)t6 = GROWTH
y=(0.65)t4 = DECAY
just took the test
y=200(0.5)2t this functiοn represents decay, y=12(2.5)t6 this functiοn represents grοwth and y=(0.65)t4 this functiοn represents decay.
What is functiοn?In mathematics, a functiοn is a relatiοnship between twο sets οf elements, called the dοmain and the range, such that each element in the dοmain is assοciated with a unique element in the range.
In general, we can determine whether a functiοn represents grοwth οr decay by examining the base οf the expοnential term.
If the base is greater than 1, the functiοn represents grοwth.
If the base is between 0 and 1, the functiοn represents decay.
Here are the classificatiοns fοr each οf the given functiοns:
y=200(0.5)2t
The base οf the expοnential term is 0.5, which is between 0 and 1. Therefοre, this functiοn represents decay.
y=12(2.5)t6
The base οf the expοnential term is 2.5, which is greater than 1. Therefοre, this functiοn represents grοwth.
y=(0.65)t4
The base οf the expοnential term is 0.65, which is between 0 and 1. Therefοre, this functiοn represents decay.
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Complete Question:
Select "Growth" or "Decay" to classify each function.
Function Which ones are growth or decay
f(x)=(1.05)t4
y=100(0.4)t
f(x)=14(10)t12
An artist built a wooden sculpture in the shape shown below.
Rectangular prism with length as 9 feet, breadth as 7 feet and height as 8 feet is given. A rectangular prism with length as 7 feet, breadth as 7 feet and height as 4 feet is cut from the right top end of the bigger prism.
Part A
Which expressions could be used to find the volume of the sculpture?
Select all that apply.
A. (7 × 8 × 2) + (7 × 7 × 4)
B. (8 × 2 × 7) + (9 × 4 × 7)
C. (2 × 4 × 7) + (7 × 4 × 7)
D. (9 × 4 × 7) + (2 × 7 × 4)
PartB
What is the volume of the sculpture?
Enter your answer in the box.
cubic feet
the expressions that could be used to find the volume of the sculpture are A and B and the volume of the sculpture is 364 cubic feet.
Part A:
To find the volume of the sculpture, we need to add the volumes of the two rectangular prisms: the original one and the one that was cut from it. We can express the volume of the original prism as:
9 × 7 × 8
And the volume of the cut prism can be expressed as:
7 × 7 × 4
So, the expressions that could be used to find the volume of the sculpture are A and B:
A. (7 × 8 × 2) + (7 × 7 × 4)
B. (8 × 2 × 7) + (9 × 4 × 7)
Part B:
Using expression A, we get:
(7 × 8 × 2) + (7 × 7 × 4) = 112 + 196 = 308 cubic feet
Using expression B, we get:
(8 × 2 × 7) + (9 × 4 × 7) = 112 + 252 = 364 cubic feet
Therefore, the volume of the sculpture is 364 cubic feet.
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4) Two Truths and a Lie. Use what you know about the patterns in area models to determine which two area models correctly represent a factorable polynomial in the form of ax^2 + bx + c where c = 40. The middle “b” term is unknown
The correct area models are 4e and none of the given models for 4d and 4c.
What is the quadratic equation?
The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The area model of 4c is incorrect because the last term of the polynomial, which is 40, is represented by the bottom right box of the area model. However, in the given area model, the box representing 40 is in the upper row.
The area model of 4e is correct because it represents the polynomial as the product of two binomials, where the factors are (x-5) and (x-8).
When multiplied using the distributive property, the resulting polynomial is x² - 13x + 40, which matches the given polynomial form.
The area model of 4d is incorrect because it does not properly represent a factorable polynomial.
It only includes three boxes, representing the three terms of the polynomial, but it does not show how the terms can be factored into binomials.
Therefore, the correct area models are 4e and none of the given models for 4d and 4c.
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PLEASE I REALLY NEED HELP PLEASE
A car was valued at $45,000 in the year 1991. The value depreciated to $12,000 by the year 2000.
A) What was the annual rate of change between 1991 and 2000?
r=-------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2003 ?
value = $----------------Round to the nearest 50 dollars.
A) The annual rate of change or APR between 1991 and 2000 is approximately -0.1091.
B) The correct answer to part A in percentage form is approximately -10.91%.
C) The value of the car in 2003 is $7,750.
What is annual rate?
The car depreciated from $45,000 to $12,000 in 9 years. Using the formula for annual rate of change or annual percentage rate (APR):
r = [tex](Vf/Vi)^{1/n}[/tex] - 1
where Vf is the final value, Vi is the initial value, n is the number of years, and r is the annual rate of change or APR.
Substituting the given values:
r = [tex]($12,000/$45,000)^{1/9}[/tex] - 1
r ≈ -0.1091
Therefore, the annual rate of change or APR between 1991 and 2000 is approximately -0.1091.
B) The correct answer to part A in percentage form is approximately -10.91%.
What is APR?
To express the answer as a percentage, multiply the annual rate of change by 100 and round to the nearest 0.01%:
r = -0.1091 × 100
r ≈ -10.91%
Therefore, the correct answer to part A in percentage form is approximately -10.91%.
C) The value of the car in 2003 is $7,750.
What is the value?
To find the value of the car in 2003, we need to use the same percentage rate of decrease from 2000 to 2003. Since 2003 is 3 years after 2000, the value will be:
value = $12,000 × (1 + r)³
value ≈ $7,729.18
Rounding to the nearest 50 dollars, the value of the car in 2003 is $7,750.
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