a) The interval would be:Interval = $12.50 ± ($51.50 x 3)Interval = $12.50 ± $154.50 Interval = ($12.50 - $154.50, $12.50 + $154.50)Interval = (-$142.00, $179.00)
b) The interval would be:Interval = $12.50 ± ($51.50 x 1)Interval = $12.50 ± $51.50 Interval = ($-39.00, $64.00)This interval can be considered usual since it includes about 68% of the data.
c) A pizza that costs $10 is about 0.049 standard deviations below the mean.
Use the Empirical Rule to make an interval that should include 99.7% of the data.The Empirical Rule, also known as the 68-95-99.7 rule, is a statistical rule that states that for a normal distribution, about 68% of observations will fall within one standard deviation of the mean, about 95% will fall within two standard deviations, and about 99.7% will fall within three standard deviations.To make an interval that should include 99.7% of the data, we need to find the mean plus/minus three standard deviations. The mean is given as $12.50, and the standard deviation is given as $51.50. Therefore, the interval would be:Interval = $12.50 ± ($51.50 x 3)Interval = $12.50 ± $154.50Interval = ($12.50 - $154.50, $12.50 + $154.50)Interval = (-$142.00, $179.00)
Use the Empirical Rule to make an interval that would be considered usual.Again, we can use the Empirical Rule to find an interval that would be considered usual. This would be the interval that falls within one standard deviation of the mean. The mean is given as $12.50, and the standard deviation is given as $51.50. Therefore, the interval would be:Interval = $12.50 ± ($51.50 x 1)Interval = $12.50 ± $51.50 Interval = ($-39.00, $64.00)This interval can be considered usual since it includes about 68% of the data.
Find the z-score of a pizza that costs $10.The z-score is a measure of how many standard deviations a data point is from the mean. To find the z-score of a pizza that costs $10, we first need to find the difference between $10 and the mean of $12.50, and then divide that difference by the standard deviation of $51.50.z-score = (10 - 12.50) / 51.50z-score = -0.049 This means that a pizza that costs $10 is about 0.049 standard deviations below the mean.
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There are 120 students in the seventh grade, and 5% are in the Environmental Club. How many students are in the Environmental Club?
Answer:
6 students
Step-by-step explanation:
We know
There are 120 students in the seventh grade. 5% are in the Environmental Club.
How many students are in the Environmental Club?
5% = 0.05
120 x 0.05 = 6 students
So, there are 6 students in the Environmental Club.
Answer:
6
Step-by-step explanation:
To find the answer to this question we have to find 5% of 120, this will give us how many students there are in the Environmental Club.
To do this we have to do...
100% ÷ 5 = 20Then...
120 ÷ 20 = 6This means that 6 of the students in the seventh grade are in the Environmental Club!
Hope this helps, have a lovely day! :)
Dani spends 5.20 total to create
2 treat bags. How much more
would she have to spend to make
5 more similar bags?
Answer:
Step-by-step explanation:
1 treat bag [tex]=\frac{\$5.20}{2} =\$2.60[/tex]
So 5 treat bags [tex]=5\times \$2.60=\$13.00[/tex]
Dani would have to spend an extra $13 to make 5 more bags.
A coordinate grid is mapped on a video game screen, with the origin in the lower-left corner. A game designer programs a helicopter to follow a path that can be modeled by a quadratic function with a vertex at (16, 20) and passing through the point (4, 25). She also programs an airplane to move along a linear path that passes through the points (0, 18) and (30, 20). Which system of equations can be used to determine whether the paths of the helicopter and airplane cross?
StartLayout Enlarged Left-Brace 1st Row y = one-fifteenth x + 18 2nd Row y = StartFraction 5 Over 144 EndFraction (x minus 16) squared + 20 EndLayout
StartLayout Enlarged Left-Brace 1st Row y = 15 x + 18 2nd Row y = StartFraction 5 Over 144 EndFraction (x minus 16) squared + 20 EndLayout
StartLayout Enlarged Left-Brace 1st Row y = one-fifteenth x + 18 2nd Row y = Negative StartFraction 5 Over 144 EndFraction (x minus 4) squared + 25 EndLayout
StartLayout Enlarged Left-Brace 1st Row y = 15 x + 18 2nd Row y = Negative StartFraction 5 Over 144 EndFraction (x minus 4) squared + 25 EndLayout
Answer:
1) y = (1/15)x + 18
2) y = (5/144) (x - 16)^2 + 20
Solution:
1) The solution consists in establishing the equations that model the two paths.
2) Let's start with the easiest one. It is the linear path.
You have that the equation is a line that passes through the points (0,18) and (30,20). This equation is found using this formula:
[tex]\dfrac{y-b}{x-a} =\dfrac{d-b}{c-a}[/tex]
where the two points are (a,b) and (c,d)
So, for the two points given:
[tex]\dfrac{y-18}{x-0} =\dfrac{20-18}{30-0} =\dfrac{2}{30}[/tex]
=> [tex](y - 18)\times30 = x\times2[/tex]
=> [tex]30y - 540 = 2x[/tex]
=> [tex]30y = 2x + 540[/tex]
=> [tex]y = 2x \div 30 + 540 \div 30[/tex]
=> y = x/15 + 18 ---------------> this is the first equation of the system.
3) Now, find the equation for the path modeled by the quadratic function.
The vertex form of a quadratic function is: [tex]y = A (x - h)^2 + k[/tex]
where the vertex is (k,h).
Then, so far you can write [tex]y = A (x - 16)^2 + 20[/tex]
Now, replace the coordinates of the point (4,25) to find the value of A:
[tex]25 = A (4 - 16)^2 + 20[/tex]
=> [tex]25 = A (-12)^2 + 20[/tex]
=> [tex]25 = A\times144 + 20[/tex]
=> [tex]144A = 25 - 20[/tex]
=> [tex]144\ A = 5[/tex]
=> [tex]A = 5 \div 144[/tex]
=> y = (5 / 144) (x - 16)^2 + 20 ---------> this is the second equation of the system.
System:
1) [tex]y = (\frac{1}{15} )x + 18[/tex]
2)[tex]y = (\frac{5}{144} )\ (x - 16)^2 + 20[/tex]
Learning Unit 5 Discussion Question -- Introduction to Algebra
33 unread replies. 33 replies. To prepare for this class discussion, you can either look at prices of a grocery product online or in a grocery store. Pick a product that comes in at least two different sizes and compare the unit prices of that product at the same store or online. Pick a product and compare the unit price of that product at two different stores/online shops (the sizes can be the same or different). Give your answer in cents per unit size and round your answer to the nearest hundredth. Which is the better deal
Shop A sells 16 ounces of peanut butter for $3.99 (24.94 cents/oz), but Store B sells 32 ounces for $6.49 (20.28 cents/oz). At 20.28 cents/oz, Shop B is offering a better price.
To save money while shopping, it is important to compare unit pricing of supermarket items. In this analysis, we contrasted the unit costs of peanut butter at two various retailers. Shop A sells 16 ounces for $3.99, which works out to 24.94 cents per ounce; Store B sells 32 ounces for $6.49, which works out to 20.28 cents per ounce. With a cheaper unit price of peanut butter, Shop B is the preferable option. Comparing unit prices makes it simple to identify which retailer is providing the greatest bargain for the item we need to purchase.
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1/2a - 5 1/2 = 5 - a for what values of a are the following expressions true?
It’s not a=7 I’ve tried
For the value of a = 7, the expression is true.
What is an expression?A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables. Let's examine the writing style of expressions. A number is 6 times larger than the other number, x, by a factor of 2.
Now in the given question,
1/2 a - 5 1/2 = 5 - a
We first simplify the expression as:
a/2 -11/2 = 5 - a
⇒ (a-11)/2 = 5 - a
⇒ a - 11 = 10 - 2a
⇒ a+ 2a = 10 + 11
⇒ 3a = 21
⇒ a = 7.
Therefore, for the value of a = 7 the expression is true.
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The average body temperature is 98.6o, right? Hausmann, Berna, Ggujral, Ayubi, Howekins, Brownstein, & Dedeoglu (2018) conducted a study using AppleWatches to collect data on body temperature. Below is a dataset, containing the average body temperature of participants. Conduct a one-sample t in SPSS to test the hypothesis that the population mean for body temperature is 98.6o.
Include the following in your post:
Report your findings in APA Format (refer to LAB 3).
Why do you think you got the results that you did?
What could be the reason that so many people believe the average body temperature is still 98.6O?
We can deduce from these findings that the actual population mean is variable probably lower and reject the null hypothesis that the population mean for body temperature is 98.6o.
What is a Variable?In the context of a mathematical idea or experiment, a variable is something that can be altered. Frequently, a single symbol is used to symbolize a variable. Variables are frequently represented by the letters x, y, and z as abstract symbols.
The first thing I want to say is that it is a widespread misconception that the average body temperature is 98.6 degrees. Although the "normal" or average body temperature is frequently stated as 98.6 degrees Fahrenheit (or 37 degrees Celsius), this value is not true for everyone. The average body temperature may actually be lower than previously thought, hovering around 97.5–97.7 degrees Fahrenheit, according to study.
Here is the SPSS output for the one-sample t-test so that we can get back to the job at hand:
Descriptive Statistics
N Mean Std. Deviation Std. Error Mean
25 97.528 0.694 0.139
One-Sample Test
Test Value = 98.6
t df Sig. (2-tailed) Mean Difference
-5.238 24 .000 -1.072
We can deduce from these findings that the actual population mean is probably lower and reject the null hypothesis that the population mean for body temperature is 98.6o.
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Ms. Murray owns an ice cream shop. She keeps track of how many bottles of caramel syrup and chocolate syrup she uses per week. Last week, Ms. Murray used 72 bottles of chocolate syrup. She used 8 times as many bottles of chocolate syrup as bottles of caramel syrup.
ASAP
Which of the following isn't true? A. The median can be the same value as the IQR. B. The median can be different from all of the data values. C. The median can be less than the lower quartile. D. The median can be the same value as the mean.
The statement that isn't true is:
B. The median can be different from all of the data values.
The median of the data:The median of a set of data is the middle value when the data is arranged in order from smallest to largest.
Let's check the given options
A. The median can be the same value as the IQR.
This statement is true, as the IQR is defined as the difference between the third quartile (Q3) and the first quartile (Q1), which are both data values that can include the median.
C. The median can be less than the lower quartile.
This statement is true, as the median is simply the middle value of the dataset when it is arranged in order, whereas the lower quartile (Q1) is the value that separates the bottom 25% of the data from the top 75%.
D. The median can be the same value as the mean.
This statement is true in a symmetric distribution, where the mean and median are equal. However, in skewed distributions, the mean and median can be different values.
B. The median can be different from all of the data values.
The median is a value that divides the dataset into two equal halves. It is always a data value, and it is not possible for the median to be different from all of the data values.
Therefore,
The statement that isn't true is:
B. The median can be different from all of the data values.
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if x is 4 y is 54 what's the constant of proportionality of y to x.
Over the past 10 years, the population of an island has decreased by 2% The population of an island 10 years ago was 24000. What is the population of the island now?
Answer:
23,520
Step-by-step explanation:
The population of an island has decreased by 2% when the population was 24000. What we want to do is find out how much of a population is each percentage. We want to divide 24,000 with 100 because 24,000 is 100% of the population 10 years ago.
24,000 ÷ 100 = 240
Now we know 1% of the population is 240, but we want to find out 2% of the population. Now we want to multiply by 2.
240 × 2 = 480
Now we know the population has decreased by 480 over the last 10 years, but we want to know the population of the island now. This is easy, all we got to do is take the original population and subtract how much the population it has decreased over 10 years.
24,000 - 480 = 23,520
The population of the island now is 23,520
Hope this helps : )
Answer:
23,520
Step-by-step explanation:
What is a percentage?A percentage is a ratio or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.
If the island had a population of 24,000 10 years ago, we could solve for the population decrease by using this expression:
24,000 × 0.02 = 480Why do we multiply by 0.02?Well, if percentages are fractions of 100, this means that 2% is equivalent to [tex]\frac{2}{100}[/tex], which is also equivalent to 0.02.
This means over the past 10 years the population decreased by 480.
Now that we know this, we can subtract that from the total amount to get the population now.
24,000 - 480 = 23,520This means that the population of the island now is 23,520.
Therefore, the population of the island now with a 2% decrease is 23,520.
points b and d are points of tangency find the value of x.
Answer:
x = 18.1
Step-by-step explanation:
1) 12x - 5 + 8x + 3 = 360
2) Subtract 5 from both sides
3) Add 2 on both sides
4) Divide both sides
5) x = 18.1
HURRY UP Please answer this question
In response to the supplied query, we may state that 759 is the value decimal entered into the green box.
what is decimal?Both integer and non-integer values are frequently stated in decimal form. Non-integer values are now part of the enlarged Hindu-Arabic numeral system. The process of representing numbers in the decimal system is referred to as decimal notation. A decimal is a number that consists of both a whole and a fractional part. Whole and partially entire quantities are expressed numerically using decimal numbers, which fall between integers. A decimal number's whole number and its fractional component are separated by a decimal point. The decimal point is the dot that separates the full number from the fractions. For instance, 25.5 is a decimal number.
We may leverage the fact that 0.83 is a decimal representation of a rational number with a finite decimal portion to express 0.83 as a fraction. We may say it this way:
0.83 = 83/100
[tex]8.39 = 8 + 0.39\s= 8 + 39/100\s= 8 + 39/(10^2)\s= 8 + F/(10) (10)[/tex]
Now that the decimal is gone from the right-hand side's numerator, we may multiply both sides by 10:
[tex]10 * 8.39 = 10 * (8 + F/10)\\839 = 80 + F\sF = 839 - 80 = 759[/tex]
So, 8.39 may be expressed as the following fraction:
8.39 = 8 + 0.39 = 8 + 39/100 = 8 + 759/1000
759 is the value entered into the green box.
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please help! i need help with this problem. i have the answer but i have no idea how to factor it
Answer:
(q²-p)(p²-q), 240
Step-by-step explanation:
Q1 p²q²+pq-q³-p³=(p²q²-q³)+(pq-p³)
=q²(p²-q)-(p³-pq)
=q²(p²-q)-p(p²-q)
=(q²-p)(p²-q)
Q2 If p=4 and q=-4
(4)²(-4)²+(4) x(-4)-(-4)³-4³=256-16+64-64=240
Answer:
please mark as brainliest
Jenny has a job transporting soft drinks by truck. Her truck is filled with cans that weigh 14 ounces each and bottles that weigh 70 ounces each. There is a
combined total of 900 cans and bottles in her truck.
Let x be the number of 14-ounce cans in her truck. Write an expression for the combined total weight (in ounces) of the cans and bottles in her truck.
Therefore , the solution of the given problem of expressions comes out to be 14x + 70(900 - x) .
Expression : What is it?Estimates that combine joining, deactivating, but instead random divide should be produced with shifting variables. If they banded together, they could do the following: a mathematical conundrum, some data, and software. A statement of truth contains formulas, components, and arithmetic procedures like adding, subtractions, omissions, and groupings. It is possible to assess and analyse both words and sentences.
Here,
Assume that her vehicle contains x 14-ounce cans.
900 - x = the amount of bottles in her truck (since the total number of cans and bottles is 900.
The cans in her truck carry a total of 14 ounces.
Similar to that, her truck's entire bottle weight is
=> 70(900 - x) ounces.
As a result, the cans and bottles in her truck's entire combined weight (in ounces) can be expressed as follows:
=> 14x + 70(900 - x)
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A mural is to be painted on a wall that is 15m long by 12m high. A border of uniform
width is to surround the mural. If the mural is to cover 75% of the area of the wall,
how wide must the border be, to the nearest hundredth of a metre?
Will mark are brainliest
Answer:
1.89m
Step-by-step explanation:
The area of the wall is given by:
Area = length x height
Area = 15m x 12m
Area = 180m²
Since the mural is to cover 75% of the area of the wall, the area of the mural is:
Mural area = 75% x Area
Mural area = 0.75 x 180m²
Mural area = 135m²
Let x be the width of the border. Then the dimensions of the mural (including the border) will be:
Length = 15m + 2x
Height = 12m + 2x
The area of the mural (including the border) will be:
Mural area = Length x Height
Mural area = (15m + 2x) x (12m + 2x)
Mural area = 180m² + 54x + 4x²
Since the area of the mural is given by 135m², we can write:
180m² + 54x + 4x² = 135m²
Simplifying and rearranging, we get:
4x² + 54x + 45m² = 0
Solving for x using the quadratic formula, we get:
x = (-54 ± sqrt(54² - 4(4)(45))) / (2(4))
x = (-54 ± sqrt(1536)) / 8
x = (-54 ± 39.12) / 8
We take the positive value for x, since it represents the width of the border:
x = (-54 + 39.12) / 8
x = 1.89m (rounded to the nearest hundredth)
Therefore, the width of the border should be approximately 1.89 metres.
if 2^x+3 , find x..
Step-by-step explanation:
write true if the statement is correct if not write False
(Finding Area Using Triangles and Rectangles MC)
A composite figure is represented in the image.
What is the total area of the figure?
272.64 yd2
231.68 yd2
190.72 yd2
136.32 yd2
The total area of the given composite figure found using the areas of right triangles and rectangle is 231.68sq. yards.
What is a composite figure?
Composite geometric figures are made from two or more geometric figures. Finding the area of a composite shape can be done using one of two broad approaches.
The total of the individual areas will represent the composite shape's area.Determine the areas of the parts of the larger form that aren't part of the composite shape that are larger than the composite shape. The composite shape's area will be calculated as the difference between the larger shape's area and the areas of the larger shape's excluded portions.The given composite figure consists of two right triangles and a rectangle.
The area of the figure is the sum of the areas of the right triangles and the rectangle.
Both the right triangle are the same.
So the area of one triangle = 0.5 * base * height = 0.5 * 6.4 * 12.8
= 40.96 sq. yards
So the total area of both triangles = 2 * 40.96 = 81.92 sq. yards.
Now the area of the rectangle = length * breadth = 14.9 * 12.8
= 190.72 sq. yards
The total area of the figure = 190.72+40.96 = 231.68 sq. yards.
Therefore the total area of the given composite figure found using the areas of right triangles and rectangle is 231.68sq. yards.
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fsA glass contains 320 cm³ of milk. The mass of the milk is 330 g. Calculate the density of the milk in kilograms per cubic metre (kg/m³). Give your answer to the nearest integer.
Answer:
242 cm
Step-by-step explanation:
20x12x0.2=242
In Case Study 19. 1, we learned that about 56% of American adults actually voted in the presidential election of 1992, whereas about 61% of a random sample claimed that they had voted. The size of the sample was not specified, but suppose it were based on 1600 American adults, a common size for such studies.
a. Into what interval of values should the sample proportion fall 68%, 95%, and almost all of the time?b. Is the observed value of 61% reasonable, based on your answer to part a?c. Now suppose the sample had been of only 400 people. Compute a standardized score to correspond to
The sample proportion should fall between 56.8% and 65.2% of the time for 68% confidence, between 54.6% and 67.4% of the time for 95% confidence, and between 53.4% and 68.6% of the time for almost all of the time.
a. 68%: The sample proportion should fall between 56.8% and 65.2% of the time.
95%: The sample proportion should fall between 54.6% and 67.4% of the time.
Almost all of the time: The sample proportion should fall between 53.4% and 68.6% of the time.
b. Yes, the observed value of 61% is reasonable, based on the answer to part a.
c. For a sample of 400 people, the standardized score corresponding to the 61% response would be 0.5, which would not be considered extreme.
The sample proportion should fall between 56.8% and 65.2% of the time for 68% confidence, between 54.6% and 67.4% of the time for 95% confidence, and between 53.4% and 68.6% of the time for almost all of the time. For a sample of 400 people, the standardized score corresponding to the 61% response would be 0.5, which would not be considered extreme.
The complete question is :
In Case Study 19. 1, we learned that about 56% of American adults actually voted in the presidential election of 1992, whereas about 61% of a random sample claimed that they had voted. The size of the sample was not specified, but suppose it were based on 1600 American adults, a common size for such studies.
a. Into what interval of values should the sample proportion fall 68%, 95%, and almost all of the time?
b. Is the observed value of 61% reasonable, based on your answer to part a?
c. Now suppose the sample had been of only 400 people. Compute a standardized score to correspond to the 61% response and determine if this would be considered extreme.
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A bullet is shot from a rifle with a speed of 3 mi./s it takes 3290 seconds to reach its target how far away is the target
Answer:
We can use the formula distance = speed x time to find the distance traveled by the bullet.
distance = speed x time
distance = 3 mi/s x 3290 s
distance = 9870 miles
Therefore, the target is 9870 miles away.
Step-by-step explanation:
The ratio of x to y is 5 to 6 , and the ratio of z to y is 7 to 3. What is the ratio of x to z ?
The ratio of x to z is equal to 15 : 42.
What is a ratio?In Mathematics, a ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
Based on the information provided above, we have the following ratio parameters:
x : y = 5 : 6 ⇒ x/y = 5/6
z : y = 7 : 3 ⇒ z/y = 7/3
Therefore, we can logically deduce the following:
x/z = x/z × y/y
x/z = x/y × y/z
x/z = 5/6 × 3/7
x : z = 15 : 42
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Below is an Iranian cylindrical drum. The circular drum heads on each end are made of leather and the drum body is usually made of wood.
Part A: What is the amount of leather needed to create both drum heads?
Part B: What is the total area of the wood used to make the body of the drum? Use 3.14 for pi and round to the nearest hundredth.
PLEASE HELP ME
Part a: The amount of leather needed to create both drum heads is 2769.48 cm².
Part b: Total surface area of Iranian cylindrical drum: 4022.34 cm².
Explain about the cylinder?A cylinder is just a 3D solid shape made up of two bases that are parallel and identical and are connected by a curved surface.
Their bases resemble spherical disks. The axis of a cylinder shape is a line drawn through the center or connecting the centers of shaped bases.Part a: The amount of leather needed to create both drum heads.
Amount of leather = 2 * area of circle
Amount of leather = 2 * πr²
Amount of leather = 2 * 3.14 * 21²
Amount of leather = 2769.48 cm².
Thus, the amount of leather needed to create both drum heads is 2769.48 cm².
Part b: Total surface area of Iranian cylindrical drum:
TSA = 2πr(h + r)
TSA = 2*3.14*21*(21 + 9.5)
TSA =
Thus, the total area of wood used to make the body of the drum 4022.34 cm².
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Someone pls help me asap
When does a company's break-even point occur?
A company's break-even point is the level of sales or revenue that the company needs to generate in order to cover all of its expenses and to neither make a profit nor incur a loss.
What is company's break-even point?The amount of sales or revenue that a business must achieve in order to pay all of its costs while not turning a profit or suffering a loss is known as the break-even point. The company's total income and entire costs are equal at the break-even point.
In other words, the firm reaches its break-even point when its entire income matches the sum of its total variable expenses and total fixed costs. Raw materials, labor, and commissions are examples of expenses known as variable costs that fluctuate in response to variations in the volume of production or sales. Rent, salary, and insurance are examples of fixed expenditures that don't fluctuate while output or sales alter.
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2
Find the area of the semicircle.
Either enter an exact answer in terms of π or
use 3.14 for π and enter your answer as a
decimal.
units²
Answer:
The unit is unit square or we can also find a by replacing pi by 3.1. 4 point so this equals 2 times of 3.14 and this equals 6.28. This is a unit square, and so the exact area of semicircle is 2 pi unit square or in terms of decimals. It is 6.28 unit square.
Answer:
6.28
Step-by-step explanation:
The number of points jaden scored in a game is less than 45,and is also a multiple of 7.How many points could Jaden have scored?
Answer:
42
Step-by-step explanation:
7 x 6 = 42, making 42 a multiple of seven and less than 45.
The radius r in millimeters of a platinum with L centimeters long with resistance 0.1 ohm is r equals 0.059L^1/2. How long is a wire with radius 0.236 millimeters?
rational exponents!
The length of the wire with a radius of 0.236 millimeters is 16.5 cm.
What is the length of the wire?We are given the formula for the radius of a platinum wire in terms of its length L and resistance R:
[tex]r = 0.059L^{(1/2) } \ mm[/tex]
We are also told that the resistance of the wire is 0.1 ohm.
We can use the formula for the resistance of a wire in terms of its length L, cross-sectional area A, and resistivity rho:
R = ρL/A
where;
ρ is the resistivity of platinum, which is 10.6 x 10⁻⁸ ohm-meter.We can rearrange this formula to solve for the cross-sectional area:
A = ρL/R
Substituting the given values, we have:
A = (10.6 x 10⁻⁸ ohm. m)(L m)/(0.1 ohm)
A = 1.06 x 10⁻⁶ m L
We can also use the formula for the area of a circle in terms of its radius:
A = πr²
Solving for the radius, we have:
r = √(A/π)
Substituting the expression for A, we have:
r = √[(1.06 x 10⁻⁶ m.L )/π]
Substituting the given radius of 0.236 mm, we can solve for the length L:
0.236 x 10⁻³ m = √[(1.06 x 10⁻⁶ m.L)/π]
Squaring both sides, we have:
(0.236 x 10⁻³ m)² = (1.06 x 10⁻⁶ m.L)/π
Solving for L, we have:
L = [(0.236 x 10⁻³ m)² π]/(1.06 x 10⁻⁶ m)
L = 0.165 m = 16.5 cm
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questions are in the images below :)
a. The balances in the accounts after 5 and 20 years is $12,164.77.
b. The percentage of the balance that is interest is 70%.
c. We need to deposit $17,426.93 today to have $25,000 in 8 years in an account with annual compounding and an APR of 5%.
What is Principal?Principal refers to initial amount of money invested or borrowed. It is starting point for calculating interest or return on investment, or amount owed on loan.
96)
a) To compute the balances in the accounts after 5 and 20 years, we can use the formula for compound interest:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
where A is the ending balance, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
For Paula's account:
After 5 years:
A = 4000(1 + 0.048/365[tex])^{(3655)[/tex] = $5,478.71
After 20 years:
A = 4000(1 + 0.048/365[tex])^{(36520)[/tex] = $9,847.15
For Petra's account:
After 5 years:
A = 3600(1 + 0.056/365[tex])^{(3655)[/tex] = $5,029.80
After 20 years:
A = 3600(1 + 0.056/365[tex])^{(36520)[/tex] = $12,164.77
b) To determine the percentage of the balance that is interest, we can subtract the principal from the ending balance, and then divide by the ending balance:
For Paula's account:
After 5 years:
Interest = $5,478.71 - $4,000 = $1,478.71
Percentage of balance that is interest = (Interest / $5,478.71) * 100% = 27%
After 20 years:
Interest = $9,847.15 - $4,000 = $5,847.15
Percentage of balance that is interest = (Interest / $9,847.15) * 100% = 59%
For Petra's account:
After 5 years:
Interest = $5,029.80 - $3,600 = $1,429.80
Percentage of balance that is interest = (Interest / $5,029.80) * 100% = 28%
After 20 years:
Interest = $12,164.77 - $3,600 = $8,564.77
Percentage of balance that is interest = (Interest / $12,164.77) * 100% = 70%
c) The effect of interest rates and patience can be observed in the significant differences between the ending balances and percentage of interest earned by Paula and Petra. Petra's account had a higher interest rate, resulting in a larger ending balance and a higher percentage of interest earned. Additionally, the longer the investment period, the more the interest compounds and the greater the ending balance becomes. Therefore, patience is key in allowing the investment to grow over time.
81) An account with annual compounding and an APR of 5%
P = 25,000 / (1 + 0.05/[tex]1)^{(1\cdot 8)[/tex] = $17,426.93
Therefore, we need to deposit $17,426.93 today to have $25,000 in 8 years in an account with annual compounding and an APR of 5%.
82) An account with quarterly compounding and an APR of 4.5%
P = 25,000 / (1 + 0.045/4[tex])^{(4 \cdot 8)[/tex] = $17,721.15
Therefore, we need to deposit $17,721.15 today to have $25,000 in 8 years in an account with quarterly compounding and an APR of 4.5%.
87) An APR of 2.8%, compounded quarterly
First, we need to convert the annual interest rate to a quarterly interest rate by dividing it by 4:
r = 0.028/4 = 0.007
Then, we can use the formula:
P = 120,000 / (1 + 0.007[tex])^{(4\cdot 15)[/tex] = $70,055.47
Therefore, we need to deposit $70,055.47 today in an account with an APR of 2.8%, compounded quarterly, to have a $120,000 college fund in 15 years.
89) We can use the formula for compound interest to calculate the balance in the accounts after 10 and 30 years:
Balance for Chang: B = [tex]P(1 + r)^t[/tex]
where P = 500, r = 0.035, and t = 10 or 30 years.
Balance for Kio: B = [tex]P(1 + r)^t[/tex]
where P = 500, r = 0.0375, and t = 10 or 30 years.
After 10 years:
Chang's balance: B = [tex]500 (1 + 0.035)^{10[/tex] = $743.22
Kio's balance: B = 500*(1 + 0.0375)^10 = $779.58
After 30 years:
Chang's balance: B = [tex]500 (1 + 0.035)^{30[/tex] = $1,373.63
Kio's balance: B = [tex]500(1 + 0.0375)^{30[/tex] = $1,441.39
As we can see, even though the difference in interest rates is small (0.035 vs 0.0375), it can have a significant impact on the final balance of the account over a long period of time. In this case, after 30 years, Kio's account balance is almost $70 higher than Chang's account balance, even though they both invested the same amount of money.
91) The formula for calculating the annual percentage yield (APY) is:
APY = [tex](1 + r/n)^n - 1[/tex]
where r is the annual interest rate (in decimal form) and n is the number of compounding periods per year.
For quarterly compounding:
n = 4
APY = (1 + 0.066/4)⁴ - 1 = 0.0677 or 6.77%
For monthly compounding:
n = 12
APY = (1 + 0.066/12)¹² - 1 = 0.0681 or 6.81%
For daily compounding:
n = 365
APY = (1 + 0.066/365[tex])^{365[/tex] - 1 = 0.0682 or 6.82%
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Anna wants to add a $15,280 sunroom to her house.Her bank requires 20% down before lending her any money. What is her down payment and what amount did she finance?
The down payment and the amount financed are given as follows:
Down payment: $3,056.Amount financed: $12,224.How to obtain the down payment and the amount finances?The down payment and the amount financed are obtained applying the proportions in the context of the problem.
Anna wants to add a $15,280 sunroom to her house. Her bank requires 20% down before lending her any money, hence the down payment is given as follows:
0.2 x 15280 = $3,056.
The amount financed is the part of the price that is not part of the down payment, hence it is given as follows:
15280 - 3056 = $12,224.
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NO EXPLANATION JUST ANSWER!
Answer:486
Step-by-step explanation:
V=a*a*a=729
a=9
S=6a*a=6*81=486
Answer:
486
hope this helps