The amount of money in the account after 6 years is $68,847.56
To solve this problem, you can use the formula for compound interest,
V = Pe^(rt)where V is the final value of the account, P is the initial principal, r is the annual interest rate (expressed as a decimal), and t is the number of years the money is invested.
The formula for compound interest, V = Pe^(rt) is used to calculate the future value of an investment. It takes into account the effect of compounding, which means that interest is earned not only on the initial investment but also on the accumulated interest over time.
Plugging in the given values, we have
V = 51200e^(0.0546) = 51200e^0.324. e^0.324 is approximately 1.38, so the final value of the account is 512001.38 = $68,847.56
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One bottle holds 67.34 onces and another bottle holds 48.5 onces combined how much do they hold?
After combine they hold 115.84 ounces.
What is Addition?A process of combining or adding two or more numbers is called addition.
We have to given that;
One bottle holds 67.34 ounces and another bottle holds 48.5 ounces.
So, After combine, we get;
Both bottle hold = 67.34 ounces + 48.5 ounces
= 115.84 ounces
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What is a 9 sided shape called?
A 9-sided shape is called a nonagon.
Therefore the answer is nonagon.
A nonagon is a polygon with nine sides and nine angles. A nonagon can be regular or irregular, depending on the lengths of its sides and angles. A regular nonagon has equal sides and angles, while an irregular nonagon has sides and angles of different lengths.
Nonagons are two-dimensional shapes, and they can be described by their number of sides, angles, and vertices. They are considered a type of polygon, which is a closed geometric figure that is made up of straight lines. In addition to nonagons, there are other types of polygons such as triangles, quadrilaterals, pentagons, hexagons, heptagons, and so on.
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Ill MARK AS BRAINLIEST(show how you solved the 2 parts :>
Mrs Lim has sponsored a total of 105 hot dogs and 126 cans of fruit juice for the refreshment of a classic picnic. Each student will receive the same amount of refreshment.
a) what is the greatest number of students who will get the refreshment ?
b) how many hot dogs will each student get?
C) how many fruit juices wil each student get
a) The greatest number of students who will get the refreshment is 210.
b) Each student will get 0.5 hot dogs.
c) Each student will get 0.6 cans of fruit juice.
a) To find the greatest number of students who will get the refreshment , we need to find the least common multiple of hot dogs and fruit juice.
The least common multiple is 210, which is the multiple of 105, and 126 is the least.
So the greatest number of students who will get the refreshment is 210.
b) To find the number of hot dogs each student will receive, we need to divide the total number of hot dogs (105) by the greatest number of students who will get the refreshment (210)
105/210 = 0.5
So each student will get 0.5 hot dogs.
c) To find the number of fruit juices each student will receive, we need to divide the total number of fruit juice (126) by the greatest number of students who will get the refreshment (210)
126/210 = 0.6
So each student will get 0.6 cans of fruit juice.
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A company creates containers of mixed nuts using the same ratios of different types of nuts in each container. In a 20 ounce container of the company's mixed nuts, there are 11 ounces of peanuts.
There are 37.8 ounces of almonds in a 42-ounce container of the company's mixed nuts.
We know that the company uses the same ratio of different types of nuts in each container. Therefore, we can use the ratio of peanuts to the total weight in the 20-ounce container to find the weight of almonds in the 42-ounce container.
In the 20-ounce container, 11 ounces of the nuts are peanuts. Therefore, 20-11 = 9 ounces of the nuts are not peanuts.
To find the weight of almonds in the 42-ounce container, we can use the same proportion of non-peanut nuts to the total weight. So,
9 ounces / 20 ounces = x / 42 ounces
Cross-multiplying we get:
9 × 42 ounces = 20 × x
x = 37.8 ounces
So, there are 37.8 ounces of almonds in a 42-ounce container of the company's mixed nuts.
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knowing the difference between an experimental group and a control group is most relevant to understanding the nature of: group of answer choices random sampling. replication. hindsight bias. independent variables.
The experimental group is given the experimental treatment, and the comparison group is statistically significant.
Which three attitudes are the basis of the scientific viewpoint?Curiosity, scepticism, and humility are described by historians of science as the three attitudes that form the bedrock of the scientific viewpoint. Larger, more representative sample sizes aid in the production of accurate and valid data.When random sampling is used, every member of the population has an equal chance of being chosen, resulting in the collection of a representative sample. The odds of generalising the study's findings to the population increase with the use of a random sample. The study's margin of error is reduced with higher study sample sizes.) Researcher control over the possibility of reporting false-negative or false-positive findings is made possible by larger sample sizes. Results will be more precisely predicted with a larger sample size.To learn more about random sampling refer to :
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Identify similarities and differences in finding the volume of cylinders, cones, and spheres.
The volume of the cone is one third the volume of the cylinder.
The volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter
How to illustrate the information?Similar to a prism, a cylinder has two bases, but they are circles rather than polygons. A cylinder's sides are also curved rather than flat. A cone has a vertex that is not on the base and a single circular base. The sphere is a figure in space with equal distances between each of its points and the center.
The cone's volume is one-third that of the cylinder. A sphere's volume is 2/3 that of a cylinder with the same radius, and its height is equal to its diameter.
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Is math in Grade 6 hard?
Sixth grade math class can be difficult, even for students who have done well in math previously. In sixth grade you begin to learn more advanced topics such as ratios and rates.
You also work more with fractions. Sixth grade is also when you begin building the foundations of algebra, geometry, and statistics.
example
given problem in maths
- x + 8 > 6 ( isolate the term in x by subtracting 8 from both sides )
- x > - 2 ( multiply both sides by - 1 )
Remembering to reverse the inequality symbol when multiplying/dividing by a negative quantity
x < 2 ← reverse symbol
From the given list the only value less than 2 is 1, hence
x = 1 ← is the only possible solution
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On a assembly line, 2 parts can be made per minute. There are 8 parts already made. To determine how many more minutes (x) it will take to make y total parts, the equation y=2x + 8 is written. What is the description of a solution to this problem?
The description for the problem involving the linear function is given as follows:
The time it will take to make a total of 20 parts is of 6 minutes.
How to interpret this problem in the context of a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the y-intercept, representing the initial value.In this problem, the function is defined as follows:
y = 2x + 8.
In which the variables are given as follows:
x is the time in minutes.y is the number of pieces made.Hence the time needed to make 20 pieces is given as follows:
20 = 2x + 8
2x = 12
x = 12/2
x = 6 minutes.
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Consider the expression.
2x (x + 3y) +5 (2x - 2)
How many terms does the expression have when simplified completely?
When given expression 2x (x + 3y) +5 (2x - 2) simplified completely then it would have 4 terms.
Consider given expression.
2x (x + 3y) +5 (2x - 2)
We simplify above expression.
2x (x + 3y) +5 (2x - 2)
= [(2x × x) + (2x × 3y)] + [(5 × 2x) - (5 × 2)] ......(distributive property)
= [2x² + (2 × 3)xy] + [(5×2)x - 10] ............(commutative property)
= (2x² + 6xy) + (10x - 10)
= 2x² + 6xy + 10x - 10
= 2x² + 10x + 6xy - 10 ...........(by commutative property of addition)
when given expression simplified completely then it would be,
2x (x + 3y) +5 (2x - 2) = 2x² + 10x + 6xy - 10
The number of terms in an expression 2x² + 10x + 6xy - 10 are 4
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List 3 whole numbers immediately after 10
The answer is 11, 12, 13
help im no good at this
Answer:
8.2 × 10⁻³
Step-by-step explanation:
1.64 × 10⁰ 1.64 × 1 1.64
-------------- = -------------- = ---------- = 0.0082
2.0 × 10² 2 × 100 200
Scientific notation: 8.2 × 10⁻³
I hope this helps!
Kate spent 44 pounds in the holidays.
she spent three times as much on clothes as she did on food.
How much did she spend on food ?
Answer:
11 pounds
Step-by-step explanation:
The ratio of the amount of money Rachel spent on food to clothes is 1/3
She spent: 44 : (1 + 3) x 1 = 11 pounds
Answer:11
Step-by-step explanation:
11 times 3 equals 33(for the clothing)
so 11 is left
In a rhombus MNLP, diagonals intersect each other at point O. If m∠MNL is 120° and the length of the side is 8 in, find m∠MNO, m∠MON, and NP. A (5pts) Find m∠MNO. Answer
In a rhombus, all sides are equal and the diagonals intersect each other at a 90 degree angle and bisect each other.
Diagonal of a rhombus bisects the angles of the rhombus at the vertex.
So as m∠MNL is 120°,
∠MNO = ∠LNO = 120/2 = 60°
The diagonals intersect each other at a 90 degree angle, therefore
m∠MON = 90°
Considering ΔMNO, right angled at O.
cos(∠MNO) = NO/ MN
cos(60) = NO/ 8
NO = 0.5×8 = 4
NP = NO + OP
NP = 2NO
NP = 2×4
NP = 8 in
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Given the table of values, determine the the constant of proportionality, then write the equation of the proportion.
The constant of proportionality is 9 and equation of the proportion.
is y= 10x.
What is Constant of Proportionality?If the ratio of one variable to the other is constant, then there is a proportional relationship between the two variables. If x and y are in a proportional relationship, then the ratio of y to x is the constant of proportionality.
Given:
As, we know using the Constant of Proportionality
y = kx
or, k = y/x where k is Constant of Proportionality.
Then, from the table we have
k = 90/9
k= 10
Thus, y = kx
or, y= 10x
Hence, the equation of the proportion is y= 10x.
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The distribution of SAT scores of all college-bound seniors taking the SAT in 2014 was approximately normal with a mean of 149714971497 and standard deviation of 322322322. Let XXX represent the score of a randomly selected tester from this group. Find P(1497
The probability is 0.4444.
What is probability?Probability is a measure of the likelihood of a particular outcome occurring in a given situation. It is the chance that something will happen or is true. Probability is expressed as a number between 0 (impossible) and 1 (certain). Probability is a mathematical way of predicting what will happen in the future based on a given set of data. It is used to analyze the likelihood of various outcomes in a range of scenarios, such as gambling, finance, insurance, and weather forecasting.
The probability of a randomly selected tester from the group of college-bound seniors having a score between 1497 and 1507 can be calculated using the standard normal distribution. First, we need to convert the scores to standard scores, or z-scores. Subtract the mean from the scores and divide by the standard deviation to get z-scores.
For XXX = 1497, z = (1497 - 1497) / 322 = 0.
For XXX = 1507, z = (1507 - 1497) / 322 = 0.31.
Using a standard normal table, we can calculate the area under the normal curve between 0 and 0.31. The probability of randomly selecting a tester with a score between 1497 and 1507 is 0.4444. The probability is therefore P(1497 ≤ XXX ≤ 1507) = 0.4444.
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Complete questions as follows-
The distribution of SAT scores of all college-bound seniors taking the SAT in 2014 was approximately normal with a mean of 149714971497 and standard deviation of 322322322. Let XXX represent the score of a randomly selected tester from this group. Find P(1497 ≤ XXX ≤ 1507).
7O POINTS HELP ASAP!!!
Given the graph of this function, determine the statement that best describes the end behavior.
x->∞,y->∞ and as x-> - ∞ , y-> - ∞ this statement best describes the end behavior.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
First, we need to analyze the plotting of the graph. When it is on the negative axis of x, as the values of x increase (x values increasing in the negative axis means it's decreasing in value), the y values also increase. So as x decreases, y increases.
On the positive axis of x, as the x values increase, the corresponding values of y also increase with x. So as x increases, y values also increase with it.
Hence, x->∞,y->∞ and as x-> - ∞ , y-> - ∞ this statement best describes the end behavior.
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Solve the following equation by first writing the equation in the form a x squared = c: 3 a squared minus 21 = 27 a. a = 4 b. a = plus-or-minus 4 c. a = plus-or-minus 16 d. a = 16 Please select the best answer from the choices provided A B C D
The best answer from the choices provided is a = plus-or-minus 16 . Option C
What is a quadratic equation?A quadratic equation can be defined as an equation that can be rearranged in a standard form
Such that;
x represents an unknown value or variableThe variables, a, b, and c represent known numbersThe variable, a ≠ 0These quadratic equation are also described as polynomial equation having its highest degree as 2.
From the information given, we have that;
3a² - 21 = 27
collect like terms
3a² = 27 + 21
Add the values
3a² = 48
Divide both sides by 3
a² = 48/3
a² = 16
Hence, the value is a² = 16
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What is the smallest positive integer that is both a multiple of $7$ and a multiple of $4$?
The smallest positive integer that is both a multiple of 7 and a multiple of 4, is 28 .
How to find the smallest positive integer ?To find the smallest positive integer that is both a multiple of 7 and a multiple of 4, first find the multiples of both 4 and 7 to see which multiples are common between them and which are the lowest.
The multiples of 4 and 7 are:
Multiples of 4 :
4, 8, 12, 26, 20, 24, 28, 32, 36, 40,
Multiples of 7 :
7 , 14 , 21 , 28 , 35 , 42 , 49
The smallest positive integer that is both a multiple of 7 and a multiple of 4 is therefore 28.
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How do you find the domain and range of a function x 4?
The domain of x=4 is (−∞,∞) and range is {y|y=4} .
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
(−∞,∞)
{x|x ∈ R}
y=4
is a straight line perpendicular to the y-axis, which means that the range is a set of one value {y|y =4}
Set-Builder Notation:{y|y =4}.
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
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A track team has 7 people eligible to run the
800-meter run. A team member can only run
the race once, and 4 people are needed to run
the race. How many different ways can the 4
people be selected, if order doesn't matter?
In 35 differnt ways (Combination) the 4 players can be selected from a team of 7.
What is permutation and Combination ?Combinations are decisions that are made by choosing some or all of a group of things, regardless of how they are arranged.
Utilizing the combinations formula, it is simple to determine how many distinct groups of r items each may be created from the provided n unique objects. The factorial of n divided by the product of the factorial of r and the factorial of the difference between n and r, respectively, is the formula for combinations.
A permutation is a combination and an ordered arrangement of possible outcomes. For instance, there are 5 chairs, and 3 people should occupy them. There are five different methods to seat the first person, four ways to sit the person after them, and three ways to seat the third. In order to determine the number of configurations for seating 3 people in 5 seats, we thus multiply the alternatives at our disposal.
Permutations are several ways to arrange things in a certain sequence. It may alternatively be stated as the linear reordering of elements in an already ordered collection.
Here we have to select 4 people from a team of 7, so its a combination
So the number of ways are = [tex]\x^{7}C\x_{4} = \frac{7!}{4!\ 3!} = 35[/tex].
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When it was raining, Elliott drove for 120 miles. When the rain stopped, he drove
20 mph faster than he did while it was raining. He drove for 300 miles after the
rain stopped. If Elliott drove for a total of 10 hours, how fast did he drive while it
was raining?
Answer:
[tex]\boxed{22}.[/tex]
Step-by-step explanation:
Since Elliott drove for a total of 10 hours, and he drove for 120 miles while it was raining and 300 miles after the rain stopped, we know that he drove for a total of 120 + 300 = <<120+300=420>>420 miles.
If he drove for a total of 10 hours and covered a distance of 420 miles, then his average speed was 420 miles / 10 hours = <<420/10=42>>42 mph.
Since Elliott drove 20 mph faster after the rain stopped than he did while it was raining, then we know that his speed while it was raining was 20 mph slower than his average speed of 42 mph. That means his speed while it was raining was 42 mph - 20 mph = <<42-20=22>>22 mph.
What is the coefficient of 5x² in 5x² 5x?
The coefficient of expression 5x^2 in 5x^2 5x is 5.
The coefficient of 5x^2 in 5x^2 5x is the number that is multiplied with 5x^2. In this expression, the number multiplied with 5x^2 is 5, so the coefficient of 5x^2 is 5.
The expanded expression is 5x^2 5x = 5x^3 + 5x^2. The coefficient of 5x^2 in this expression is still 5.
The coefficient of 5x^2 in 5x^2 5x is the number that is multiplied with 5x^2. When we expand the expression 5x^2 5x, it becomes 5x^3 + 5x^2. The number that is multiplied with 5x^2 in this expression is still 5, so the coefficient of 5x^2 is 5.
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A retail store sold a case of candles for $17.85 that had been marked up 110%. What was the original price of the table
The original price of the case of candles before markup was $8.50.
Markup price is the price that comes after setting up additional layer of pricing on the original price of a good. In this case also markup price is there. To find the original price of the case of candles before markup, we can use the following formula:
Original price = Marked up price / (1 + markup percentage)
In this case, the original price would be:
$17.85 / (1 + 110%) = $17.85 / 2.10 = $8.50
So the original price of the case of candles before markup was $8.50.
Thus, Original price is $8.5
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What is 10 by the power of 6?
Answer:1000000
Step-by-step explanation:
Find four consecutive odd integers such taht 4 times the sum of the first and third is 4 larger than 4 times the fourth
The four consecutive odd integers = 15, 17, 19, 21
What are integers ?Positive, negative, and zero are all examples of integers.
The Latin word "integer" signifies "whole" or "intact."
As a result, fractions and decimals are not included in integers.
All whole numbers and negative numbers are considered integers.
This means that if we combine negative numbers with whole numbers, a collection of integers results.
An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.
Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043. a collection of numbers, denoted by the symbol Z.
According to our question-
x + x + 6 = -(x + 4) + 55
x + x+6 = (-x - 4) + 55
2x + 6 = -x + 51
Collect like terms
2x + x = 51 - 6
3x = 45
x = 15
Second integer = x + 2 = 15 + 2 = 17
Third integer = x + 4 = 15 + 4 = 19
Fourth integer = x + 6 = 15 + 6 = 21
The four consecutive odd integers = 15, 17, 19, 21
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Find the surface area and volume for this following pyramid
We calculated volume of pyramid = 160 cubic inches and surface area = 214.59 square inches.
what is pyramid?
A three-dimensional geometrical figure having flat polygon base along with a number of lateral triangular shaped faces.
How to calculate the volume and surface area of the pyramid?The given pyramid is a rectangular pyramid having length 10 inch and width 8 inch. The height of pyramid is 6 inches.
length, l = 10 inch
width, w = 8 inch
height, h = 6 inch
Now the volume will be, V = 1/3 × l × w ×h
V = 1/3 × 10 × 8× 6
hence, the volume = 160 cubic inches
We calculate the surface area of the given pyramid,
formula for surface area, SA = l × w + 1/2 × w ×√(4h²+l²) + 1/2 × l ×√(4h²+w²)
SA = 10 × 8 + 1/2 × 8 ×√(4×6²+10²) + 1/2 ×10×√(4×16²+8²)
Surface area = 214.593 square inches
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20. Kim works on commission. If her monthly earnings for the first
four months of the year were $1625, $960, $1235, and $1420,
estimate what her annual earnings will be.
A) $14,240 B) $15,390 C) $15,720 D) $16,150 E) $16,280
O A
OB
OC
OD
ΟΕ
Since, Kim works on commission and her trend of monthly earnings are not constant, Calculate the average from the data and estimate for the whole year , The answer is C) $15,720
What is statistics?Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It helps to make sense of large amount of data and use it to draw conclusions and make informed decisions. It provides methods to summarize, describe and analyze data, as well as techniques to infer characteristics of a population from a sample.
What is mean of the data?The mean is a measure of central tendency and a way to describe the average value of a dataset. It is calculated by adding up all the values in a dataset and then dividing by the number of values. The resulting value is the mean of the dataset, also known as the arithmetic average. Mean is commonly used to describe a large data set, while median is used to describe data with values have outliers.
salary for four months = $1625, $960, $1235, and $1420.
Average = ($1625 + $960+ $1235+$1420) /4 = $1310
for whole year = $1310 * 12 = $15,720
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a cylinder has a volume of 24 cubic feet, what is the equation on how to find the volume?
The equation on how to find the volume is πr²h = 24
How to determine the equation on how to find the volume?From the question, we have the following parameters that can be used in our computation:
Volume = 24 cubic feet
The volume of a cylinder can be calculated as
Volume = πr²h
Where
r = radius
h = height
Substitute the known values in the above equation, so, we have the following representation
πr²h = 24
Hence, the equation is πr²h = 24
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Find the Average Rate of Change of the graph over the interval -4 < x < 5
Answer:
AROC = - [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
the average rate of change of g(x) in the closed interval [ a, b ] is
[tex]\frac{g(b)-g(a)}{b-a}[/tex]
here [ a, b ] = [ - 4, 5 ] , then
g(b) = g(5) = - 1 ← point (5, 1 ) on graph
g(a) = g(- 4) = 5 ← point (- 4, 5 ) on graph
average rate of change = [tex]\frac{-1-5}{5-(-4)}[/tex] = [tex]\frac{-6}{5+4}[/tex] = [tex]\frac{-6}{9}[/tex] = - [tex]\frac{2}{3}[/tex]
Isabella is 30 miles into a 70-mile backpacking trip in the wilderness.
Isabella can hike 8 miles per day. How many more days does Isabella
need to finish?
Isabella needs how
more days.
Answer: Five Days
Step-by-step explanation:
Isabella can hike 8 miles per day. So:
[tex]\frac{30miles}{8miles} = 3.75 days[/tex]
It will take:
[tex]\frac{70 miles}{8 miles} = 8.75 days[/tex]
..in total to hike 70 miles.
So, subtracting the two values:
[tex]8.75 - 3.75 = 5[/tex]
She still needs to hike five days in order to finish the trail.