The investment compounded annually has a higher final value than the investment you described because the annual compound interest rate is higher.
What is compound interest?
Compound interest is a type of interest that is calculated on the initial principal of an investment as well as any accumulated interest. In other words, compound interest is interest that is earned on both the original principal and on the accumulated interest from previous periods.
To compare the investment you described to an investment of the same principal at the same rate compounded annually, we need to calculate the final value of each investment after 18 years.
For the investment you described, the final value can be calculated using the formula:
FV = P(1 + r/n)^(nt)
Where FV is the final value, P is the principal, r is the annual interest rate, n is the number of interest periods per year, and t is the number of years.
Plugging in the values given in the problem, we get:
FV = $6,000(1 + 0.06/6)^(6*18) = $6,000(1.01)^108 = $12,688.80
For the investment compounded annually, the final value can be calculated using the same formula, but with n = 1:
FV = $6,000(1 + 0.06/1)^(1*18) = $6,000(1.06)^18 = $15,848.75
Hence, the investment compounded annually has a higher final value than the investment you described because the annual compound interest rate is higher. The difference in final value between the two investments is $15,848.75 - $12,688.80 = $3,159.95.
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In the picture below, which lines are lines of symmetry for the figure?
A. only 2
B. 1, 2, and 3
C. 2 and 3
D. 1 and 3
(A) only 2 is the line of symmetry of the given figure.
What are lines of symmetry?A form or item is divided into two equal and symmetrical portions by a line of symmetry.
Because it divides the figure symmetrically and the separated portions resemble mirror images of one another, we also refer to this line as the axis of symmetry or the mirror line.
The four lines of symmetry in a square are lines across the opposing vertices and the midpoints of the opposing sides.
Together, these four lines of symmetry make up a square.
Consequently, a square has two diagonal, one horizontal, and one vertical line of symmetry.
So, according to the given figure we can easily observe and tell that line 2 is the only one that divides the diagram into 2 identical parts.
Therefore, (A) only 2 is the line of symmetry of the given figure.
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13. 30% of what number is 97 14. 50% of what number is 11? 15. 25% of what number is 20? 16. 60% of what number is 217 17. 75% of what number is 127 18. 10% of what number is o? 19. 120% of what number is 48? 150% of what number is 75? 21. The length of a rectangle is lo inches. If the width 50% of its length, what is the width of the rectang 20.
The values are (13) 323.33 (14) 22 (15) 80, (16) 361.67, (17) 169.33, (18) 0 (19) 40, (20) 50 (21) the width is 5 inches
How to solve for percentage?We should know that percentage is a ration of fraction of 100
The given percentages are as follows:
(13) 30% of what gives 97
let the number be x in all cases
(30/100)*x=97
30x=9700
x=323.33
(14) (50/100)*x=11
50x=1100
x=22
(15) (25/100)*x=20
25x=2000
x=80
(16) (60/100)*x=217
60x=21700
x=361.64
(17) (75/100)*x=127
75x=12700
x=169.33
(18) (10/100)*x=0
10x=100*0
10x=0
x=0
(19) (120/100)*x=48
120x=100*48
120x=4800
x=40
(20) (150/100)*x=75
150x=7500
x=50
(21) lenght = 10 inches
width = 50% of 10
= (50/100)*10
= 5 inches
Therefore the width is 5 inches
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PLEASE HELP 70 BRAINLY POINTS IF YOU ANSWER THIS QUESTION
A probability value is listed at the top of each column. Determine the probability for each situation, then drag and drop each situation into the column under its correct probability.
Probability of drawing a even number of dice is 0.5, The probability of flipping a head on a coin is 0.5,The probability of choosing a red block out of a bag containing 1 red, 1 green and 3 green blocks is 0.2, The probability of choosing a soccer ball out of a bag containing 4 soccer balls, 1 playground ball and 3 basketballs is 0.5 and The probability of choosing a tennis ball out of a bag containing 5 rubber balls, 3 tennis balls, 6 bouncy balls and 1 squishy ball is 0.2.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
The probability of drawing a even number of dice.
A dice has 3 even numbers, 2, 4 and 6.
probability of drawing a even number of dice=3/6=1/2=0.5
The probability of flipping a head on a coin =1/2=0.5
The probability of choosing a red block out of a bag containing 1 red, 1 green and 3 green blocks.
1/5=0.2
The probability of choosing a soccer ball out of a bag containing 4 soccer balls, 1 playground ball and 3 basketballs.
4/8=1/2=0.5
The probability of choosing a tennis ball out of a bag containing 5 rubber balls, 3 tennis balls, 6 bouncy balls and 1 squishy ball.
The probability is 0.2
Hence, probability of drawing a even number of dice is 0.5, The probability of flipping a head on a coin is 0.5,The probability of choosing a red block out of a bag containing 1 red, 1 green and 3 green blocks is 0.2, The probability of choosing a soccer ball out of a bag containing 4 soccer balls, 1 playground ball and 3 basketballs is 0.5 and The probability of choosing a tennis ball out of a bag containing 5 rubber balls, 3 tennis balls, 6 bouncy balls and 1 squishy ball is 0.2.
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Write an inequality for the graph of (-2,-2) (0,-6)
The answer is 24
sorry if i did not say more its hard to explain sorry again
Which of the scatter plots below shows the most accurate line of best fit?
PLS LOOK AT PICTURE AND HELP ME, IM BEING TIMED
Answer:
Z
Step-by-step explanation:
The manager of Jim's Grill tracked and charted how many customers they have to better schedule her staff. Based on the graph, about how many customers are in the restaurant at the slowest time of the , between the two peaks?
Which function represents g(x), a reflection of f(x) = 4(one-half) Superscript x across the x-axis?
g(x) = −4(2)x
g(x) = 4(2)−x
g(x) = −4(one-half) Superscript x
g(x) = 4(one-half) Superscript negative x
Answer:
The function that represents g(x), a reflection of f(x) = 4(one-half) Superscript x across the x-axis, is g(x) = −4(one-half) Superscript x. This function is obtained by negating the exponent of the original function, which reverses the direction of the exponential growth and creates a mirror image of the original function across the x-axis. The other options listed do not correctly reflect the original function across the x-axis.
Step-by-step explanation:
plsssssssssssss helppppppppppppp ....
Answer:3/4 10
Step-by-step explanation:
Suppose particular plane needs to attain speed of k feet per second In order to take off: The plane can attaln that speed in 30 seconds Assume acceleration Is constant; v(o) = 0, and s(0) when answering the questlons below. Use lower case k. (a) Flnd formulas for acceleration_ velocity, and position of the plane_ Your answers will have k In It: a(t) Select-= v(t) Select s(t) Selec (D) If the plane accelerates to feet per second in 30 seconds how far will it travel In that time? Your answer will have k In It. feet (c) If a runway Is 3450 feet long and the plane uses the entire runway to take off, what Is the value of k?
Formula available for acceleration, velocity and position of plane are
k²=2as, k=30a, s=450a and the value of k is 230 ft/sec
what is velocity?rate of changes of distances with respect to time.
what is acceleration?rate of changes of velocity with respect to time.
Given, final velocity, v= k ft/s
time needed to attain speed k is 30 s
time, t= 30 sec
acceleration, a = constant
initially at time t=o, velocity and distance travel by aircraft was also o
initial velocity u =0, distance s = 0
as per the formula regarding velocity, distance, time and acceleration
v² = u²+2as
as per the question final velocity v= k, initial velocity u=0
k² = 2as
again, the formula v= u+at
the velocity of v after 30 second
k= a×30
acceleration, a= k/30
from the other formula, s=ut+1/2×at²
distance travel by aircraft after 30 second with initial velocity 0.
s= u×0+1/2×a(30) ²
s= 450a
previously we got a=k/30
now, s =450×k/30= 15k
if the runway is 3450 feet long and the plane needs to use the entire runway to take off then the value of k will be
s=15k
k=230 ft/sec
hence, the value of k is 230 ft/sec
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The graph below shows the number of free throws made by five players on a basketball team.
Weekly Free Throw Numbers for Players
#Free Throws
10+
99876543N
Player 1 Player 2 Player 3 Player 4 Player 5
Week 1 Week 2 Week 3
What was the total number of free throws made for Player 2?
24
17
23
8
Total number of free throws made for player 2 are 23 using histogram.
Define histogram.A histogram is a graphical depiction of continuous or discrete data. In a histogram, the frequency is represented by the area of a bar. Frequency density, which is proportional to frequency, is plotted on the y-axis, and intervals representing the range of values are plotted on the x-axis. One common graphing tool is the histogram. It is employed to present interval-scaled summaries of discrete or continuous data. It is frequently used to conveniently depict the main characteristics of the data distribution. A histogram is a graph in which the horizontal axis represents the values of the observations, and the vertical axis represents the density of those observations.
Given,
Histogram given,
Total number of free throws made for player 2 are:
8 + 9 + 6
23
Total number of free throws made for player 2 are 23 using histogram.
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evaluate 150-(2=x)3 when x=2
The value of the expression 150 - 3x when x =2 is 144.
What is an expression?Expression in mathematics is combination of variables with the use of operations and given rules. It can be in the form of equation, numbers etc.
Given expression,
150 - 3x.
And we have x = 2.
Substituting the value of x to the expression
So,
150 -3x = 150 - 3(x = 2)
= 150 - 3(2)
= 150 - 6
= 144
Therefore, the answer is 144.
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The owner of bookstore buys used books from customers for $1.50 each .the owner then resells the used books for 400% of the amount he paid for them.what is the price of a used book in this bookstore
The selling price of a used book at the store where the owner buys a used book for $1.50 and resells the used book at a price of 400% the price at which he buys the used book is $6.00
What is the selling price of a commodity?The selling price of an item is the price which is displayed on the item on the shelves of a store. The selling price is often different from the price at which the item is bought, or produced, which is often lesser than the price at which the item is sold.
The amount at which the owner buys each used books = $1.50
The amount at which the owner of the used book store sells the books = 400% of the amount he paid for the books
400% of an amount x is equivalent four times the amount. (4 × x)
The price at which the owner sells a used book at his store, P, is therefore;
P = 400% × $1.50 = 400/100 × $1.50 = $6.00
The price of a used book at the store is $6.0
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Find the critical z value for a confidence level of 85%. (round answer to 2 decimal places)
. I want to know what Z-table to use and how to read it because it get me confused in reading the z table to answer this type of question
Using a z-table for the value, the critical z-value for a confidence level of 85% is; ±1.439.
How to find the critical z-value?The critical value of a distribution is defined as the value beyond which the rejection region lies.
Now, for a confidence interval , the rejection region lies beyond two values, the positive and the negative critical value.
We are given that the confidence level is 85%.
Thus, the computation of the critical value of z for 85% confidence level is expressed as follows;
±z_α/2 = ±z_0.15/2
This is simplified to get;
±z_0.075 = ±1.439
That value is concluded to be the critical z-value at the given confidence level.
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Two cars leave town at the same time. One travels west at 56 mph, and the other
travels south at 42 mph. After one hour, how far apart are the cars?
ongo if starting in
The distance between the cars after a hour is 14 meters.
How to calculate the distance of the cars?Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.
In this case, the cars leave town at the same time. One travels west at 56 mph, and the other travels south at 42 mph.
With the speed, the total distance after an hour will be:
= 56 - 42
= 14 meters
The cars are 14 meters apart.
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Refer to the golden ticket parking lottery example (page 296). At the following month's school assembly, the two lucky winners were once again members of the AP Statistics class. This raised suspicions about how the lottery was being conducted. How would you modify the simulation in the
example to estimate the probability of getting two winners from the AP Statistics class in back-to-back
months just by chance?
Answer: i dont kno man
Step-by-step explanation:
Lauren visits the park every 4 days and goes to the library every 10 days. If Lauren does both of these today, how many days will pass before Lauren gets to do them both on the same day again?
A.20 days
B. 14 days
C. 6 days
D. 40 days
Answer:
20 days
Step-by-step explanation:
A 55 inch pipe is cut into two pieces. One piece is four times the length of the other find the length of the shorter piece.
Answer:
11 inches
Step-by-step explanation:
4x + x = 55 Combine like terms
5x = 55 Divide both sides by 5
x = 11 This is the length of the shortest piece the other piece is 44 4(11)
Answer:
11 inches, 44 inches
Step-by-step explanation:
First of all, we need to make this equation, into an algebraic one:
4x + x = 55
The x represents the number of inches for the rope.
Now you simplify:
5x = 55
This equation can be simplified to a regular division problem:
55/5 = x
Using basic division, x is equal to 11 inches.
Now, this is just the shorter rope.
Note that the other piece is 4 times larger than the short one:
4 x 11 = 44
Thus 11 inches and 44 inches is the answer
Matthew has 8.2 meters of wire. He uses 3.65 meters for craft project. He wants to use the wire he left to complete one of the following projects. For which of the projects does he have enough wire? Choose all the correct answers.
He can make another project and still have 0.90 m of wire left.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
Matthew has 8.2 meters of wire.
He uses 3.65 meters for the craft project.
Now, He wants to use the wire he left to complete one of the following projects.
The left wire is 8.2-3.65 = 4.55 m
So he can make another project and still have 0.90 m of wire left.
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What is 45 less than the product of 18 and a number written as an algebraic expression? 18n − 45 45 − 18n 18(n − 45) n(18 − 45)
The algebraic expression 18n - 45 is correct for the statement "45 less than the product of 18 and a number written as an algebraic expression"
Word problem in algebraWe can represent an unknown number using letters and then carry out basic mathematics operations to get the value of the unknown number.
Let us represent the unknown number with the letter "n"
The product of 18 and the number will be;
18 × n = 18n
45 less than the product of 18 and the number (n) is thus written algebraically as;
18n - 45
Therefore, 45 less than the product of 18 and a number(n) is written as an algebraic expression as 18n - 45.
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bella answered 33 questions on her math test. she earned a 92% on the test. how many questions did she answer correct
Answer: 30.36
Step-by-step explanation:
92% of 33 is 30.36. I don't know how Bella got 30.36 questions correct, but that is what I got.
This design covers the floor of a huge hall. What fraction of the floor is covered by black tiles? What fraction of the floor is covered by white tiles?
The fraction of the floor is covered by white tiles is 1/3.
What fraction of the floor is covered by white tiles?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
Assumed figure:
Places covered by white tiles = 18
Total tiles = 54
The Fraction covered by white tiles will be:
= Number of whitw tiles / Total tiles
= 18/54
= 1/3
The Fraction is 1/3.
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What is the formula for simple interest?
a. (rate) x (interest) - (principal) x (time)
b. Interest - (principal) x (rate) x (time)
C.
interest
rate
d. rate= (interest) x (principal) x (time)
principal
time
Answer: C
Step-by-step explanation:
A 14 km road needs repaired. Workers can repair 3 1/2 km of the road per week. How many weeks will it take to repair the road?
Answer:
3×1/2 = 1.5km per week
14÷1.5=9.33 if you round it it would take 9weeks
Which of the following properly expresses the
verbal
statement "The square root of a number, x, is 5
less than
the sum of the number and 2" ?
F. √x = 5-(x + 2)
G√√√x = (x + 2)-5
"The square root of a number, x, is 5less than the sum of the number and 2" is √x = (x+2)-5
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given verbal statement is "The square root of a number, x, is 5
less than the sum of the number and 2"
The x is the given number.
So square root of a number, x means √x
5 less than the sum of the number and 2.
sum of the number and 2 means x+2 and 5 less than the sum of the number and 2 means (x+2)-5
So √x = (x+2)-5 is the equation.
Hence, √x = (x+2)-5 expresses the verbal statement "The square root of a number, x, is 5less than the sum of the number and 2"
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A recreation center charges $50 to rent the gym for 1 hour, and $100 to rent the gym for 3 hours. Jon says the price per hour is $50. Find and correct Jon’s mistake. Assume the relationship is linear.
The rent of the gym for one hour is $50 and for three hours it is $100.
What is division?It is the basic arithmetic operation, in which you are separating the number into some parts. One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.
Given:
A recreation center charges $50 to rent the gym for 1 hour, and $100 to rent the gym for 3 hours,
Calculate the price if you rent a gym for 3 hrs = 100 / 3 = $33.33
Therefore, the rent of the gym for one hour is $50 and for three hours it is $100.
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Solve for the short leg of the 30-60-90 triangle.
Answer:
b = 2
Step-by-step explanation:
because of the 60° in the corner we know this triangle is the left half of an equilateral triangle (where all 3 sides are equally long, and all 3 angles are 60°).
therefore, b is half of the baseline of that equilateral triangle = 4/2 = 2.
so, b = 2 is the correct answer.
A company loses $80 as a result of a shipping delay. The 4 owners of the company must share the loss equally. Write an expression for the earnings per person. Evaluate the expression
Answer:20
Step-by-step explanation: 80 divided by 4 is 20
25. If 5F+8/G =3R-1/S
is solved for F, then F =
After solving the equation the value of F = (3GR -G - 8S) / 5S
Define Algebraic Expression
In mathematics, an expression that includes variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.)
Given expression is,
5F + 8 / G = 3R - 1 / S
Multiply both side by G
( 5F + 8 / G ) * G= (3R - 1 / S) * G
Simplify it,
5F + 8 = G(3R - 1) / S
Now, solve for F
5F = (3GR - G / S )- 8
5F = 3GR - G - 8S / S
F = 3GR - G - 8S / 5S
Hence, After solving the equation the value of F = (3GR -G - 8S) / 5S
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Order ³√97, 78/9, √45 from greatest to least.
³√97, 78/9, √45
78/9, √45, ³√97
³√97, √45, 78/9
78/9, ³√97, √45
78/9, √45 , ³√97 is the order of numbers from greatest to least.
Given,
The numbers;
³√97, 78/9, √45
We have to order these numbers from greatest to least.
Ordering of numbers;
A series of numbers can be arranged in numerical order. Both ascending and descending orders are possible. For instance, suppose you arranged a group of numbers in ascending order as 2, 55, 103, 256, and 802, for instance. This can make it much simpler to look through a large collection of numbers.
Here,
First we have to find the values of the numbers.
The value of ³√97 = 4.59
The value of 78/9 = 8.66
The value of √45 = 6.71
So,
The greatest one is 78/9 and the least one is ³√97
Therefore,
The order of numbers from greatest to least is 78/9, √45 , ³√97
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Use point-slope form to write the equation of a line that passes through the point
(9, 15) with slope -4/3
Answer:
Hope it helps
Step-by-step explanation:
y - 15 = -4/3(x - 9)