The distance from frank's house to john's house and then back to frank's house is less than a mile by 1/5 units.
How do you figure out the overall distance?Simply multiplying the distance between two points while travelling from one location to another and back will give you the total distance travelled when travelling from one location to another and returning to the starting point.
The distance from frank's house to john's house = 4/10.
The distance back to Frank's house = 4/10.
Total distance = 4/10 + 4/10
Total distance = 8/10
The distance is thus,
1 - 8/10
Take the LCM:
(10 - 8) / 10
2/10 = 1/5
Hence, the distance from frank's house to john's house and then back to frank's house is less than a mile by 1/5 units.
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Help what’s the value of x ?
The value of x, given the triangle and the sides, would be 21. 67 units .
How to find x ?We are given the hypotenuse of the triangle and the length of the side that is adjacent to the angle given.
This means that the value of x would be found by the operation of Cos. The value of x can be found to be :
Cos ( 37 degrees ) = 17. 3 / x
x × Cos ( 37 degrees ) = 17. 3
x = 17. 3 / Cos ( 37 degrees )
x = 17. 3 / 0. 7986355
x = 21. 67 units
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Write an expression to represent the statement 2 times as much as the difference of 1.02 and 0.98
Answer:
Below
Step-by-step explanation:
the difference of 1.02 and 0.98 :
(1.02 - 0.98)
2 times as much :
2 * ( 1.02-0.98)
Answer:
2(1.02-.98)
Step-by-step explanation:
Each pair of polygons are similar. Find the value of x.
Solving a system of equations we will see that x = 2.
How to find the value of x?We know that the two rectangles are similar, so if k is the scale factor between them, we can write:
3x - 1 = k*4
8x -1 = k*12
So we have a system of equations.
Taking the quotient between the two equations we will get:
(3x - 1)/(8x - 1) = k*4/k*12
(3x - 1)/(8x - 1) = 4/12
3x - 1 = (1/3)*(8x - 1)
3x - 1 = (8/3)*x - 1/3
3x - 8/3x = 1 - 1/3
(1/3)*x = 2/3
x = 3*(2/3) = 2
x = 2
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In a basket of apples, 12% of them
are rotten and 66 are in good
condition. Find the total number of
apples in the basket.
Answer:
The total number of apples is 550
Step-by-step explanation:
12% - Turn into a fraction of 12/100
12/100
X = total number of apples
*Make another fraction of x the denominator and the 66 that are in good condition as the numerator*
12/100 = 66/X
Cross multiply
12 * X = 12x
66 * 100 = 6600
Divide
6600/12 = 12x/12 - cancel
6600/12= 550
X = 550
Challenge A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins, 14% are pennies and 30% are dimes. There are 4 more nickels than pennies. How much money does the bag contain?
Answer:
the bag contains $10.89.
Step-by-step explanation:
Let's start by using algebra to represent the number of coins in terms of one variable. Let x be the number of pennies in the bag. Then:
The number of nickels is 4 more than the number of pennies, so there are x + 4 nickels.
The number of dimes is 30% of the total, so there are 0.3 * 50 = 15 dimes.
The number of quarters is the remaining coins: 50 - (x + x + 4 + 15) = 31 - 2x.
To find the total amount of money, we need to multiply the number of each type of coin by its value and add them up. Using the values of the coins:
Pennies: x * $0.01
Nickels: (x + 4) * $0.05
Dimes: 15 * $0.10
Quarters: (31 - 2x) * $0.25
Adding these expressions and simplifying, we get:
Total = 0.01x + 0.05(x + 4) + 0.10(15) + 0.25(31 - 2x)
= 0.01x + 0.05x + 0.20 + 1.50 + 7.75 - 0.50x
= 0.06x + 9.45
Now we need to find x, the number of pennies. We know that 14% of the coins are pennies, so:
0.14 * 50 = 7 = x + (x + 4) + 15 + (31 - 2x)
Solving for x, we get:
7 = 50 - x - 19
x = 24
So there are 24 pennies, 28 nickels, 15 dimes, and 3 quarters in the bag. The total amount of money is:
Total = 0.06(24) + 9.45 = $10.89
Therefore, the bag contains $10.89.
Which expression represents the prime factorization of 192?
A. 2 x 2 x 2 x 2 x 12
B. 2 x 2 x 2 x 2 x 2 x 3
C. 3 x 2 x 2 x 2 x 2 x 2 x 2
D. 2 x 2 x 2 x 2 x 2 x 3 x 3
Answer:
c
Step-by-step explanation:
2 x 2=4
2 x 2 =4
2 x 2 = 4
4 ^3 = 64
48 x 3 =192
Or:
192/2 = 96
96/2=48
48/2 = 24
24/2= 12
12/3=4
4/2=2
2 x 2 x 2 x 2 x 2 x 2 x 3
ΔABC and ΔDEF are similar
triangles. Find BC.
The length of BC in the triangle is 24 units.
How to find the similar triangle?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
Therefore, using proportion,
BC / x = 12 / x - 4 = x + 7 / 5
12 / x - 4 = x + 7 / 5
cross multiply
12 × 5 = (x - 4)(x + 7)
60 = x² + 7x - 4x - 28
x² + 3x - 28 - 60 = 0
x² + 3x - 88 = 0
x² - 8x + 11x - 88 = 0
x(x - 8) + 11(x - 8) = 0
(x + 11)(x - 8) = 0
Therefore,
x = - 11 and x = 8
Hence,
BC / x = 12 / x - 4
BC / 8 = 12 / 8 - 4
BC / 8 = 12 / 4
4BC = 96
BC = 96 / 4
BC = 24 units
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Mr sato has $800. He spends $600 on rent. Then he s$85 on groceries. How much money does he have left
$800 - $600 - $85 = $115
∴ Mr Sato has $115 left.
Answer:
172
Step-by-step explanation:
take $800 subtract $600 and then subtract $85
If ∑X = 4,390 and n= 4, what is M?
a. 1,097.5
b. 17,560
c. need more information
d. .0100
Answer:
c. need more information
Step-by-step explanation:
You want M, given that ∑X = 4390 and n=4.
RelationshipTwo expressions for different variables are given, but there is no given relationship between them or to the variable of interest: M.
You need more information.
Please help I’ll mark your answer brainliest!
The total amount of fencing change by 236.66 feet.
The average rate of change is 2.3666.
What is average rate of change?It quantifies how much the function changed per unit on average over that time interval. The slope of the straight line connecting the interval's ends on the function's graph is used to calculate it.
First, When width is 200 ft then
length = 19000/ 200 = 95 feet
and, When width is 300 ft then
length = 19000/ 300 = 63.33 feet
1) The amount of Fencing
= 3 x width + 2 x length
= 3 x 200 + 2 x 95
= 600 + 190
= 790 feet
2) The amount of Fencing
= 3 x width + 2 x length
= 3 x 300 + 2 x 63.33
= 900 + 126.66
= 1026.66 feet
So, the Change is
= 236.66 feet
Thus, the avreage rate of change
= 236.33/ (300- 200)
= 2.3666
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What is the solution to the division problem below? (You can use long division
or synthetic division.)
2x³-4x²-3x-9
——————-
X-3
OA. 2x² + 3x+3
OB. 2x² + 4x+3
OC. 2x²+2x+3
OD. 2x²+x+3
The solution to the division problem 2x³-4x²-3x-9/ x-3 is 2x² + 6x + 15
Describe Synthetic Division?Synthetic division is a method of polynomial division used to divide a polynomial by a linear expression of the form x - a, where a is a constant. It is a shorthand way of performing long division for polynomials and is particularly useful when the divisor is of the form x - a, as it eliminates the need for writing out the full divisor in each step of the division process.
The advantage of synthetic division is that it is quicker and easier than long division, especially for dividing polynomials by linear expressions. It can also be used to evaluate a polynomial at a specific value of x, by setting the divisor to x - a and using the result in the final row of the synthetic division as the value of the polynomial at x = a.
We can use long division to solve this problem:
2x² + 6x + 15
---------------------
x - 3 | 2x³ - 4x² - 3x - 9
- (2x³ - 6x²)
---------------
2x² - 3x
- (2x² - 6x)
------------
3x - 9
- (3x - 9)
--------
0
So the solution to the division problem is:
2x² + 6x + 15
Therefore, the answer is (none of the above).
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Help, please! A road-building company plans to construct a bridge across a pond to connect Main Street and Second Street, as shown in the diagram below. How long will this bridge need to be? Show your work.
Answer:
Refer to photo above ......alright
In a recent year, the Better Business Bureau settled 75% of complaints they received. You have been hired by the Bureau to investigate complaints this year involving computer stores. You plan to select a random sample of complaints to estimate the proportion of complaints the Bureau is able to settle. Suppose your sample size is 197. What is the probability that the sample proportion will be at most 2 percent more than the population proportion?
The probability that the sample proportion will be at most 2% more than the population proportion is approximately 0.7007.
The sample size is n = 197, and the population fraction of complaints resolved by the Better Business Bureau is 0.75. P(p 0.77), where p is the sample percentage, is the chance that the sample proportion is no more than 2% greater than the population proportion.
The distribution of the sample proportion can be approximated by the central limit theorem as having a mean of 0.75 and a standard deviation of sqrt[(0.75)(0.25)/197] = 0.038.
The sample proportion is then standardised as follows:
Z = (p - μ) / σ = (0.77 - 0.75) / 0.038 = 0.526
We are looking for P(Z 0.526). We can determine that P(Z 0.526) = 0.7007 by using a calculator or a conventional normal distribution table.
Hence, 0.7007 is around how likely it is that the sample proportion will be at most 2% higher than the population proportion.
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» Complete the sentence.
8.347 rounded to the nearest hundredth is
8.347 rounded to the nearest hundredth is 8.35
The complete sentence is 8.347 rounded to the nearest hundredth is 8.35.
Given sentence is
8.347 rounded to the nearest hundredth is ......
To find the nearest hundredth value
here, count the place value from left to right
place value of 7 is ones.
place value of 4 is hundredth.
So, 8.347 rounded to the nearest hundredth is 8.35.
Therefore, the complete sentence is 8.347 rounded to the nearest hundredth is 8.35.
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the value of (25-y) half dollars is
The requried value of (25-y) half dollars is 12.5 - 0.5y dollars.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.
Here,
Assuming you want to find the value of a certain number of half-dollars when each half-dollar has a value of 50 cents, we can use the following formula:
Value = Number of coins x Value of each coin
Here, the number of half-dollars is (25-y), and the value of each half-dollar is 50 cents or $0.5. So, we can write:
Value of (25-y) half dollars = (25-y) x 0.5
Value of (25-y) half dollars = 12.5 - 0.5y
Therefore, the value of (25-y) half dollars is 12.5 - 0.5y dollars.
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Find how the perimeter and the area of the figure change when its dimensions change
The dimensions of the triangle have been doubled in this case so, the perimeter will also be doubled, and the area will be four times.
How do you calculate a triangle's area and perimeter?The entire area filled by a triangle's three sides on a two-dimensional plane is known as the triangle's area. A = 1/2 b h is the basic equation for a triangle's area, where b and h represent the base and height of the triangle, respectively.
The triangle's perimeter is equal to the product of its three sides.
This formula can be used to determine any triangle shape, including scalene, isosceles, and equilateral triangles. Remember that the base and height of a triangle are perpendicular to one another.
In the given question the original dimensions of the equal sides = 2.5 units.
The new dimensions of the equal sides = 5 units.
The dimensions here got doubled.
Therefore, when the dimensions of the triangle are doubled, the perimeter also gets doubled and the area of the triangle will increase four times.
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Find domain, range, vertical asymptotic, horizontal asymptote, x-intercept, y-intercept of f(x)= -1/x-5+3
Pic attached below
The features of the rational function are listed below:
Domain: All real numbers except x = 5.
Range: All real numbers except f(x) = 3.
Vertical asymptote: x = 5
Horizontal asymptote: f(x) = 3
x-Intercept: x = 16 / 3
y-Intercept: f(0) = 16 / 5
How to determine the features of a rational function
In this problem we find the definition of a rational function:
f(x) = - 1 / (x - 5) + 3
Whose features introduced below must be derived:
DomainRangeVertical asymptoteHorizontal asymptotex-Intercepty-InterceptDomain
Domain of rational functions are all real numbers expect when x - 5 = 0.
Dom {f(x)} = R - {5}
Range
Range of rational functions are all real numbers except horizontal asymptote.
Ran {f(x)} = R - {3}
Vertical asymptote
x = 5
Horizontal asymptote
f(x) = 3
x-Intercept
- 1 / (x - 5) + 3 = 0
1 / (x - 5) = 3
1 = 3 · (x - 5)
1 = 3 · x - 15
3 · x = 16
x = 16 / 3
y-Intercept
f(0) = - 1 / (0 - 5) + 3
f(0) = 1 / 5 + 3
f(0) = 16 / 5
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Critique Reasoning Mario says that he drew two tangents to a circle
that meet at a point outside the circle. He also says that the two points
where the two tangents meet the circle separate the circle into two
semicircles. Is it possible for Mario to have drawn this figure? Explain.
No, it is not possible for Mario to have drawn this figure.
What are the properties of the circle?The circumference, which is the distance around the object, the diameter, which is the length of a circle measured from one end to the other and passing through its center, and the radius, which is equal to half of the diameter, are the three key characteristics.
If two tangents to a circle meet at a point outside the circle, they must be parallel to each other.
If the two points where the two tangents meet the circle separate the circle into two semicircles, then the center of the circle must lie on the line containing the two points.
However, since the tangents are parallel, they do not intersect the line containing the two points, and therefore, the center of the circle cannot lie on this line.
This contradicts the definition of a circle, which states that the center of a circle is equidistant from all points on the circle.
Therefore, Mario's reasoning is flawed, and it is not possible for him to have drawn this figure.
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Fully simplify.
Answer:
10y¹(−9x²)
Answer:
respuesta es : -810 xy
Step-by-step explanation:
:)
the spaghetti has ? g of fibers per serving
The correct answer is 4g. Spaghetti is a great source of fiber, with 4g per serving.
What is fiber?Fiber is a type of carbohydrate found in plant-based foods. It is not digested or absorbed by the body, but instead passes through the digestive system and out of the body. Fiber helps promote healthy digestion by adding bulk to the stool, helping it to pass through the intestines more quickly.
Fiber is an essential part of a healthy diet. It helps to keep your digestive system functioning properly, reduce cholesterol levels, and aid in weight management. It can be found in many plant-based foods, as well as some animal-based products. Spaghetti is a great source of fiber, with 4g per serving. This is a good amount for a meal, and it can help you meet your daily fiber needs. Eating a variety of foods that are high in fiber can help you stay healthy and reach your dietary goals. Getting enough fiber in your diet can also help reduce your risk of diabetes, heart disease, and stroke. So, the correct answer is 4g of fiber per serving of spaghetti.
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if y varies directly with x, and x = 7 when y = 28, find y when x = 13. pleaseee help meeeee
The values of x and y equals to 13 , 52 respectively .
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
If y varies directly with x, it means that y is proportional to x, and we can write this relationship as:
y = kx
where k is the constant of proportionality.
To find the value of k, we can use the given information that x = 7 when y = 28:
28 = k * 7
Simplifying this equation, we get:
k = 28/7 = 4
Now that we have found the value of k, we can use the equation y = kx to find y when x = 13:
y = 4 * 13 = 52
Therefore, The values of x and y are 13 , 52 respectively .
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How would you find the volume of the figure represented by the given net? (Note: The area of each circular base is the same.) asap please
Multiply (1,105.28)(200.96).
Multiply (200.96)(22).
Add 1,105.28 + 200.96 + 200.96.
Add 1,105.28 + 200.96 + 22.
The supplied net's representation of the rectangle has a volume of 1,105.28 Plus 200.96 + 200.96.
What is the equation for a rectangular cube's volume?You discovered through this activity that the formula of volume is V = l w h, which can alternatively be expressed as volume equals length times width times height. Volume is defined as the base area multiplied by the height, or V = B h. Spherical prisms and cubes are the only objects for which the form, V = l w h, is true.
Length times width equals the rectangle's area.
[tex]Area = length*width[/tex]
We have provided the size of a rectangle, which is 1,105.28, and the area of a circle, which is 200.96.
Each round base has the same area.
By summing all the forms, we can get the total volume of the figure.
As a result, [tex]1,105.28 + 200.96 + 200.96[/tex] is the volume of the image represented by the specified net.
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Question Which statements are true? Select each correct answer. Responses 24g4+18g2=6g2(4g2+3g) 24 g begin power 4 end power plus 18 g squared equals 6 g squared left parenthesis 4 g squared plus 3 g right parenthesis 4g2−g=g2(4−g) 4 g squared minus g equals g squared left parenthesis 4 minus g right parenthesis 9g3+12=3(3g3+4) 9 g cubed plus 12 equals 3 left parenthesis 3 g cubed plus 4 right parenthesis 35g5−25g2=5g2(7g3−5)
All four statements are true. The first statement is true because 24g4+18g2 can be factored into 6g2(4g2+3g). The second statement is true because 4g2−g can be factored into g2(4−g). The third statement is true because 9g3+12 can be factored into 3(3g3+4). The fourth statement is true because 35g5−25g2 can be factored into 5g2(7g3−5).
What are parenthesis?Parenthesis are punctuation marks that are used to set apart a clause or phrase within a sentence. They are also known as round brackets and are used to add additional information or asides to a sentence. Parenthesis are used to provide additional information, to emphasis a point, to give examples, to define terms, and to explain ideas.
The first statement is 24g4+18g2=6g2(4g2+3g). This translates to 24g to the fourth power plus 18g squared equals 6g squared left parenthesis 4g squared plus 3g right parenthesis. The second statement is 4g2−g=g2(4−g). This translates to 4g squared minus g equals g squared left parenthesis 4 minus g right parenthesis. The third statement is 9g3+12=3(3g3+4). This translates to 9g cubed plus 12 equals 3 left parenthesis 3g cubed plus 4 right parenthesis. The fourth statement is 35g5−25g2=5g2(7g3−5). This translates to 35g to the fifth power minus 25g squared equals 5g squared left parenthesis 7g cubed minus 5 right parenthesis.
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Find the value of x
Check the picture below.
PLEASE HELPP!!!
The amount of money in an account may increase due to rising stock prices and decrease due to falling stock prices. Marco is studying the change in the amount of money in two accounts, A and B, over time.
The amount f(x), in dollars, in account A after x years is represented by the function below:
f(x) = 9,628(0.92)x
Part A: Is the amount of money in account A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)
Part B: The table below shows the amount g(r), in dollars, of money in account B after r years:
r (number of years) 1 2 3 4
g(r) (amount in dollars) 8,972 8,074.80 7,267.32 6,540.59
Which account recorded a greater percentage change in amount of money over the previous year? Justify your answer. (5 points)
The amount of money in account A is decreasing by 8% per year. Account B recorded a greater percentage change in amount of money over the previous year.
What is amount?Amount is an indefinite quantity of something, usually money or a measurement of quantity. It is often used to describe the total amount of money received or spent in a particular instance or over a period of time.
The amount of money in account A is decreasing by 8% per year. This can be seen by looking at the 0.92 in the equation. This is the rate of decay, and represents a 8% decrease every year.
Part B: Account B recorded a greater percentage change in the amount of money over the previous year. Looking at the table, the amount of money decreased by 10.51%, 10.22%, and 11.94% in the first, second, and third years respectively. This is greater than the 8% decrease in account A.
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60 points! Complete each proof using the most appropriate method.
The statements are true by following the principles of congruency.
What are congruent triangles and their property?
Two harmonious triangles have identical areas and peripheries. Each of a triangle's sides and angles is an exact match to its harmonious triangle's corresponding sides and angles. We can use five different parcels to show that any two triangles are harmonious SSS, SAS, AAS, ASA, and RHS.
The SAS criterion stands for the Side- Angle- Side criterion. This standard countries that two triangles are harmonious if they've matching sides and included angles on contrary sides of each other.
Side- Side- Side criterion is appertained to as the SSS criterion. According to this standard, two triangles are harmonious if their separate triangles' three sides are equal to one another.
1. In the first figure,
KL = LN [L is the mid - point]
ML = LP [L is the mid - point which bisects it]
∠MLK = ∠ NLP [Vertically opposite angle]
By Angle side Angle property, both the triangles are congruent
2. In the given figure,
∠ABD = ∠CBD [As BD bisects the angle ABC]
BD = BD [Common side]
∠BAD = ∠BCD [As triangles ΔBAD ≅ ΔBCD]
By Angle - side - angle property, ΔABD ≅ ΔCBD
3. Given,
QS = SU [S is the midpoint]
QR ≅ ST [Given]
RS ≅ TU [Given]
By Side - Side - Side property, ΔQRS ≅ ΔSTU
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What is the five-number summary for this data set?
14, 17, 19, 23, 25, 28, 30, 34, 40, 43
Assume the numbers in each answer choice are listed in this order: min, Q1,
median, Q3, max.
OA. 14, 19, 29, 34, 43
B. 14, 23, 26.5, 30, 43
C. 14, 19, 26.5, 34, 43
OD. 14, 23, 29, 30, 43
Answer:
To find the five-number summary of a data set, we need to find the minimum value, the first quartile (Q1), the median, the third quartile (Q3), and the maximum value.
We can first put the data set in order from smallest to largest:
14, 17, 19, 23, 25, 28, 30, 34, 40, 43
The minimum value is 14, and the maximum value is 43.
To find the median, we need to find the middle value. Since there are 10 numbers in the data set, the median is the average of the fifth and sixth values:
Median = (25 + 28) / 2 = 26.5
To find the first and third quartiles, we can use the median as a reference point. The first quartile (Q1) is the median of the lower half of the data set, and the third quartile (Q3) is the median of the upper half of the data set.
The lower half of the data set consists of the first five values:
14, 17, 19, 23, 25
The median of these values is:
Q1 = (19 + 23) / 2 = 21
The upper half of the data set consists of the last five values:
28, 30, 34, 40, 43
The median of these values is:
Q3 = (34 + 40) / 2 = 37
Therefore, the five-number summary for this data set is:
Minimum = 14
Q1 = 21
Median = 26.5
Q3 = 37
Maximum = 43
Looking at the answer choices, we can see that option C is the correct answer:
OA. 14, 19, 29, 34, 43
B. 14, 23, 26.5, 30, 43
C. 14, 19, 26.5, 34, 43
OD. 14, 23, 29, 30, 43
Jeremy is saving money for new tires for his car. What he saves
goes into his savings account. After one month, he has saved
$230. After four months, he has $329 saved.
According to the given information, Jeremy is saving approximately $20.56 per week for his new tires.
What is basic arithmetic?
Basic arithmetic refers to the fundamental operations of arithmetic, which include addition, subtraction, multiplication, and division. These operations are used to perform calculations with numbers, such as counting, computing sums, finding differences, calculating products, and determining quotients.
We can use this information to find Jeremy's weekly savings rate.
To find the weekly savings rate, we need to first find out how much Jeremy saves in a week.
For the first month, which is four weeks, Jeremy saves $230.
For the next three months, which is 12 weeks, he saves an additional $329 - $230 = $99.
Therefore, in total, Jeremy saves $230 + $99 = $329 in 16 weeks.
His weekly savings rate is then:
$329 / 16 weeks = $20.56 per week (rounded to the nearest cent)
So, Jeremy is saving approximately $20.56 per week for his new tires.
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So confused on the last question! Could somebody help me? :)
a. Use the appropriate formula to find the value of the annuity.
b. Find the interest.
Periodic Deposit
$2000 at the end of each year
Rate
3.5% compounded annually
Time
10 years
The annuity is $2800 and interest is $800.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].
Given that, P= $2000 at the end of each year, R= 3.5% compounded annually and time = 10 years
Amount = 2000(1+3.5/100)¹⁰
= 2000(1+0.035)¹⁰
= 2000(1.035)¹⁰
= 2000×1.4
= $2800
Interest = 2800-2000
= $800
Therefore, the annuity is $2800 and interest is $800.
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