[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]
[tex]\qquad \begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 4500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases}[/tex]
[tex]A=4500\left[ \cfrac{\left( 1+\frac{0.04}{1} \right)^{1 \cdot 10}-1}{\frac{0.04}{1}} \right]\left(1+\frac{0.04}{1}\right) \\\\\\ A=4500\left[ \cfrac{(1.04)^{10}-1}{0.04} \right](1.04) \implies A \approx 56188.58[/tex]
so every year you were putting in 4500 bucks, so for 10 years that'd be a total deposits for 4500*10 = 45000, so let's squeeze out the 45000 from the the total, that gives us 56188.58 - 45000 ≈ 11188.58.
so, if we take 56188.58 to be the 100%, what's 11188.58 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 56188.58 & 100\\ 11188.58& x \end{array} \implies \cfrac{56188.58}{11188.58}~~=~~\cfrac{100}{x} \implies 56188.58x=1118858 \\\\\\ x=\cfrac{1118858}{56188.58}\implies x\approx \stackrel{\%}{19.91}[/tex]
Two basketball players are trying to have the most
points per game for the season. The current leader has
2112 points in 77 games and the second place player
has 2020 in 74 games. Assuming the current leader
plays no more games, how many points per game will
the second place player have to score in each of the
next three games to take the lead in this category?
The second place player must earn 0.0467 points per game in each of the next three games to take the lead in this category.
What is PPG Statistics?
The average amount of points scored by a player per game played in a sport, over the length of a run of games, a season, or a career, is known as points per game, or PPG. It is computed by dividing the total points by the number of games. Basketball and ice hockey are two sports where the jargon is frequently utilized.The points per game is an important statistic and it can range between 0 to 40+.First, calculate the PPG earned by the current leader of the season.
The total points earned by the current leader amount to 2112 and he had participated in a total of 77 games.
The following formula can be used to determine the PPG earned by the current leader per game,
PPG = Total Points / Total Games
[tex]\implies PPG=\frac{2112}{77}\\ \implies PPG = 27.42[/tex] -----(1)
Now, calculate the PPG of the player who is ranked in the second place for the season.
The total number of points earned by the second place player is 2020 and he played a total of 74 games.
The second place player earned the following points per game,
PPG = Total Points / Total Games
[tex]\implies PPG=\frac{2020}{74}\\ \implies PPG = 27.29[/tex] ---(2)
The difference in score with the leading team can be found by subtracting (2) from (1),
[tex]\implies 27.42-27.29=0.13[/tex]
So, to be the leading player, the second place player must obtain a lead of 0.14 points per game in the next three games if the current player plays no more games.
In such a situation, the total PPG of the player should be 27.43 and the number of games to be played is 3.
So, the number of points required to take lead can be calculated as,
PPG = Total Points / Total Games
[tex]\implies 27.43=P/3[/tex]
So, the Total Points required, [tex]P=27.43 \times 3 =82.29[/tex]
And, the PPG required by the second place player to score in each of the next three games is calculated as,
[tex]\frac{0.14}{3}=0.0467[/tex]
Therefore, the second place player must earn 0.0467 points per game in each of the next three games to take the lead in this category.
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Keith drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 12 hours. When Keith drove home, there was no traffic and the trip only took 8 hours. If his average rate was 20 miles per hour faster on the trip home, how far away does Keith live from the mountains?
Do not do any rounding.
Keith live 480 miles far way from the mountains.
How far away does Keith live from the mountains?The distance between two locations is represented by the length of the line linking them. If the two points are on the same horizontal or vertical line, subtracting the various coordinates will show how far apart they are.
Consider the provided information.
Keith drove to the mountains last weekend. The trip took 12 hours because of the high traffic on the way there.
Let the distance is D and average rate or speed is x miles.
Distance = speed × time
Substitute the respective values.
D = x * 12
D= 12x
When Keith drove home, there was no traffic and the trip only took
hours. The average rate was 8 miles per hour faster on the trip home,
The average rate or speed during return is x+20 miles.
Substitute the respective values in the above formula.
D = (x+20) ×8
D= 8x+160
Equate both the equations.
8x+160 = 12x
4x= 160
x=160/4
=40
Substitute the value of x in D= 12x
D=12(40)
D= 480
Hence, Keith live 480 miles far way from the mountains.
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Writing Equations of lines
Write the equation of each line with the given information
Slope = 7, y-intercept = -3
doreen schmidt is a chemist. she needs to prepare 36 ounces of a 11%
The answer to Question based on Conversion of Units is 1008gm
What is Conversion OF Units?
It is a method to convert units from one version from another.
Solution:
Here in this Question we must know the conversion that 1 ounce is nearly equal to 28gms
Hence if Doreen Schmidt needs to prepare 36 ounces of 11% solution he needs to have exact measurement of chemicals
Hence we can say must have that 36 ounces of chemicals to make that
Hence by unit conversion 36 multiplied by 28 which comes out to be 1008gm of chemical he needs to have
to make 11% solution
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An employee earns $175 for 15 hours work. Do these quantities (salary and time) vary indirectly or directly?
Based on the information given the constant of variation is 11.67.
What is the rate of change?
The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time
by using this formula
Constant of variation = Amount earned/Time
Where:
Amount earned=$175
Time=15 hours
Let's plug in the formula
Constant of variation=$175/15
Constant of variation=11.66
Constant of variation=11.67 (Approximately)
Hence, the constant of variation is 11.67.
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What is the measure of angle x? (5 points)
A pair of parallel lines is cut by a transversal. An exterior angle on the left of the transversal is labeled as 45 degrees. An interior angle on the right of the transversal, which is not vertically opposite to the 45 degree angle, is labeled as x.
Question 2 options:
1)
45 degrees
2)
90 degrees
3)
135 degrees
4)
140 degrees
Answer:
idek
Step-by-step explanation:
The coordinate plane shows the location of teammates during a game of ultimate Frisbee. Each interval on the coordinate plane represents 1 foot
Jonathan
4
Malik
3
Marianne
Ellena
If Marianne throws the Frisbee directly to Malik, how far, in feet (ft), will the Frisbee travel? Round your answer to the nearest tenth.
A rubber bouncy ball is dropped from a height of 106.00 inches onto a hard flat floor
Answer:
explain m ore
Step-by-step explanation:
In a raffle, one ticket will win a $560 prize, one ticket will win a $490 prize, one ticket will win a $270 prize, one ticket will win a $180 prize, and the remaining tickets will win nothing. There are 500 in the raffle. If you have a ticket, what is the expected payoff?
The expected payoff from the raffle is given as follows:
$3.
How to obtain the expected payoff?The payoff is modeled by a discrete distribution, hence the expected payoff is the expected value of the said discrete distribution.
There are 500 tickets in the raffle, hence the probabilities are given as follows:
P(X = 560) = 1/500.P(X = 490) = 1/500.P(X = 270) = 1/500.P(X = 180) = 1/500.P(X = 0) = 496/500.The expected value of a discrete distribution is calculated as the sum of all outcomes multiplied by it's respective probability, hence:
E(X) = 560 x 1/500 + 490 x 1/500 + 270 x 1/500 + 180 x 1/500 + 0 x 496/500 = $3.
(all the outcomes and their probabilities are taken from the distribution built in this problem).
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Solve for x using the Pythagorean Thereon
Using the Pythagorean Theorem for the right angled triangles and observing the given figure, The value of x can't be solved because the hypotenuse must be the longest side of the right angled triangle which is violated in this question.
What is a triangle?A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed. It implies that the internal angles of a triangle add up to 180 degrees.
What is the formula for Pythagorean Theorem?The required formula is:
[tex]h^{2}=p^{2}+b^{2}[/tex]
In the triangle, Hypotenuse is not the biggest side. So, We can't solve for the value of x.
[tex]10^{2} = 15^{2}+x^{2}[/tex]
[tex]x=\sqrt{10^{2}-15^{2}}[/tex]
which yields a negative number inside square root which is not possible to solve.
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hi can help with question
The linear regression equation in this problem is given as follows:
y = 4.774x + 39.474.
Then the estimates are given as follows:
a) x = 3 hours: 53.8.
b) x = 4.5 hours: 61.
c) x = 13 hours: 101.5.
d) x = 1.5 hours: 46.6
How to obtain the linear regression equation?The linear regression equation is obtained inserting the points of the table into a linear regression calculator.
From the table in this problem, the points are given as follows:
(0,39), (1,45), (2,52), (4, 49), (5, 61), (5,72).
Inserting these points into a calculator, the equation is given as follows:
y = 4.774x + 39.474.
Then the estimates are obtained with the numeric values, as follows:
a) x = 3 hours: y = 4.774(3) + 39.474 = 53.8.
b) x = 4.5 hours: y = 4.774(4.5) + 39.474 = 61.
c) x = 13 hours: y = 4.774(13) + 39.474 = 101.5.
d) x = 1.5 hours: y = 4.774(1.5) + 39.474 = 46.6.
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If D is the Midpoint of AC and E is the midpoint of BC find the value of X
D is the midpoint of AC, and E is the midpoint of BC, hence the value of x for the given problem will be 9 units.
What is similar triangle?If the respective sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are comparable (or proportion). Triangles that are similar will have the same shape but may not be the exact same size. According to the fundamental principles of triangles, two triangles are said to be congruent if their size and shape are the same, but two triangles are said to be similar if their shape is the same but their sizes differ. The proportions of similar triangles are the same.
Here,
Since these are similar triangle,
BE=EC
BC=BE+EC
BC=2BE
6/(3x-15)=1/2
12=3x-15
3x=27
x=9
The value of x for the given problem where D is the Midpoint of AC and E is the midpoint of BC will be 9 units.
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A ship is tied to a dock with a rope
length 10 m. At low tide, the rope is
stretched tight, forming an angle of 45⁰ with the horizontal. At high tide, the stretched rope makes an angle of 30° with the horizontal. How much closer to the dock, horizontally, is the ship at low tide than at high tide?
1 meter and 59 centimeters.
Describe the hypotenuse.The longest side in a right triangle is called the hypotenuse. In other terms, the hypotenuse is the side that faces the right angle.
theorem of Pythagoras
[tex]a^{2} +b^{2} = c^{2}[/tex]
A is a right triangle's side.
B is the right triangle's side.
c = hypotenuse
Think of a right triangle where the height and distance are the legs and the hypotenuse is the rope.
We are aware that:
cos(45°) =x/10
cos(30°) =y/10,
where x represents the distance between the ship and the dock at low tides and y represents the distance during high tides.
We are searching for the y-x distance difference (since it will be farther away during high tides).
Using the previous equations:
x=cos(45°) and y=cos(30°)
Hence:
y - x = 10(cos(30°) - cos(45°))
Hence, the exact value of the distance is 10(cos30° - cos45°)
Using a calculator, this is approximately 1.59 meters.
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Find the coordinates of endpoint G
Answer:
(-8, -10)
Step-by-step explanation:
(-4 + x)/2 = -6
-4 + x = -12
x = -8
(4 + y)/2 = -3
4 + y = -6
y = -10
Answer: (-8, -10)
The selling price of an item is $. It is marked down by %, but this sale price is still marked up from the cost of $. Find the markup from cost to sale price.
The markup from cost to sale price is $135.
What is the cost price?
Cost price, for instance, equals selling price plus profit ( when selling price and profit are given ) Cost is equal to Selling price plus Loss ( when selling price and loss is given ).
Cost price = 100 Selling Price + 100 + Profit (where the Selling Price and Profit Percentage are supplied)
Given the selling price of the item = $650
The cost = $450
Therefore,
10% × $650 = $585
$585-$450=$135
Hence, the markup from cost to sale price is $135.
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Complete question:
The selling price of an item is $650 It is marked down by 10%, but this sale price is still marked up from the cost of $450.Find the markup from cost to sale price.
Your friend just returned to the United States from their trip to Nepal and wants to exchange their 10,323 Nepalese rupees for U.S. dollars. How many dollars will they receive if the current exchange rate is 1 U.S. dollar to 124 Nepalese rupees? $103.23 $90.83 $83.25 $14.89
Answer: C) $83.25
Step-by-step explanation: First you multiply 124 by whatever amount equivocates to 10,323 then multiply 1 by that same amount and you get the answer, 124 x 83.25 = 10,323, and 1 x 83.25 = 83.25
You have a whole pizza in the refrigerator. On your first trip you eat half of it. On each other trip you eat another half of what is left. After five trips what fractional part of the pizza have you ate?
Answer: You would have eaten 31/32 of the pizza.
Step-by-step explanation:
1/2 + 1/2^2+1/2^3+1/2^4+1/2^5 =
1/2(1-(1/2)^5)/1-1/2 =
1-1/32=
31/32
good question.
A number is between 58 and 68. It has prime factors of 2, 3, and 5. What is the number?
Answer:
60
Step-by-step explanation:
1. A mass of 30kg is suspended from a massless rope on one side of a massless, frictionless pulley. A mass of 10kg is connected to the rope on the other side of the pulley and is sitting on a ramp with an angle of inclination of 30. The system is shown in the following diagram.
a. The coefficient of friction is } 0.10. What is the acceleration of the system?
b. What is the tension in the rope?
a. Acceleration of the system (a) = 6.125 m/s^2
b. The tension in the rope (T) = 110.25
What is the definition of acceleration ?
Acceleration defines that the rate at which velocity changes with time, in terms of both speed and direction.
For 30 kg mass
m . g - T = m . a
30 x 9.8 - T = 30. a ⇒ (1)
For 10 kg mass
T - m base 2 g Sin θ = m base 2 a
T - 10 x 9.8 Sin 30° = 10 x a ⇒ (2)
a. Adding equation (1) and (2)
294 - 49 = 30 a + 10 a
245 = 40 a
a = 245/40
a = 6.125 m/s^2
Therefore, acceleration = 6.125 m/s^2
b. Sub a value in equation (1) we get,
T = 110.25
Therefore , tension in the role = 110.25
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A cola company decides to test 7 different brands of soft drinks. The company
decides to compare each brand with the other brands by pairing them together.
How many different pairs will result from selecting two different brands at a time?
There were 700 colonies of bacteria on day 1 of culturing. With a growth rate of 2.3, determine how many days it will take the bacteria to multiply to 10 000 000 colonies.
Round your answer to four decimal places.
Use A = Pert
The number of days it will take the bacteria to multiply to 10,000,000 colonies will be 39,493.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
There were 700 provinces of microbes on day 1 of refined. With a development pace of 2.3. Then the equation is given as,
[tex]\rm A = 700 \times (2.3)^{t - 1}[/tex]
Then the number of days it will take the bacteria to multiply to 10,000,000 colonies will be given as,
[tex]\rm 10,000,000 = 700 \times (2.3)^{t - 1}\\[/tex]
Take log on both sides, then we have
(t - 1) × log 2.3 = 14,285.71
t - 1 = 39,492.99
t ≈ 39,493 days
The number of days it will take the bacteria to multiply to 10,000,000 colonies will be 39,493.
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help me solve plsssssss
Answer:
2. C
3. BCEF
4. C
Step-by-step explanation:
2. In a function, the x value cannot have two y values (for example: if the points are (1,2) and (1,3) then that is not a function).
In this question, none of the x values repeat with multiple y values, so it is a function. the answer is C.
It is not D, because not all straight lines are functions. If the straight line is vertical, then there is only one x value and it has infinitely many values for y. So, not all straight lines are necessarily functions.
3. Range is the y values. The points are (3,4), (-2,3), (7,1), (2, 1/2)
Here, the y values are 4, 3, 1, and 1/2
Choices B,C,E,F are the answers.
4. If the domain is x[tex]\geq[/tex]0, then 0 is the lowest we can plug into x.
y=2(0)+6
y=6
So, the answer is C. y[tex]\geq[/tex]6
You were on the right track :)
Box measures 32 inches long, 6 inches wide and 8 inches high. What is the diagonal length
of the box?
Answer:
[tex]2\sqrt{281}[/tex] inches
Step-by-step explanation:
Using the 3D Pythagorean theorem, the diagonal has length [tex]\sqrt{32^2+6^2+8^2}=2\sqrt{281}[/tex] inches.
The scatterplot shows x, the high temperature in degrees Fahrenheit (°F), and y, the aquifer level in feet, for ten days in the same area.
Based on the scatterplot, which equation best represents these data?
y = 656 − 0.1 x
y=661−0.1x
y = 656 − 0.5 x
y=661−0.5x
Therefore, the equation that best fits these facts as the answer to this problem is y=661-0.1x.
Describe a scatter plot.The term "scatter plot" refers to a particular sort of graph in which the x- and y-axes are used to represent the values of two variables, with the dots that arise indicating any association between the data.
Given the correlation between the data at this moment and the graph provided in the question, y=661-0.1x is an equation that best captures the scatterplot's line of best fit.
y=661-0.1x is the equation whose solution best fits this data.
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Eliza and Sahana have agreed to go to the movies the weekend after they have earned the same amount of money for the same number of work hours. How much will they have earned?
The number of hours will be 10 hours if Eliza and Sahana have agreed to go to the movies the weekend after they have earned the same amount of money.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Eliza has = 14 + 7x
x is the number of weeks
For Sahana:
y - 8.40 = (16.80-8.40)/(2-1)[x - 1]
y = 8.4x - 8.4 + 8.4
y = 8.4x
14 + 7x = 8.4x
x = 10 hours
Thus, the number of hours will be 10 hours if Eliza and Sahana have agreed to go to the movies the weekend after they have earned the same amount of money.
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You are offered a job in sales where you can choose to
either make a salary $500 (constant) every week or
commission of $20 per sale. Write 2 equations that
represent this scenario and solve the system
Dollars
600
400-
-300-
200-
-100-
(0, 500)
(1,500)
(0, 0) (1, 20)
20
Sales
20
The equations will be 20x and 500w.
How to express the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, when offered a job in sales where you can choose to either make a salary $500 (constant) every week or commission of $20 per sale. This will be:
Let the sales be x
The equation will be:
= 20 × x
= 20x.
The second equation will be:
= 500 × w
where w = number of weeks.
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the sum of 9 and the quotient of x and 7
Dontrell bought 5 pounds of potatoes for $3.52. What equation can be used to represent the total amount he paid, y, for x pounds of potatoes?
Enter the correct equation in the box.
____________________
Step-by-step explanation:
y = 3.52x
This equation states that the total amount paid, y, is equal to 3.52 multiplied by the number of pounds of potatoes, x.
Jazzmen's heart rate is 47 beats per minute. If this is her average heart rate, how
many times will her heartbeat in 50 years?
Answer:1235160000 beats
Step-by-step explanation:
There are 525600 minutes in a year
47*525600= 24703200
24703200*50= 1235160000
What are the measures of 21 and Z2? Explain.
I need help please help me
The measure of [tex]\angle 1[/tex] is [tex]60^{\circ}[/tex] because it is related to one of the angles of the triangle by the alternate interior angles theorem.
The measure of [tex]\angle 2[/tex] is [tex]120^{\circ}[/tex] because it is adjacent to one of the angles in the triangle.