Amelia uses 99 balls of yarn in all to make the sweaters and scarves.
What is addition ?
Addition is a basic mathematical operation that combines two or more quantities to find a total or a sum. It is denoted by the symbol "+" and is usually taught in elementary school. In addition, the order of the numbers does not matter, meaning that you can add them in any order and still get the same result. For example, 3 + 5 is the same as 5 + 3, and the answer is 8 in both cases.
According to the question:
To find the total number of balls of yarn that Amelia uses, we can start by finding the total number of balls of yarn she uses to make the sweaters and scarves separately, and then add those amounts together.
To make 7 sweaters, Amelia uses 7 x 9 = 63 balls of yarn.
To make 9 scarves, Amelia uses 9 x 4 = 36 balls of yarn.
Adding these together, we get:
63 + 36 = 99
So, Amelia uses 99 balls of yarn in all to make the sweaters and scarves.
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Which of the following is true regarding cross-sectional data sets? Check all that apply. The data consist of a sample of multiple individuals. It can be assumed that the data were obtained through a random sampling of the underlying population. These data require attention to the frequency at which they are collected (weekly, monthly, yearly, etc.). The data are collected at approximately the same point in time.
The correct options are:
The data contain a sample of multiple individuals.
The data are collected are approximately at the same point in time.
Cross-sectional data sets are a type of research design used in statistical analysis. They consist of a sample of multiple individuals or entities observed at a single point in time. One of the characteristics of cross-sectional data sets is that they do not involve any observation or measurement over time, making them different from longitudinal or time-series data sets.
One advantage of cross-sectional data sets is that they are relatively easy and inexpensive to collect. It can be assumed that the data were obtained through a random sampling of the underlying population, making them representative of the larger population. However, these data require attention to the frequency at which they are collected (weekly, monthly, yearly, etc.), as the timing of data collection can impact the results.
Overall, cross-sectional data sets can provide a snapshot of a population or phenomenon at a specific point in time, making them useful for a wide range of research questions in social, economic, and political sciences.
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Question 1 of 20
What is the solution to the following inequality?
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading greater than -1.12°C.
The probability of getting a measurement above -1.12°C is 0.8686, or almost 87%.
The probability formula is what?Typically, the probability is defined as the ratio of favorable events to all other outcomes in the sample space.Probability of an event P(E) = (Number of favorable outcomes) is how it is stated (Sample space).
We must determine the area under the normal distribution curve to the right of -1.12°C in order to determine the likelihood of getting a reading higher than that value.
We may convert the value of -1.12°C to a z-score, which represents the amount of standard deviations from the mean, using a calculator or a typical normal distribution table:
z = (x - μ) / σ
z = (-1.12 - 0) / 1.00
z = -1.12
The area under the normal distribution curve to the right of a particular z-score can also be found using a calculator. For instance, we can type the following into a calculator that has a normal distribution function:
P(Z > -1.12)
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Julian Nestor is ready to purchase a new stroller. It is regularly priced at $127.99. The sale price is $88.54. What is the markdown?
Answer:
$39.45, about 31%
Step-by-step explanation:
You want to know the markdown represented by a sale price of $88.54 on a regular price of $127.99.
MarkdownThe dollar amount of the markdown is ...
88.54 -127.99 = -39.45
The price was marked down $39.45.
The percentage markdown from the original price is ...
-39.45/127.99 × 100% ≈ -30.823% ≈ -31%
The original price was marked down about 31% to get the sale price.
__
Additional comment
The negative price change means the price was marked down. If the change were positive, it would signify a markup.
PLEASE HELP 30 POINTSSS !
Answer:
The required length is 10 feet
Step-by-step explanation:
Let the required length be l
From pythogras theorem;
[tex]{ \tt{l {}^{2} = {6}^{2} + {8}^{2} }} \\ { \tt{ {l}^{2} = 36 + 64}} \\ { \tt{ {l}^{2} = 100 }} \: \: \: \: \: \: \: \: \\ { \tt{ \sqrt{ {l}^{2} } = \sqrt{100} }} \\ { \tt{l = 10 \: feet}}[/tex]
(b) do these data appear to follow a normal distribution? explain your reasoning using the graphs provided below.
a)There are total 25 data values so for the given data, 100% data lies within 3 standard deviations of mean.
b). Second graph demonstrates that there is strong linear relationship between the theoretical and sample quantities
a) Here we have μ=61.52 and [tex]\sigma=4.58[/tex]
The 68-95-99.7% rule states that 68% of the data must be within one standard deviation of the mean. Thus, 68% of the data should fall between 61.52-4.58=56.94 and 61.52+4.58=66.1. 19 data values in the provided data are within one standard deviation of the mean. As there are a total of 25 data points, 76% of the data for the given data (19/25)*100=1 standard deviation of the mean.
The 68-95-99.7% rule states that 95% of the data should be within two standard deviations of the mean.
Specifically, 95% of the data should fall between 61.52+2*4.58=70.68 and 61.52-2*4.58=52.36. 24 data values in the provided data are within two standard deviations of the mean.
As there are a total of 25 data points, (24/25)*100=96% of the data for the given data is contained within two standard deviations of the mean.
The 68-95-99.7% rule states that 99.7% of the data should be within three standard deviations of the mean.
It follows that 99.7% of the data should fall between 61.52+3*4.58=75.26 and 61.52-3*4.58=47.78. 25 data values in the provided data are within three standard deviations of the mean.
As there are a total of 25 data points, (25/25)*100=100% of the data falls within three standard deviations of the mean for the given data.
Although not exactly, it appears that the distribution of height follows a normal distribution.
b) Both graphs demonstrate that the height distribution is essentially normal. Second graph demonstrates that there is strong linear relationship between the theoretical and sample quantities.
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The complete question is:
Heights of female college students. Below are heights of 25 female college students.
(a) The mean height is 61.52 inches with a standard deviation of 4.58 inches. Use this information to determine if the heights approximately follow the 68-95-99.7% Rule.
(b) Do these data appear to follow a normal distribution? Explain your reasoning using the graphs provided below.
When you calculate (In) 7, you would be finding the
value of which of the following expressions?
O log10 7
O log, 10
O log, e
O log 7
Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.
what is logarithm?In mathematics, the logarithm is the reciprocal of a power. As a result, the exponent by which b must be raised to achieve a number x matches its logarithm in base b. For example, because 1000 = 103, the base-10 logarithm is 3, or log10 = 3. For example, the base 10 logarithm of 10 is 2, but the square of 10 is 100. Log 100 = 2. A logarithm (or log) is the mathematical word used to answer questions such as how many times a base of 10 must be multiplied by itself to get 1,000. The answer is 3 (1,000 = 10 10 10).
When you compute (In), you are calculating the natural logarithm of 7, which is indicated as ln(7) or loge (7).
As a result, the expression you'd be looking up the value of is: ln(7) or loge (7).
Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.
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Replace the loading system by an equivalent resultant force and couple moment acting at point o. Assume F1 = {-300i + 170j + 190k}N (Figure 1) Part A Determine the resultant force. Enter the 2, y and a components of the resultant force separated by commas. A vec O ? FR = Submit Request Answer Part B Determine the couple moment acting at point 0. Enter the x, y and 2 components of the couple moment separated by commas. Figure O AQ O vec O ? < 1 of 1 > (Mon= N.mn Submit Request Answer 1 m OS Provide Feedback F = (-450k) N
The resultant force is equal to F1, which is {-300i + 170j + 190k}N, and the couple moment acting at point 0 is (-0.19i - 0.34j + 0.15k) N.m.
To determine the resultant force acting at point O, we can add all the forces acting at point O. In this case, we have only one force F1 = {-300i + 170j + 190k}N. Therefore, the resultant force acting at point O is F1 itself.
To determine the couple moment acting at point O, we can use the formula:
M = r x F
where r is the position vector from point O to any point on the line of action of force F.
Since we don’t know the position vector r, we can choose any arbitrary point on the line of action of force F. Let’s say we choose point A which lies on the line of action of force F and is perpendicular to it.
Therefore, r = OA where OA is the position vector from point O to point A. We can find OA by subtracting position vectors of points O and A i.e., OA = A - O.
Now, let’s calculate M using M = r x F.
M = (OA) x F1
M = (A - O) x {-300i + 170j + 190k}N M
= (-0.19i - 0.34j + 0.15k) N.m
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Complete question is:
Replace the loading system by an equivalent resultant force and couple moment acting at point o. Assume F1 = {-300i + 170j + 190k}N
Part A Determine the resultant force. Enter the 2, y and a components of the resultant force separated by commas.
Part B Determine the couple moment acting at point 0. Enter the x, y and 2 components of the couple moment separated by commas.
3 minutes 4 seconds − 1 minute 16 seconds = minutes seconds
the result of the subtraction is 2 minutes 48 seconds
Convert minutes into seconds
To convert minutes into seconds, you can multiply the number of minutes by 60, since there are 60 seconds in a minute. For example, if you want to convert 1 minutes into seconds, you would do:
1 minutes ×60 seconds/minute = 60 seconds
Therefore, 5 minutes is equal to 300 seconds.
Solving the problem:3 minutes 4 seconds - 1 minute 16 seconds
We can start by subtracting the seconds:
3 minutes - 1 minute = 2 minutes
And add the borrowed 60 seconds to the seconds place:
-12 seconds + 60 seconds = 48 seconds
Therefore, the result of the subtraction is 2 minutes 48 seconds
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A worker earning an hourly wage changes positions within a company. The new position comes with a 20% raise in hourly wage. The
worker also receives a $2 increase in hourly wage. Use composition of functions to write a function that represents the worker's new
hourly wage when the 20% raise is applied before the $2 raise.
f(x) =
This function gives the same result as the previous function we derived, but it expresses the calculation as a composition of the two separate functions that represent each raise separately.
What is function?A function is a set of instructions or statements that perform a specific task or computation and returns a value or result. In programming, a function is typically defined using a specific syntax and can be called or invoked by other parts of the program to carry out a particular operation.
Functions are used in programming to break down complex tasks into smaller, more manageable pieces of code, which can then be reused in multiple parts of the program. They can also help to improve the organization, readability, and maintainability of code.
by the question.
let the worker's original hourly wage be represented by the variable x. Then the function for the worker's new hourly wage when the 20% raise is applied before the $2 raise can be expressed as follows:
[tex]f(x) = (1.20x) + 2[/tex]
In this function, the expression (1.20x) represents the worker's hourly wage after the 20% raise is applied, and the additional $2 raise is added to this amount to determine the final hourly wage.
We can also express this function using function composition notation. Let g(x) represent the function that applies the 20% raise to the worker's hourly wage and let h(x) represent the function that adds the $2 raise to the resulting hourly wage. Then we have:
[tex]g(x) = 1.20x[/tex]
[tex]h(x) = x + 2[/tex]
Using function composition, we can write the function for the worker's new hourly wage as:
[tex]f(x) = h(g(x)) = h(1.20x) = 1.20x + 2[/tex]
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Help please! I have no idea!!!!
The values of the function from the graph are h(7) = 10, h(0) = 9, h(t) = 8, t = 5 and h(t) = 0, t = 4
How to determine the value of the functionGiven that the graph is the graph of height as a function of time
To calculate the values of h(t) from the graph of g(x), we need to follow these steps
Identify the value of t on the x-axis where you want to calculate the value of h(t)Locate that point on the graphWrite the values from the pointUsing the above, we have the following
h(7) = 10
h(0) = 9
h(t) = 8, t = 5
h(t) = 0, t = 4
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Pls solve #5 will give brainliest for right answer
Answer: 200 texts
Step-by-step explanation:
If they paid the same amount, we can set the equations equal to each other and solve for x using inverse operations.
Given:
0.1x + 10 = 0.15x
Subtract 10 and 0.15x from both sides of the equation:
-0.05x = -10
Divide both sides of the equation by -0.05:
x = 200
find the center and radius of the circle whose equation is x^2+y^2+4x+12y =-15
Answer:
center: (-2,-6)
radius: 5
Step-by-step explanation:
You have to complete the square again. This time the x's and the y's both need work. So first, organize. Put the x's together and put the y's together. Leave a little room to work. Take the x term and the y term and CUT them in HALF and Square 'em. That is what you add in to complete the square. Add the same thing to both sides.
see image.
in a popular shopping Centre waiting time for an ABC bank ATM machine is found to be uniformly distributed between 1 and 5 minutes what is the probability of waiting between 2 and 4 minutes to use the ATM
so here we get two outcomes one is 2 and other is 4.
so there is total 2 outcomes.
total no. of possibility is 5
so the probability of waiting between 2 and 4 minutes to use the ATM is 2/5.
Give a reason for your answer to the following question. Assume that all variables represent integers.
If n = 4k + 3, does 8 divide n2 − 1?
Yes, 8 divides n^2 - 1 when n = 4k + 3.
We are given that n = 4k + 3, where k is an integer. We want to determine if 8 divides n^2 - 1, which means we want to know if there exists an integer m such that n^2 - 1 = 8m.
To start, we can rewrite n^2 - 1 as (n + 1)(n - 1). This is a common trick in number theory problems involving divisibility, and it can often help us factorize expressions in a useful way.
Substituting n = 4k + 3, we get:
(n + 1)(n - 1) = (4k + 3 + 1)(4k + 3 - 1) = (4k + 4)(4k + 2)
Now, we want to determine whether 8 divides this expression. In other words, we want to know if there exists an integer m such that:
(4k + 4)(4k + 2) = 8m
We can simplify the left-hand side of this equation by factoring out 4
4(k + 1)(2k + 1) = 8m
Now, we see that 8 divides the left-hand side of the equation, since it is equal to 4 times an even number. Moreover, (k + 1) and (2k + 1) are both integers, so we can conclude that 8 divides n^2 - 1 when n = 4k + 3.
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Jonathan and Amber went to the store together to buy school supplies.
Jonathan purchased 2 notebooks and 5 elastic book covers for $6.75. Amber
purchased 4 notebooks and 2 elastic book covers for $7.50. What is the price
of a single notebook?
P
The price of a single notebook is $
Answer:
The answer is 1.5$
Step-by-step explanation:
Let the price of 1 notebook be x$ and 1 elastic book cover be y$
In first case,
2x+5y=$6.75
2x = $6.75-5y
x=($6.75-5y)/2------------- eqn i
In second case,
4x+2y=$7.50
4×($6.75-5y)/2 +2y=$7.50 [From eqn i]
($27-20y)/2 +2y=$7.50
($27-20y+4y)/2=$7.50
($27-16y)/2=$7.50
$27-16y=$7.50×2
$27-16y=$15
$27-$15=16y
$12=16y
y=$12/16
y=$0.75
The price of single elastic book cover is $0.75
Substituting the value of y in eqn i we get
x=($6.75-5y)/2
x=($6.75-5×$0.75)/2
x=($6.75-$3.75)/2
x=$3/2
x=$1.5
Hence, the price of single notebook is $1.5 Ans
Hey mate, please mark me as brainliest if you got the answer.
algebraically determine the values of x that satisfy the system of equations below
The solutions to the system of equations are (x,y) = (0,1) and (5/2,3)
What is Algebraic Equations?
An algebraic equation is also known as a polynomial equation because both sides of the equal sign contain polynomials. An algebraic equation is built up of variables, coefficients, constants as well as algebraic operations such as addition, subtraction, multiplication, division, exponentiation, etc.
To solve the system of equations algebraically, we can set the two expressions for y equal to each other and solve for x:
[tex]-2x + 1 = -2x^2 + 3x + 1[/tex]
Simplifying, we get:
[tex]-2x^2 + 3x + 1 + 2x - 1 = 0[/tex]
[tex]-2x^2 + 5x = 0[/tex]
Factorizing x, we get:
x(-2x + 5) = 0
Therefore, the solutions for x are:
x = 0 or x = 5/2
To find the corresponding values of y, we can substitute these values of x into either of the original equations for y:
For x = 0:
y = -2(0) + 1 = 1
For x = 5/2:
[tex]y = -2(5/2)^2 + 3(5/2) + 1 = -13/2 + 15/2 + 1 = 3[/tex]
Therefore, the solutions to the system of equations are:
(x,y) = (0,1) and (5/2,3)
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Can someone please help with these 4
Answer:
Step-by-step explanation:
1) b (acute is less than 90)
2) a (obtuse: more than 90, less than 180)
3) c
4) c
Answer:
1. NOM, JOK, KOL
2. MOL, NOK, MOJ
3. NOJ, JOL
4. NOL, MOK
1. Investigations have revealed that 60% of the road accident deaths occurred on highways
and 40% on rural roads. If out of a sample 100 accidents investigated, the number of accidents
on highways was 80 and rural roads 20. Determine the number of accidents on highways and
rural roads after 4 years.
Answer: To determine the number of accidents on highways and rural roads after 4 years, we need more information. The given data only tells us about the distribution of accidents in a sample of 100 accidents investigated, but it doesn't provide any information about the rate of change or trend of accidents over time.
Assuming that the rate of accidents on highways and rural roads remains the same, we can make a projection based on the given data. If 60% of the road accident deaths occur on highways and 40% on rural roads, we can estimate the number of accidents on highways and rural roads after 4 years as follows:
Number of accidents on highways after 4 years = 80 * (100/60) = 133.33 (rounded to 133)
Number of accidents on rural roads after 4 years = 20 * (100/40) = 50
Note that this is only a projection based on the assumption that the rate of accidents remains the same. In reality, the number of accidents can vary depending on various factors such as changes in traffic volume, weather conditions, road infrastructure, and driver behavior, among others. Therefore, this projection should be taken as an estimate and not as an accurate prediction.
Step-by-step explanation:
What is the slope of the line in the following graph?
Answer:
A. Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
A rectangular fish tank 60 cm x 15 cm x 34 cm is 13 full of water. Find the volume of water needed to fill the tank completely.
Step-by-step explanation:
The volume of the rectangular fish tank is:
V = l x w x h = 60 cm x 15 cm x 34 cm = 30,600 cm³
Since the tank is 1/3 full, the volume of water in the tank is:
V_water = (1/3) x V = (1/3) x 30,600 cm³ = 10,200 cm³
To find the volume of water needed to fill the tank completely, we can subtract the volume of water already in the tank from the total volume of the tank:
V_needed = V - V_water = 30,600 cm³ - 10,200 cm³ = 20,400 cm³
Therefore, 20,400 cm³ of water is needed to fill the tank completely.
My cookbook's pancake recipe states that it makes 12 standard sized pancakes. The nutritional information says 2 pancakes is a serving containing 150 calories. For breakfast, I prepared half a recipe, but made smaller sized pancakes, so ended up preparing 8 pancakes. I ate 4 of them. How many calories did I consume?
Answer:
225 calories
Step-by-step explanation:
1 recipe makes
12 standard sized pancakes
2 pancakes are 1/6 of the recipe
1/6 of the recipe has 150 calories
6 × 150 calories = 900 calories
The full recipe of 12 pancakes has 900 calories
1/2 recipe was made
1/2 recipe has 1/2 × 900 calories = 450 calories
1/2 recipe made 8 pancakes
4 pancakes are half of the half recipe or 1/4 recipe
1/4 × 900 calories = 225 calories
Use the slope and y-intercept to identify the equation of this line.
The equation of the line is y = -2x. The correct option is the last option y = -2x
Writing the equation of the line in the given graphFrom the question, we are to write the equation of the line in the given graph using the slope and y-intercept from the graph
First, we will determine the slope of the graph
The slope of the graph calculated from the formula
Slope = Change in y / Change in x
Slope = (y₂ - y₁) / (x₂ - x₁)
Picking the points (-1, 2) and (0, 0)
Slope = (0 - 2) / (0 - (-1))
Slope = -2/(0 + 1)
Slope = -2/1
Thus,
Slope = -2
From the graph, the y-intercept of the graph is 0
Then,
From the slope-intercept form of the equation of a line,
y = mx + c
Where m is the slope
and c is the y-intercepts
The equation of the line is
y = -2x + 0
y = -2x
Hence, the equation is y = -2x
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Determine whether the function is linear. If it is, identify the rate of change. X -7, -5, -3, -1, 0 Y 11, 14, 17, 20, 23
Answer: Yes;
Step-by-step explanation: The function is linear in that the X values are increasing by 2 and the Y values are increasing by 3.
Answer:
Not linear
Step-by-step explanation:
X | -7 | -5 | -3 | -1 | 0
Y | 11 | 14 | 17 | 20 | 23
-5 - (-7) = +2
14 - 11 = +3
-3 - (-5) = +2
17 - 14 = +3
-1 - (-3) = +2
20 - 17 = +3
0 - (-1) = +1
23 - 20 = +3
There is a linear function graphed that would pass through the first 4 points, but not the last one;
You can discern this as there is a common pattern we can identify, everytime the x-value increases by 2 the y-value increases by 3, except with the last coordinates;
The rate of change, also known as the gradient, is the change in x divided by the change in y (Δx/Δy);
In the case of the first 4 points, the rate of change would be 3/2 or 1.5;
This simply means when x increases by 1, y increases by 1.5, IF the function is linear;
However, as mentioned the last point doesn't fit the pattern;
There, we can see the y-value increases by 3 when the x-value only increases by 1;
This means the point (0, 23) isnt on the graph of the function, the points (0, 21.5) and (1, 23), on the other hand, would be.
Calculate the frequency in hertz of electromagnetic radiation that has a wavelength of 585.0 nm. (c = 3.00 X 10⁸ m/s)
The frequency in hertz of electromagnetic radiation which has a wavelength of 585nm is 5.13×10¹⁴ Hz.
The frequency(f) of electromagnetic radiation is related to its wavelength (λ) by the equation : f = c/λ;
Where, c = the speed of light in a vacuum, which is 3.00×10⁸ m/s.
So, to calculate the frequency of radiation with a wavelength of 585.0 nm, we need to convert the wavelength to meters:
⇒ 585.0 nm = 585.0×10⁻⁹ m;
Substituting the value in the above formula,
We get,
⇒ f = c/λ = 3.00×10⁸/(585.0×10⁻⁹)
⇒ 5.13×10¹⁴ Hz.
Therefore, the frequency of electromagnetic radiation is approximately 5.13 × 10¹⁴ Hz.
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so you need to select 6 varieties without replacement from 10 varieties: c(10,6) b) if there are at least two varieties.
The number of ways to select half dozen donuts from 10 varieties is 210 ways.
The total number of varieties of donuts is = 10 varieties;
we have to select half a dozen donuts, which means we have to select 6 varieties of donuts from the total of 10 varieties of donuts.
Using formula of Combination, we can compute the number of ways to choose a half dozen donuts from 10 varieties:
which is written as :
⇒ ¹⁰C₆ = 10! / (6!×4!) = (10×9×8×7)/(4×3×2×1) = 210,
Therefore, there are total of 210 ways in which half dozen donuts can be selected from 10 varieties, where no two donuts are of the same variety.
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The given question is incomplete, the complete question is
How many ways are there to choose a half dozen donuts from 10 varieties, If there are no two donuts of the same variety (means you need to select 6 varieties without replacement from 10)?
12. Nora and Sara both worked to make some money and earned a total of $95. If Sara earned $15
more than Nora, how much did they both earn? Step by Step Please!!
Answers:
Nora = $40
Sara = $55
=========================================================
Work Shown:
n = amount Nora earned
s = amount Sara earned
n+s = 95 .... total amount earned
s = n+15 .... since Sara earned $15 more than Nora
--------------
I'll use the substitution method to solve.
n+s = 95
n+n+15 = 95 ....... replaced "s" with n+15
2n+15 = 95
2n = 95-15
2n = 80
n = 80/2
n = 40 dollars is the amount Nora earned
s = n+15
s = 40+15
s = 55 dollars is the amount Sara earned
--------------
Check:
Nora+Sara = 40+55 = 95 dollars total earned
This confirms the answer. Also, we can see that Sara earned $15 more than Nora to help further confirm the answer.
What is the amount of interest to be paid if u got a reducing balance loan of $2700 and you will repay it over 5 years by quarterly installments of $1899.75 at interest rate 14% p.a. (compounded quarterly)
The total interest to be paid over the 5-year period is $403.22.
What is reducing balance loan?In a loan with a declining balance, interest is added to the outstanding balance at the start of each period, such as each month or each quarter. The outstanding balance, which decreases as the borrower makes repayments, is used to determine the interest rate. As a result, the borrower gradually pays less interest and more of each payment is used to lowering the main balance due. The lowering balance approach is frequently applied to mortgages, personal loans, and auto loans.
Given that, the quarterly installments are $1899.75.
For the entire year for a total of 5 years the total amount is:
Total amount = 4 * 5 * $1899.75 = $37995
For reducing balance loan the interest is calculated as:
For the first quarter, the interest to be paid is:
interest = (total amount - 0) * (0.14 / 4)
interest = (37995 - 0) * (0.14 / 4) = $94.50
Similarly for the remaining quarters we have:
Second quarter = $87.95
Third quarter: $81.05
Fourth quarter: $73.76
Fifth quarter: $65.96
The total interest to be paid over the 5-year period is:
$94.50 + $87.95 + $81.05 + $73.76 + $65.96 = $403.22
Hence, the total interest to be paid over the 5-year period is $403.22.
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Find two vectors v1 and v2 whose sum is (0, -1, -3), where v1 is parallel to (5, 0, -4) while v2 i perpendicular to (5, 0, -4).
v1 = ?
v2 = ?
Two vectors v₁ and v₂ whose sum are (0, -1, -3), where v₁ is parallel to
(5, 0, -4) while v₂ is perpendicular to (5, 0, -4).
v1 = [40/13, -8/13 ]
v2 = [-1/13, -5/13]
Parallel vectors will be multiples of each other.
Perpendicular vectors will have a dot product of 0.
Let v₁ = [a, b] and v₂ = [c, d]
v₁ || [-5,1] means v₁ = N [-5,1] = [a, b]
So a = -5N and b = N
v₂ • [-5,1] = 0 (because they are perpendicular)
So [c, d] • [-5,1] = -5c + d = 0 or d = 5c
⇒ v₁ + v₂ = [a, b] + [c, d] = [3, -1]
So a + c = 3 and b + d = -1
Now,
Substitute -5N for
a. Substitute N for b.
and Substitute 5c for d.
This gives us a system of equations with two equations and 2 unknowns:
-5N + c = 3
N + 5c = -1
Multiply everything in the bottom equation by 5
-5N + c = 3
5N + 25c = -5
Now add vertically, eliminating the variable N and finding
26c = -2
or, c = -1/13
Now we work our way backwards.
-5N + c = -5N + (-1/13) = 3
-5N = 40/13
(-1/5) (-5N) = (40/13)(-1/5)
and
N = -8/13 and b = N so b = -8/13
d = 5c so d = -5/13
a = -5N, so a = 40/13
So the two vectors are:
v₁ = [40/13, -8/13 ]
v₂ = [-1/13, -5/13]
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Suppose some computations were done on a calculator.
The result displayed was 7.97E33 for one computation.
The result displayed was 7.6E-37 for another computation.
Write these numbers in scientific notation.
(a) 7.97E33 =
(b) 7.6E-37 =
Answer:
(a) 7.97E33 = 7.97 x 10^33
(b) 7.6E-37 = 7.6 x 10^-37
Step-by-step explanation:
In scientific notation, a number is written as the product of a decimal number between 1 and 10 and a power of 10. The decimal number is called the mantissa, and the power of 10 is called the exponent. The mantissa indicates the significant digits of the number, while the exponent tells us the size of the number relative to 1. In the given calculator computations, the numbers are already written in scientific notation, where "E" represents the exponent notation. We just need to convert them into the standard form of scientific notation by expanding the notation as a product of the mantissa and the power of 10.