Answer:
The value of the investment will be worth $2466 in the year 2017
Step-by-step explanation:
In this question, we are tasked with finding the specific year in which an amount invested in a money market account reaches a particular value
To get this year, what we need to do is to get the value of t from the exponential equation given in the question. To get t, we simply make the value of A set to the particular value in the question.
Hence, we use [tex]A = 1700e^{0.062t} \\[/tex]
Now, we plug the value of A = 2466 and take the natural logarithm of both sides i.e [tex]Log_{e}[/tex] or simply ln
From;
[tex]2466 = 1700e^{0.062t}[/tex]
ln 2466 = ln[tex]1700e^{0.062t}[/tex]
ln 2466 = 0.062t ln1700
7.81 = 0.062t × 7.44
t = 7.81/(0.062 × 7.44)
t = 16.93 approximately 17 years
This means that the value of the investment will have that worth in the year 2000+17 = year 2017
In ΔFGH, the measure of ∠H=90°, HG = 48, FH = 55, and GF = 73. What ratio represents the tangent of ∠G?
Answer:
55/48
Step-by-step explanation:
We can find the tangent of ∠G using the trigonometrical ratios which may be expressed in the form SOA CAH TOA Where,
SOA stands for
Sin Ф = opposite side/hypotenuses side
Cosine Ф = adjacent side/hypotenuses side
Tangent Ф = opposite side/adjacent side
Considering triangle ΔFGH, where ∠H=90°
The opposite side is FH, the hypotenuse side is GF and the adjacent side is HG hence,
Tan ∠G = FH/HG
= 55/48
Answer:
55:48
Step-by-step explanation:
Given a right angles triangle ∆FGH
where ∠H=90°, HG = 48, FH = 55, and GF = 73,
Based on the diagram attached
To find the tangent of angle G, we will use the concept of SOH CAH TOA in trigonometry identity.
According to TOA:
Tan ∠G = Opposite/Adjacent
Note that the opposite side will be the side facing the angle we are considering i.e ∠G
Opposite = 55
Adjacent will be the base of the triangle = 48
Tan∠G = 55/48
The ratio that represents the tangent of ∠G is 55:48
A company figured that if it had 50 more employees and paid each one $2 per day less, the payroll would increase $620 per day. If it had 50 less employees and paid each $4 per day more, the payroll would decrease $640 per day. How many employees does the company now have? a) 150 b) 125 c) 80 d) 140 e) 180
Answer: 50 more because it makes sense and 2 dolllors it digures
Step-by-step explanation:
a the answerb thats what i put
. Given the first term "a" and the common ratio "r", generate the next three terms in the geometric sequence: a = 12.3; r = 0.5. (Write in decimal form to the thousandths place.) *
Answer:
i wanna say 12.8, 13.3, 13.8
im not sure though, i hope this helps
Bus A and Bus B leave the bus depot at 7 am. Bus A takes 25 minutes to do its route and bus B takes 40 minutes to complete its route. At what time are they both back at the bus depot together?
Bus A and Bus B leave the bus depot at 7 am. At 10:20 AM are they both back at the bus depot together.
Given:
Bus A takes 25 minutes to complete its route once Bus B takes 40 minutes to complete its route To find time when they will be back at the bus depot together we need to find LCM of 25 & 40 Minutes=> 25 = 5 * 5
=> 40 = 2 * 2 * 2 * 5
LCM = 2 * 2 * 2 * 5 * 5=> = 200
Thus, After 200 minutes Buses will be back at the bus depot together
200 minutes = 3 hr 20 Minutes 7 : AM + 3 hr 20 Minutes => = 10 : 20 AMThus, At 10: 20 AM Buses would be back at the bus depot together.
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Bus A and Bus B will both be back at the depot at the same time at 10:20am.
Explanation:To solve the problem, we need to determine when both Bus A and Bus B will be back at the depot at the same time. Since Bus A takes 25 minutes to complete its route and Bus B takes 40 minutes, we need to find the common multiple of these two numbers. The smallest common multiple of 25 and 40 is 200. This means that both buses will be back at the depot at the same time after 200 minutes.
Since the buses leave the depot at 7:00 am, we add 200 minutes (or 3 hours and 20 minutes) to this time. Therefore, it's at 10:20 am that both buses are back at the depot at the same time.
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200% of d is 18 what is d
Answer:
d = 9
Step-by-step explanation:
200% = double
aka 2d = 18
d = 9
Answer:
d = 9
Step-by-step explanation:
Of means multiply and is means equals
200% * d = 18
Changing to decimal form
2.00 * d = 18
Divide each side by 2
2d/2 = 18/2
d = 9
Which of the following illustrates the product rule for logarithmic equations?
log (4x) = log24 = log2x
log2(4x) = log24-log2x
o log2 (4x) = log24-log2x
log2(4x) = log24+log2x
Since the product of 4x is written as the sum log 4 and log x hence the expression log2(4x) = log2(4)+log2(x) illustrates the product rule for logarithmic equations
Product rule of logarithmAccording to the law of logarithm
log (ab) = loga + logb
The product of log becomes sum
From the given log functions,
log2(4x) = log2(4)+log2(x)
Since the product of 4x is written as the sum log 4 and log x hence the expression log2(4x) = log2(4)+log2(x) illustrates the product rule for logarithmic equations
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A car leaves town, A at the speed of 90 km/h. Three hours later leaves the same city another car in pursuit of the first with a speed of 120 km / h. How much time will take to reach it?
Select the appropriate response:
A) t = 6hrs
B) t = 12 hrs
C) t = 30 min
D) None of the answers are correct
Option B is correct, it will take 2hrs to reach it.
What is Distance?The length along a line or line segment between two points on the line or line segment.
Distance=√(x₂-x₁)²+(y₂-y₁)²
A car leaves town, A at the speed of 90 km/h.
Distance covered by A: 90t
Three hours later leaves the same city another car in pursuit of the first with a speed of 120 km / h
Distance covered by B: 120(t - 3)
90t = 120(t - 3)
Apply distributive property
90t = 120t - 360
30t = 360
Divide both sides by 360
t = 12
Hence, option B is correct, it will take 2hrs to reach it.
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The box plot and histogram show the number of minutes sixth-grade students spent reading the previous night. A box-and-whisker plot. The number line goes from 20 to 80. The whiskers range from 25 to 70, and the box ranges from 40 to 55. A line divides the box at 50. A bar graph titled Minutes spent reading. 4 students spent 25 to 34 minutes; 4 spent 35 to 44; 6 spent 45 to 54; 4 spent 55 to 64; 2 spent 65 to 74. Which statements best describe the box plot or histogram? Check all that apply. Using the information in the box plot, the total number of students surveyed is 70 – 25, or 45. Using the information in the histogram, the total number of students surveyed is 4 + 4 + 6 + 4 + 2 = 20. Referring to the box plot, the median of the data is 50. Referring to the histogram, the median of the data is 49.5. The range of the data can be found using the box plot. The range of the data can be found using the histogram.
The statement best describes the box plot or histogram is B,C and E
We have given that,
The box plot and histogram show the number of minutes sixth-grade students spent reading the previous night.
What is the box and whisker method?A box and whisker plot is defined as a graphical method of displaying variation in a set of data
A box-and-whisker plot
B-Using the information in the histogram, the total number of students surveyed is,
=4 + 4 + 6 + 4 + 2
= 20.
C-Referring to the box plot, the median of the data is 50.
E-The range of the data can be found using the box plot.
Therefore the statement best describes the box plot or histogram is B,C and E.
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Answer:
B,C,E
Step-by-step explanation:
What is the slope of the line that passes through (0,5) and (8,27)?
Answer:
the slope of the line is 2.75
Slope intercept form (y = mx + b) y = 2.75x + 5
In college basketball, some teams get most of their points from just one player, and other teams are more balanced in scoring. Consider the following facts about the scoring distributions for some NCAA Division I basketball teams. Each team has 121212 players. At Baylor University, there are 666 players who each score 121212 points per game, and there are 666 players who each score 000 points per game. At the University of Maryland, 111 player scores 585858 points per game, 111 player scores 141414 points per game, and the rest of the players score 000 points per game. At Dartmouth College, 444 players score 555 points per game, 444 players score 666 points per game, and 444 players score 777 points per game.
Which of the following is true? Choose all answers that apply: Choose all answers that apply:
(Choice A) A At Dartmouth, the mean number of points per player per game is greater than the median number of points per player per game.
(Choice B) B At Maryland, the mean number of points per player per game is greater than the median number of points per player per game.
(Choice C) C The median number of points per player per game is the same at all 333 schools.
(Choice D) D The mean number of points per player per game is the same at all 333 schools.
Answer:
(B) At Maryland, the mean number of points per player per game is greater than the median number of points per player per game.
(D)The mean number of points per player per game is the same at all 3 schools.
Step-by-step explanation:
Baylor University
6 players who each score 12 points per game
6 players who each score 0 points per game.
The Scores are: 0,0,0,0,0,0,12,12,12,12,12,12
[tex]Mean=\frac{0+0+0+0+0+0+12+12+12+12+12+12}{12} \\Mean=6\\Median=\frac{12+0}{2}=6[/tex]
University of Maryland
1 player scores 58 points per game,
1 player scores 14 points per game,
The rest(10) of the players score 0 points per game.
The Scores are: 0,0,0,0,0,0,0,0,0,0,14,58
[tex]Mean=\frac{0+0+0+0+0+0+0+0+0+0+14+58}{12} \\Mean=6\\Median=\frac{0+0}{2}=0[/tex]
Dartmouth College
4 players score 5 points per game,
4 players score 6 points per game,
4 players score 7 points per game.
The Scores are: 5,5,5,5,6,6,6,6,7,7,7,7
[tex]Mean=\frac{5+5+5+5+6+6+6+6+7+7+7+7}{12} \\Mean=6\\Median=\frac{6+6}{2}=6[/tex]
The following applies:
(B) At Maryland, the mean number of points per player per game is greater than the median number of points per player per game.
(D)The mean number of points per player per game is the same at all 3 schools.
In college basketball, the mean and median number of points per player per game can be different depending on the scoring distribution of the team. At Dartmouth, the mean is greater than the median due to players scoring different points. At Maryland, the mean is also greater than the median due to a few players scoring higher points. The median and mean can vary across different schools and teams.
Explanation:Choice A: At Dartmouth, the mean number of points per player per game is greater than the median number of points per player per game. The mean is calculated by summing up all the scores and dividing by the total number of players, while the median is the middle value when the scores are arranged in increasing order. With players scoring different points per game at Dartmouth, there will be players scoring more than the mean, pulling the mean up and making it greater than the median.
Choice B: At Maryland, the mean number of points per player per game is greater than the median number of points per player per game. With only a few players scoring points other than 0, these outlier scores will cause the mean to be greater than the median.
Choice C: The median number of points per player per game can be different at different schools. In the case of Dartmouth, the median could be greater than the mean due to a large number of players scoring the same lower points per game. In the case of Maryland, with a few players scoring higher points, the median could be lower than the mean.
Choice D: The mean number of points per player per game can be different at different schools, as explained in Choices A and B.
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The volume of gas varies inversely as the pressure. A volume of gas is 120 cubic feet under 6 pounds of pressure. What is the volume at the same temperature when the pressure is 8 pounds?
The volume of gas is 80 cubic feet at the same temperature when the pressure is 8 pounds.
Step-by-step explanation:
The given is,
Volume of gas is 120 cubic feet under 6 pounds of pressure.
Volume of gas varies inversely as the pressure.
Pressure is 8 pounds
Step:1
From the given,
Volume of gas varies inversely as the pressure,
[tex]P_{gas}[/tex] ∝ [tex]\frac{1}{V_{gas} }[/tex].......................................(1)
Ratio of volume to pressure of gas is,
= [tex]\frac{120}{6}[/tex] = 20
Step:2
Pressure of gas is increased 6 to 8 pounds,
Change in pressure = 8 - 6 = 2 pounds
Change in volume = Ratio × change in pressure
= 20 × 2 = 40 cubic feet
Step:3
From the equation (1),
The pressure is increased, the volume of gas is reduced.
Volume of gas at pressure of 8 pounds = 120 - 40
= 80 cubic feet
Result:
The volume of gas is 80 cubic feet at the same temperature when the pressure is 8 pounds.
Whats the answer?? I'm horrible at math ;-;
Answer:
Matt's Answer.
Step-by-step explanation:
Note that in the equation, you need a radius (r). However, a diameter is given, which is 15 centimeters. This means that, to solve this equation, you must first divide 15 by 2, to be able to continue to solve. In Matt's case, he failed to do that.
~
What is 5,384,981 to the nearest ten-thousands place?
Answer:
5,380,000
Step-by-step explanation:
Tyrone had a chocolate bar, of which he gave one-half to his friend Nora. Nora gave one-half of her piece to her friend Eduardo. What fractional part of the original chocolate bar did Eduardo get?
Howard is designing a chair swing ride. The swing ropes are 5 meters long, and in full swing they tilt in an
angle of 29º. Howard wants the chairs to be 2.75 meters above the ground in full swing.
How tall should the pole of the swing ride be?
Round your final answer to the nearest hundredth.
meters
------
2.75 m
Answer:
7.12m
Step-by-step explanation:
THIS IS THE CORRECT QUESTION:
Howard is designing a chair swing ride. The swing ropes are 5 meters long, and in full swing they tilt in an angle of 29 degrees. Howard wants the chairs to be 2.75 meters above the ground in full swing. How tall should the pole be? Round your answer, if necessary, to 2 decimal places.
From the question:
Length of the rope is = 5 m long.
The tilted angle is 29°
The distance from the ground is 2.75 m
To Find the height of the pole,
SEE THE ATTACHMENT BELOW;
Find the missing length of the triangle.
5.6 in.
10.6 in.
Answer:
9 in
Step-by-step explanation:
The missing length of the right angle triangle is approximately 12 in.
The missing length of the right-angle triangle can be found using the Pythagorean theorem. The theorem states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. In this case, the length of one side of the triangle is 5.6 in and the length of the other side is 10.6 in. Let's substitute these values into the formula:
a² + b² = c²
(5.6 in)² + (10.6 in)² = c²
31.36 in² + 112.36 in² = c²
143.72 in² = c²
Now, we can take the square root of both sides to find the length of the hypotenuse:
c = √143.72 in² ≈ 12 in
Therefore, the missing length of the right angle triangle is approximately 12 in.
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5/6 times 1/3. dived by 2/3 divided 1/2
Answer:
5/6 (please give branliest)
Step-by-step explanation:
5/6 * 1/3 = 5/18
5/18 / 2/3 = 5/12
5/12 / 1/2 = 5/6
Answer:
I'm pretty sure it is 5/6
Step-by-step explanation:
there are 390 students at a school if each classroom holds 30 students how many classroom are needed at the school?
Answer:
13
Step-by-step explanation:
390 divided by 30 equals 13
Answer:
the school need 13 classrooms
Step-by-step explanation:
390:30=13
You deposit $1500 in an account that pays 7% annual interest. Find the balance after 2 years when the interest is compounded daily.
Answer:
$1,725.39
Step-by-step explanation:
-Take 1 year =365 days.
#We calculate the effective interest rate for 7% compounded daily;
[tex]i_m=(1+i/m)^m-1\\\\=(1+0.07/365)^{365}-1\\\\=0.072501[/tex]
#We now use this rate to calculate the compounded amount after two years:
[tex]A=P(1+i_m)^n\\\\=1500(1.072501)^2\\\\=1725.39[/tex]
Hence, the balance after 2 years $1,725.39
To find the balance after 2 years with daily compounded interest, the formula [tex]A = P(1 + r/n)^(nt)[/tex] is used, with a principal of $1500, an annual rate of 7%, and n being 365. After calculations, the final balance would be approximately $1717.40.
Explanation:To calculate the balance after 2 years when the interest is compounded daily, we can use the formula for compound interest: A = P(1 + r/n)nt, where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial sum of money).r is the annual interest rate (in decimal form).n is the number of times that interest is compounded per unit t.t is the time the money is invested for in years.In your case, you deposit $1500 in an account that pays 7% annual interest. Since the interest is compounded daily, we will use 365 for n. Here's your calculation:
Convert the annual interest rate from a percentage to a decimal by dividing by 100: 7% / 100 = 0.07.Calculate the balance using the compound interest formula: A = 1500(1 + 0.07/365)(365)(2).Compute the value of (1 + 0.07/365) and then raise it to the power of 730 (which is 365 days times 2 years).The resulting amount is the new balance in your account after 2 years, including the interest that was compounded daily.After doing the math, your compounded balance after 2 years will be approximately:
A = 1500(1 + 0.07/365)730
A ≈ $1500 * 1.14493150684931506849
A ≈ $1717.40
This means that after 2 years, you will have approximately $1717.40.
A truck is carrying 100 pounds of grapes, which are 99% water (and 1% skin, fiber, etc…). When the truck breaks down and the grapes sit in the back of the truck for 4 hours, they become 98% water. At that moment, how many pounds do the grapes weigh?
Answer:
The grapes have a weight of 50 pounds
Step-by-step explanation:
To calculate the weight of the grapes, we proceed as follows;
Let's categorize the skin, fiber as solids
At first, we had 1% solids and 99% water.
This means 99 pounds of water and 1 pound of solid
It must be known that the 1% solid remains the same after drying and what we have lost simply is the water,
This means that 2% of the total weight is now same 1 pound of solid after drying
Mathematically, this means
2/100 * new total weight = 1 pound
New total weight = 1 pound × 100/2 = 50 pounds
What is the solution to the equation 2 x + 4 = 24?
x = 1
x = 3
x = 6
x = 10
Brainliest if answered correctly!
Answer: [tex]x=10[/tex]
Subtract 4 from both sides
[tex]2x+4-4=24-4\\2x=20[/tex]
Divide both sides by 2
[tex]2x/2=20/2[/tex]
[tex]x=10[/tex]
Find the vertical asymptotes of the following function:
y=x+2
_______
x^2 +2x−8
Select the appropriate response:
A) horizontal asymptotes x = −4, 5
B) horizontal asymptotes x = −4, 4
C) vertical asymptotes x = −8, 4
D) vertical asymptotes x = −4, 2
Help please! 50 points!
Answer:
D) vertical asymptotes x = −4, 2
Step-by-step explanation:
First you factor the denominator: x^2 +2x−8
Find factors of -8(c) that add together to give 2(b): 4 and -2
Rewrite the equation: x^2+4x-2x-8
Factor out common variables: x(x+4)-2(x+4)
Group the things inside and outside the parentheses together: (x-2)(x+4)
Solve: x-2=0 so x=2 and x+4=0 so x=-4
Answer:
D) vertical asymptotes x = −4, 2
Step-by-step explanation:
x² + 2x - 8 = 0
x² + 4x - 2x - 8 = 0
x(x + 4) - 2(x + 4) = 0
(x + 4)(x - 2) = 0
x = 2, -4
Plot point A at (4,3). Translate point A left 5 units. Label this point B. Give the coordinates of point B.
Not going to plot the points for you. I expect that is within your comprehension.
If you plot point B five units to the left of A, that means x is going to decrease by 5. That means that the coordinates of B are B(4 - 5, 3) = B(-1, 3).
Hope this helps.
What is the slope of the line
Answer:
-1
Step-by-step explanation:
The rise over run is -2 over -2.
-2/-2=-1
How do you identify an exponential equation as growth or decay? Y = a(b)^x
Step-by-step explanation:
y = a (b)ˣ
If 0 < b < 1, the function is exponential decay.
If b > 1, the function is exponential growth.
At 11:55 p.m., Thomas ties a weight to the minute hand of a clock. The clockwise torque applied by the
weight (i.e. the force it applies on the clock's hand to move clockwise) varies in a periodic way that can be
modeled by a trigonometric function.
The torque peaks 15 minutes after each whole hour, when the minute hand is pointing directly to the right,
at 3 Nm (Newton metre, the SI unit for torque). The minimum torque of -3 Nm occurs 15 minutes
before each whole hour, when the minute hand is pointing directly to the left.
Find the formula of the trigonometric functid that models the torque applied by the weight t minutes
after Thomas attached the weight. Define the function using radians.
T(t) =(
Answer:
T(t) = 3sin((t-5)π/30)
Step-by-step explanation:
5 minutes after Thomas ties it on, the torque is zero and increasing. So, the sine function is shifted right 5 minutes. The maximum value is 3, so that is the multiplier of the sine function. The period is 60 minutes, so the coefficient of t is (2π/60) = π/30. The function you want is ...
T(t) = 3sin((t-5)π/30)
Evaluate the expression
Answer:
the correct answer is 4. because the cube root of 64 is 4
Answer:
Step-by-step explanation:
Recall that 4^3 = 64.
Thus, the opposite operation is the cube root of 64: ∛64 = 4
Help me what is this
Answer:
Dog
Step-by-step explanation:
This seems to be a Chihuahua breed of a dog
Answer:
doggo
Step-by-step explanation:
answer question below please
solve for x
Answer:
The answer to your question is x = 12
Step-by-step explanation:
Data
BC = 7
DE = x
AB = 7
BD = 5
Process
To solve this problem use proportions and cross multiplication. Compare the ΔADE and ΔABC.
DE / (AB + BD) = BC / AB
-Solve for DE
DE = BC (AB + BD) / AB
-Substitution
DE = 7(7 + 5) / 7
-Simplification
DE = 7(12) / 7
DE = 84/7
-Result
DE = 12
Which sample fairly represents the population? Select two options.
measuring the height of every fiftieth person on the school roster to determine the average height of the boys in the school
A.) calling every third person on the soccer team's roster to determine how many of the team members have completed their
fundraising assignment
b.) observing every person walking down Main Street at 5 p.m. one evening to determine the percentage of people who wear
glasses
c.) sending a confidential e-mail survey to every one-hundredth parent in the school district to determine the overall satisfaction
the residents of the town
d.) taking a poll in the lunch room (where all students currently have to eat lunch) to determine the number of students who want
to be able to leave campus during lunch
Answer:
b) observing every person walking down Main Street at 5 p.m. one evening to determine the percentage of people who wear glasses.
d) taking a poll in the lunch room (where all students currently have to eat lunch) to determine the number of students who want to be able to leave campus during lunch.
Step-by-step explanation:
These are the two options that are most likely to give you a sample that fairly represents the population. In the first case, the sample that you obtain is likely to be a good representation because Main Street is a road where a great variety of people walk. Moreover, 5 pm is also a time that will allow you to see a great number of different people. The second answer will also give you a good sample, as the poll would include all students in the lunch room, which is all students in the school (the whole population).