The future value F of the given principal under compound interest for the
time period and interest rate specified is $17,149.99.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = the number of times compounded in a year.
We have,
t = 13 years
r = 2.75%
Compounded monthly
This means,
n = 12
P = $12,000
Now,
A = P [tex](1 + r/n)^{nt}[/tex]
A = 12000 [tex](1 + 0.00229)^{156}[/tex]
A = $17,149.99
Thus,
The future value is $17,149.99.
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determine if the ordered pair (6, 4) is a solution to the inequality
Y > -1/2x + 7 
Yes, because (6, 4) is above the line
No because (6, 4) is below the line
Yes, because (6, 4) is on the line
No, because (6, 4) is on the line
The ordered pair (6, 4) is not a solution to the inequality Y > - (1/2)x + 7 as,
No, because (6, 4) is below the line.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, An inequality Y > - (1/2)x + 7.
Form for the ordered pair (6, 4) we have,
4 > - (1/2)×4 + 7.
4 > - 2 + 7.
4 > 5 which is not true.
Therefore, The ordered pair is not a solution to the inequality.
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A theme park has a ride that is located in a cylinder with a height of 10 yards. The ride goes around the outside of the cylinder, which has a circumference of 515.75 yards. What is the surface area of the cylinder? Estimate to the nearest hundredth, using 3.14 for . Apply the formula for surface area of a cylinder .
Answer:
10218.4 square yards
Step-by-step explanation:
The surface area of a cylinder can be found by using the formula:
2πr(r + h)
where r is the radius of the base and h is the height of the cylinder.
First, we need to find the radius of the cylinder:
515.75 / (2 * π) ≈ 161.8
Now, we can use the formula to find the surface area:
2 * π * 161.8 * (161.8 + 10) ≈ 10218.4
The surface area of the cylinder is approximately 10218.4 square yards, rounded to the nearest hundredth.
What is the image point of (-9,-6)(−9,−6) after the transformation T_{0,4}\circ R_{90^{\circ}}T
0,4
∘R
90
∘
?
\big((
,
\big))
attempt 1 out of 2
Alyssa Freeland
Composition of Transformations
Feb 01, 12:47:03 PM
Watch help video
What is the image point of (-9,-6)(−9,−6) after the transformation T_{0,4}\circ R_{90^{\circ}}T
0,4
∘R
90
∘
?
What is the image point of (-9,-6)(−9,−6) after the transformation T_{0,4}\circ R_{90^{\circ}}T
0,4
∘R
90
∘
?
\big((
,
\big))
attempt 1 out of 2
Alyssa Freeland
Composition of Transformations
Feb 01, 12:47:03 PM
Watch help video
What is the image point of (-9,-6)(−9,−6) after the transformation T_{0,4}\circ R_{90^{\circ}}T
0,4
∘R
90
∘
?
The image point of (-9, -6) after the transformation T<0, 4> R90° is (6, 13).
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
The transformation shifts a point up by 4 units on the y-axis. The transformation is a point 90 degrees counterclockwise.
So, to find the image point of (-9, -6) after the transformation, we first apply the rotation R90° :
(-9, -6) → (6, 9)
Next, we apply the translation T<0, 4> :
(6, 9) → (6, 13)
So, the image point of (-9, -6) after the transformation R90° is (6, 13).
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Answer questions 14-16.
Answer:
14. D
15. angle 2= 125 angle 6= 55
16. yes, because if corresponding angles are congruent, then the lines are parallel.
Step-by-step explanation:
14. alternant exterior are outside of the parallel lines. angle HBF and angle ABD are not.
15. corresponding angles are congruent. angle 5 is the vertical angle of angle 2, meaning that they are congruent. angle 6 are linear pair, meaning they equal to 180. 180-125 is 55, which is the angle measure for angle 6.
What number could replace m below
m/8= 1/2
Answer:
4
Step-by-step explanation:
if you want to see that the fractions are equal, you should first make their denominators equal
[tex]\frac{m}{8} = \frac{4}{8}[/tex]
8 times 1 = 8, so m times 1 should equal 4
therefore, m=4
Answer:
[tex] {\red{ \boxed{\sf{m = 4}}}} \\ [/tex]
Step-by-step explanation:
[tex] \sf\frac{m}{8} = \frac{1}{2} \\ \\ \sf{m = \frac{8 \times 1}{2} } \\ \\ \sf{ m = \frac{8}{2} } \\ \\ \sf{m = \frac{2 \times 4}{2 \times 1} } \\ \\ \sf{m = \frac{4}{1} } \\ \\ \sf{so...} \\ \\ \sf{m = 4}[/tex]
Pls help me find this answer
The value of d/dx (fourth root 5x) is 5/4x^-1/3
What is differentiation?Differentiation is a method used to compute the rate of change of a function f(x) with respect to its input x . This rate of change is known as the derivative of f with respect to x .
Differentiation is used to determine the instantaneous rate of change of quantities. For instance, if we want to find the velocity of a car, we can do it by using differentiation. Mathematically, it is expressed as v = d s /d t , where s is displacement and t is time.
if y =x^n
dy/dx = nx^n-1
therefore to find d/dx(fourth root 5x)
fourth root 5x = 5x^1/4
= d/dx(5x^1/4)
=1/4×5x^1/4-1
= 5/4x^-1/3
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Given the following definitions:
U = {1, 2, 3, 4, 5, 6, 7}
A = {1, 2, 4, 5}
B = {1, 3, 5, 7}
How many elements are in (A' ∪ B)' ?
A car dealership has been keeping detailed records of the colors of cars sold during the current year. This chart shows the probabilities for each color.
What is the probability that for the next two cars sold, the first will be black and the second will be silver?
The requried probability that for the next two cars sold, the first will be black and the second will be silver is 41%.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
To find the probability that a customer will purchase a silver or white car, we add the probabilities of each individual color:
silver = 23%
white = 18%
silver or white = 23% + 18% = 41%
So, the probability that a customer will purchase a silver or white car is 41%.
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6x=16 2/7 ( 2/7 is a fraction.) What is the value of x?
Answer:
x is 3.43
Step-by-step explanation:
[tex]{ \tt{6x = 16 \frac{2}{7} }} \\ \\ { \tt{6x = \frac{(16 \times 7) + 2}{7} }} \\ \\ { \tt{6x \times 7 = 144}} \\ \\ { \tt{42x = 144}} \\ \\ { \tt{x = \frac{144}{42} }} \\ \\ { \tt{x = 3.43}}[/tex]
Answer:
If the time is 3:45 how many minutes is it slow or fast
xavier said the missing length is about 18 units. without calculating, how can you tell that xavier solved incorrectly
Answer: the missing side is longer than the other sides. the other sides' measurements are over 18, so it doesn't make sense.
Step-by-step explanation:
0.1p - 0.00025p^2 suppose that a population develops according to the logistic equation where is measured in weeks. (a) what is the carrying capacity? (b) is the solution increasing or decreasing when is between and the carrying capacity? (c) is the solution increasing or decreasing when is greater than the carrying capacity? note: you can earn partial credit on this problem.
Carrying capacity is the value of p where [tex]0.1p-0.00025p^{2} =0[/tex]. Soln: increasing between 0 and K, decreasing when p > K.
The largest population that can be supported in a certain ecosystem is known as the carrying capacity. It can be found by setting the derivative of the logistic equation to zero, which represents the maximum population growth rate. The carrying capacity of the logistic equation, [tex]0.1p-0.00025p^{2} =0[/tex], can be found by solving for p when the derivative is equal to zero. The solution is p = 40,000.
When t is between 0 and the carrying capacity, the population is increasing because the derivative of the logistic equation is positive. When t is greater than the carrying capacity, the population is decreasing because the derivative of the logistic equation is negative.
The logistic equation represents the growth of a population with time, where p is the population size, and t is measured in weeks. The carrying capacity is the maximum population size that can be sustained in the environment and is given by the value of p that makes the right-hand side of the equation equal to 0. The solution is increasing when t is between 0 and the carrying capacity, and decreasing when t is greater than the carrying capacity.
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K
What is the minimum number of pitches that a baseball player who pitches a complete game can make in a
regulation 9-inning baseball game?
The minimum number of pitches that a baseball player who pitches a complete game can make in a regulation 9-inning baseball game is given as follows:
27 pitches.
How to obtain the minimum number of pitches?The minimum number of pitches is obtained applying the proportions in the context of this problem.
Each baseball game is composed by nine innings, and for each inning the pitching team must get three outs.
Hence the number of outs in a baseball game is given as follows:
9 x 3 = 27 outs.
The minimum number of pitches for one out is of one pitch, hence the minimum number of pitches for an entire game is given as follows:
1 x 27 = 27 pitches.
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For the pair of functions, find the indicated sum, difference, product, or quotient. f(x) = x² + 1, g(x) = 9x + 5 Find (fg)(x).
Answer:The product of the two functions, f and g, is given by fg(x) = (x² + 1)(9x + 5). This can be expanded to give fg(x) = 9x³ + 14x² + 5x + 5.
Step-by-step explanation:
What kind of angle is this
30 points can someone help please
Answer:
[tex]y = 4[/tex]
Step-by-step explanation:
Since each box is the same, that means Box A = Box B, which means 8y+1=6y+9
[tex]8y + 1 = 6y + 9[/tex]
Now to get y's on one sides of the equal sign and numbers on the other.
First we can subtract 1 from each side to get
[tex]8y = 6y + 8[/tex]
Next we'll subtract 6y from both sides
[tex]2y = 8[/tex]
Lastly, we divide both sides by 2
[tex]y = 4[/tex]
Answer:
y=4
Step-by-step explanation:
set up the equation like 8y+1=6y+9.
subtract the one to the other side to get the 8y isolated.
8y=6y+8
subtract6 6y from 8y.
2y=8
divide to find y.
y=4
Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. (Round your answer to three decimal places.)
Radius r Arc Length s Central Angle θ
86 km 166 km radians
The central angle of the circle with a radius of 86 km that intercepts an arc of length 166 km is approximately 3.142 radians.
The formula for the central angle of a circle given the arc length is:
θ = 2 * arccos(s/(2 * r))Plugging in the given values, we get:
θ = 2 * arccos(166/(2 * 86))
= 2 * arccos(1)
= 2 * 90°
= 180°
= 3.142 radians (rounded to three decimal places)
So the central angle of the circle with a radius of 86 km that intercepts an arc of length 166 km is approximately 3.142 radians. The central angle of a circle given arc length is given in the formula; for a given 86 km radius & 166 km arc, the central angle is approximately 3.142 radians.
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Evaluate the expression 5x + 3y - 2 when x = 2 and y = 5
Answer: 25
Step-by-step explanation: just replace the variables with the numbers and multiply and then add!
Answer:The result can be shown in multiple forms.
Point Form:
(-1,-1)
Equation Form:
x= - 1,y = -1
Step-by-step explanation:
just do it
21. Graph of f passes through (-1, 5) and is perpendicular to the line whose equation is x = 6
The slope-intercept equation of a linear function f whose graph satisfies the given condition is y = 5.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y represents the data points.Since the line is perpendicular to x = 6, which is a vertical line, the other line must be horizontal with a slope of zero (0). Therefore, the required equation is given by:
y - y₁ = m(x - x₁)
y - 5 = 0(x - (-5))
y - 5 = 0(x + 5)
y - 5 = 0
y = 5.
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In the Fall 2011 STA 2023 Beginning of the Semester Survey, students were asked how many parties they attended every week and how many text messages they sent per day. The researcher decided to make the number of parties attended per week the explanatory variable and the number of text messages sent per day the response variable. The least squares regression line for this relationship is y-hat = 64.96 + 25.41x. Interpret the y-intercept if appropriate. 1000 2002 Legend Fitted line Parties Do not interpret. The predicted number of text messages per day for someone who has not attended a party this week is 64.96. The predicted number of text messages per day for someone who has not attended a party this week is 25.41. The predicted number of parties attended this week for someone that hasn't sent any text messages is 64.96. The predicted number of parties attended this week for someone that hasn't sent any text messages is 25.41.
The predicted number of text messages sent per day for someone who has not attended a party this week is 64.96 and the predicted number of text messages sent per day for someone who has attended one party this week is 90.37 (64.96 + 25.41).
The least squares regression line is a mathematical formula that is used to predict the response variable (in this case, the number of text messages sent per day) based on the explanatory variable (the number of parties attended per week). The formula for the least squares regression line is y-hat = b0 + b1x, where y-hat is the predicted response variable, b0 is the y-intercept, b1 is the slope, and x is the explanatory variable. In this example, the y-intercept is 64.96 and the slope is 25.41. This means that the predicted number of text messages sent per day for someone who has not attended a party this week is 64.96 and the predicted number of text messages sent per day for someone who has attended one party this week is 90.37 (64.96 + 25.41).
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Jason and his dad plant corn in their vegetable garden. Once the corn stalks reach 7 feet tall, the corn can be harvested. Jason measures the corn and notices that the corn stalks grow about 3.5 inches each week. The corn stalks are currently 63 inches tall. How many more weeks must pass before they are ready to be harvested?
Answer:
6 weeks
Step-by-step explanation:
7 ft = 84 in
84-63=3.5*(number of weeks)
21=3.5*(number of weeks)
21/3.5=number of weeks
6= number of weeks
Answer:
6 weeks
Step-by-step explanation:
7 feet is 84 inches 7 x 12 is 84
we must find the difference
84-63=21
now we divide 21 by 3.5
and week get how much weeks we have left
21/3.5=6
Is the question below
(one solution)
(infinite number of solutions) or
(no solution)
Answer:
One Solution
Step-by-step explanation:
The graph shows two lines crossing each other once, therefore meaning there is only one solution in this graph.
two marbles are drawn at random and without replace- ment from a box containing two blue marbles and three red
The probability of drawing one blue marble and one red marble is thus 6/25 or 24%.
The probability of drawing two marbles from a box containing two blue marbles and three red marbles is calculated as follows. The total number of possible outcomes is calculated by multiplying the number of marbles in the box (2 blue and 3 red) by the number of marbles drawn (2): 5 x 5 = 25. The number of possible outcomes in which two blue marbles are drawn is calculated by multiplying the number of blue marbles in the box (2) by the number of marbles drawn (2): 2 x 2 = 4. The probability of drawing two blue marbles is thus 4/25 or 16%. Similarly, the probability of drawing two red marbles is 12/25 or 48%. The probability of drawing one blue marble and one red marble is calculated by multiplying the number of blue marbles in the box (2) by the number of red marbles in the box (3): 2 x 3 = 6. The probability of drawing one blue marble and one red marble is thus 6/25 or 24%.
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The table below shows the number of male and female participants on each team Which team contains a ratio of 1/3 male to female
The team that contains a ratio of 1/3 male to female is the team for which the number of females is three times the number of males.
How to obtain the ratio between two amounts?The ratio between two amounts a and b is obtained applying a proportion.
A proportion is applied because the ratio is given by the division of the amount a by the amount b.
The ratio for this problem is given as follows:
Male / Female = 1/3
Applying cross multiplication, we have that:
Female = 3 Male (team has three times more females than males).
Missing InformationThe problem is incomplete, hence the answer was given in general terms.
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15, 15 moved 10 units down on a graph
Answer: if you are on a graph and go down 15 it would be
Step-by-step explanation:
15 minus 10 equals
Five scout leaders are taking their troops to an overnight scout competition in NYC. Because of limited funds, there are only 3 rooms that are free for the 5 scout leaders to stay in. Some scout leaders have differences of opinions as to how they lead their troops and cannot share a room, as shown here. Is there a way that these 5 scout leaders can spend the night at the hotel using these 3 free rooms?
Answer:2
Step-by-step explanation:
if the unit price for watermelon is $0.24 per pound and jared pays $1.68 for a watermelon how many pounds does his watermelon weigh
The weight of Jared's watermelon is 7 pounds.
What is the unit price?
A unit price is the cost of a single object or unit of measurement, such as a pound, a kilogram, or a pint, and it is used to compare the prices of similar products offered in various weights and quantities. Selling more than one unit of the same product at a discount from its unit price is known as multiple pricing.
Given price of watermelon per pound weight is $0.24.
And Jared paid $1.68 for a watermelon.
Then,
Let the weight of the watermelon Jared bought be 'x' pounds
0.24/1 = 1.68/x
x=1.68/0.24
x=7
Therefore, The weight of the watermelon Jared bought is 7 pounds.
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Which one of the following transactions would be included in GDP?
a. Ciara pays $50 for a used picture frame at a neighborhood garage sale.
b. Malik donates $500 to his town's junior college scholarship fund.
c. Malik pays $500 to fix the front end of her car damaged in a recent accident.
d. Kayla pays $5,000 to purchase 100 shares of a company stock.
show that each conditional statement in exercise 12 is a tautology using the fact that a conditional statement is false exactly when the hypothesis is true and the conclu- sion is false.
From conditional statements, there can be built a Tautology.
According to the question, when the Hypothesis is true and the conclusion is false, the result will be false. And that's correct.
But when a conditional statement can a Tautology, given the fact that not always a conditional statement will return the logical value of truth? Look at this example below:
1)James is from Orlando and he lives in Florida. Therefore, James is from Orlando.
2)James is from Orlando and he does not live in Florida. Therefore, James is from Orlando.
3)James is not from Orlando and lives in Florida. Therefore, James is from Orlando.
4)James is not from Orlando and he does not live in Florida. Therefore, James is from Orlando.
What we have above is symbolic for:
p∧q→p
And this is tautological, since no matter, what we have line 2 for p∧q, q being false it does not change the value for false, in any way for the whole proposition p∧q→p. What gives us a Tautology?
This, p∧q→p can be rewritten as p∧q⇒p.
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x/5 + 3 = 2 what is x
Answer:
-5
Step-by-step explanation:
Answer:
x = -5
Step-by-step explanation:
hope it helps on quiz/test/assignemnt/homework !!!!!!
let $k$ be the product of all factors $(b - a)$ (not necessarily distinct) where $a$ and $b$ are integers satisfying $1 \le a < b \le 20$. find the greatest positive integer $n$ such that $2^n$ divides $k$.
The greatest positive integer [tex]$n$[/tex] such that [tex]$2^n$[/tex] divides [tex]$k$ is $n = 4$[/tex].
[tex]$k = (2 - 1)(3 - 1)(4 - 1)...(20 - 1)$[/tex]
We can rewrite [tex]$k$[/tex] as [tex]$k = 2^1 \cdot 3^1 \cdot 4^1 \cdot ... \cdot 20^1$[/tex], and then use the formula [tex]$2^n \mid (p_1^{\alpha_1} \cdot p_2^{\alpha_2} \cdot p_3^{\alpha_3} \cdot ... \cdot p_m^{\alpha_m})$ $\iff$ $2^n \mid p_1^{\alpha_1}$[/tex] and [tex]$2^n \mid p_2^{\alpha_2}$[/tex] and[tex]$2^n \mid p_3^{\alpha_3}$ and ... and $2^n \mid p_m^{\alpha_m}$[/tex]
Since all of the exponents [tex]$\alpha_1, \alpha_2, \alpha_3, ..., \alpha_m$[/tex] are equal to 1, we can simplify this to: [tex]$2^n \mid p_1$ and $2^n \mid p_2$ and $2^n \mid p_3$ and ... and $2^n \mid p_m$[/tex]
In this case, [tex]$p_1 = 2$, $p_2 = 3$, $p_3 = 4$[/tex], and so on, so [tex]$2^n$[/tex] must divide all of the prime numbers from 2 to 20 in order for it to divide k. The highest power of 2 that divides all of these prime numbers is [tex]$2^4$[/tex], so the greatest positive integer n such that [tex]$2^n$[/tex] divides [tex]$k$ is $n = 4$[/tex].
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