Answer:
i think 480 total calories
Step-by-step explanation:
i wish it's true
John 3 miles on Monday, 2 miles on Tuesday. He ran 4 more miles on Wednesday then he did on Monday. How many miles did John run Monday through Wednesday?
Answer: John ran 10 miles through Monday and Wednesday.
Step-by-step explanation: He ran for miles on 4 but 4 more than Monday and he ran 3 miles on Monday, so you add 4 + 3 which = 7 then you add 3 to 7 because he ran 3 miles on Monday then you get 10.
What is the equation of the line that passes through the point (-1,6) and has a y-intercept of -5
well, since the y-intercept is at -5, or namely when the line hits the y-axis is at -5, that's when x = 0, so the point is really (0 , -5), and we also know another point on the line, that is (-1 ,6), to get the equation of any straight line, we simply need two points off of it, so let's use those two
\(\stackrel{y-intercept}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{0}}} \implies \cfrac{6 +5}{-1} \implies \cfrac{ 11 }{ -1 } \implies - 11\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{- 11}(x-\stackrel{x_1}{0}) \implies y +5 = - 11 ( x -0) \\\\\\ y+5=-11x\implies {\Large \begin{array}{llll} y=-11x-5 \end{array}}\)
Please answer in an hour! You will get a thumbs up.
Question 1 (a)
Assume you purchase a new tractor on Jan 1, 2022 for a cost of $200,000. You estimate you will be able to use the tractor for 10 years, and it will have a salvage value of 10% of the original by the end of its useful life. Determine the book value at the end of the first year (December 31, 2022) using straight-line depreciation.
options:
$18,000
$180,000
$185,000
$182,000
Question 1 (b)
A balance sheet (using current and noncurrent assets and liabilities- no intermediate) shows that a farmer has current assets of $80,000 and owner equity of $100,000. Her current ratio is 2 and her debt/equity ratio is 1.0. Determine the farmer's noncurrent liabilities.
Question 1 (b) options:
$40,000
$60,000
$100,000
unable to determine
Question 1a
To calculate the book value at the end of the first year using straight-line depreciation, we need to determine the annual depreciation expense first. The straight-line method assumes that the asset depreciates by an equal amount each year over its useful life. Therefore, we can use the following formula to calculate the annual depreciation:
Annual Depreciation = (Cost - Salvage Value) / Useful Life
Substituting the given values, we get:
Annual Depreciation = ($200,000 - $20,000) / 10 years = $18,000 per year
This means that the tractor will depreciate by $18,000 each year for the next 10 years.
To determine the book value at the end of the first year, we need to subtract the depreciation expense for the year from the original cost of the tractor. Since one year has passed, the depreciation expense for the first year will be:
Depreciation Expense for Year 1 = $18,000
Therefore, the book value of the tractor at the end of the first year will be:
Book Value = Cost - Depreciation Expense for Year 1
= $200,000 - $18,000
= $182,000
So the book value of the tractor at the end of the first year, December 31, 2022, using straight-line depreciation is $182,000. so the answer is D
Question 1(b)
To determine the farmer's noncurrent liabilities, we need to use the information provided to calculate the total liabilities and then subtract the current liabilities from it. Here's the step-by-step solution:
Calculate the total current liabilities using the current ratio:
Current Ratio = Current Assets / Current Liabilities
2 = $80,000 / Current Liabilities
Current Liabilities = $80,000 / 2
Current Liabilities = $40,000
Calculate the total liabilities using the debt/equity ratio:
Debt/Equity Ratio = Total Liabilities / Owner Equity
1.0 = Total Liabilities / $100,000
Total Liabilities = $100,000 * 1.0
Total Liabilities = $100,000
Subtract the current liabilities from the total liabilities to get the noncurrent liabilities:
Noncurrent Liabilities = Total Liabilities - Current Liabilities
Noncurrent Liabilities = $100,000 - $40,000
Noncurrent Liabilities = $60,000
Therefore, the farmer's noncurrent liabilities are $60,000. so the answer is B.
I need help on this question
Answer:
5 square feet
Step-by-step explanation:
First, you need to convert the inches into feet
24: 2
30: 2.5
2*2.5= 5
So it is 5square feet
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. If Shawn knows that the slope of the line is 4 and the line passes through the point (1,-8), which equation should he use to find the y-intercept and what is the y-intercept of the line? Choices are as follows: b = y + mx b = y - mx b = \(\frac{y-m}{x}\) b = -12 b = -4 b = 2
Answer:
b=y-mx
Step-by-step explanation:
We know that y=mx+b is the slope intercept form of a line and we know that the slope of the line is 4. So:y = 4x+bHowever, we need to find the y intercept of the line which is b. Using the point (1,-8), we can find the y intercept. We need to find the equation to find the y-intercept. So:y = mx+b b=y-mxAnd now, we can substitute 4 for m which is the slopeb=y-4xUsing the point (1,-8) we can find the y-intercept b=(-8)-4(1)b=-8-4b=-12the equation of the line is y = 4x - 12 with the slope being 4 and y-intercept is -12. The equation we used is b = y-mx
(10 points) two companies market new batteries targeted at owners of personal music players. duratunes claims a mean battery life of 11 hours, while rockready advertises 12 hours. the standard deviations are 2 hours for duratunes and 1.5 hours for rockready. (1) you are headed for 8 hours at the beach. which battery is most likely to last all day?
The rockready battery is most likely to last all day at the beach.
When you're headed to the beach and you have to choose between two batteries that are marketed to owners of personal music players, you would want to know which battery is most likely to last all day. Duratunes claims a mean battery life of 11 hours with a standard deviation of 2 hours, while Rockready advertises 12 hours with a standard deviation of 1.5 hours. The answer to the question is Rockready battery. The explanation is given below:Let's assume that the distribution of battery lives is normal for both batteries. Thus, for the Duratunes battery, the mean (μ) and standard deviation (σ) are 11 hours and 2 hours, respectively. The mean and standard deviation for the Rockready battery are 12 hours and 1.5 hours, respectively. We must compute the probabilities that each battery will last at least 8 hours.Below is the formula to calculate the probabilities for both batteries: z = (x - μ) / σHere, x represents the number of hours the battery lasts. We get the following values of z:Duratunes battery: z = (8 - 11) / 2 = -1.5Rockready battery: z = (8 - 12) / 1.5 = -2.67We will use the normal distribution table to determine the probabilities associated with these z-values. We will find the area to the left of each z-value in the table. Because we want to find the probability that each battery lasts at least 8 hours, we will subtract this probability from 1. In other words:P(Duratunes battery lasts at least 8 hours) = 1 - P(z < -1.5) = 1 - 0.0668 = 0.9332P(Rockready battery lasts at least 8 hours) = 1 - P(z < -2.67) = 1 - 0.0038 = 0.9962Therefore, the Rockready battery is most likely to last all day at the beach.
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HELP
18 kg of apples cost $106.20. How much would 31 kg cost?
Answer:
31kg will cost $ 182.9
Step-by-step explanation:
If 18kg = $106.20
than 31kg = ?
= 31kg/18kg × $106.20
= 3,292.2 /18
=$182.9
Interest rate in the US is 5% p. a. and in Mexico 45% p. a.Spot rate =6.25 (pesos per dollar)One year ahead forward rate = 7.25 (pesos per dollar)What is the profit made if an investor borrows $100, converts to pesos and invests in Mexico for a year? The forward rate is used for conversion back to the dollar.a) $20b) $25c) $30d) $35
The profit made as of investor borrows $100 is $25.
Investing in foreign currencies can be a profitable venture, but it comes with a certain level of risk.
If an investor borrows $100, converts it to pesos, and invests the pesos in Mexico for one year, the profit made is $25.
This is calculated by borrowing $100 and converting it to 625 pesos at the spot rate of 6.25 pesos per dollar.
The 625 pesos are then invested in Mexico for a year at a 45% interest rate, resulting in 281.25 pesos.
The 281.25 pesos are then converted back to dollars at the forward rate of 7.25 pesos per dollar, resulting in $38.75.
The resulting profit is $38.75 - $100 = -$61.25.
Investing in foreign currencies is not without its risks.
When investing in foreign currencies, the exchange rate can change drastically over short periods of time, resulting in losses or gains.
Additionally,
The interest rate in the country of investment can also change, resulting in different levels of returns.
The profit made if an investor borrows $100, converts to pesos and invests in Mexico for a year is $25.
The calculation is as follows:
Borrow $100 and convert to pesos:
100 x 6.25 = 625 pesos
Invest 625 pesos in Mexico for one year:
625 x 45% = 281.25 pesos
Convert 281.25 pesos back to dollars at the forward rate:
281.25 / 7.25 = $38.75
Profit = $38.75 - $100 = -$61.25
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John is running a study on whether a particular SAT training class is effective. The students take the SAT before and after taking the class. The 95% confidence interval for the difference is scores (after - before) is [5, 15]. Which of the following is NOT true?
a. There is statistically significant evidence that the training class increases SAT scores.
b. The average increase in SAT score among the students was 10.
c. This is an example of a paired design.
d. The training class caused a big improvement in the students' SAT scores.
If John is running a study on whether a particular SAT training class is effective, the students take the SAT before and after taking the class and the 95% confidence interval for the difference in scores (after - before) is [5, 15], then the statement which is NOT true is 'The training class caused a big improvement in the student's SAT scores.' The answer is option d.
Given that the 95% confidence interval for the difference in scores (after - before) is [5, 15], we can infer that the training class is effective in increasing the SAT scores of the students. The average increase in the SAT score among the students was 10, which means that the students who took the training class have a higher average score than those who did not. Therefore, option (a) is true. A paired design is a type of experiment where two groups of subjects are paired together and compared to each other. In a paired design, each subject receives both treatments or is observed twice. The 95% confidence interval is defined as the range of values in which 95% of the observed data is likely to fall. The confidence interval provides a range of values that can be considered plausible estimates of the population parameter. Thus, option (d) is not true.Learn more about confidence interval:
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answer question below
Answer:
(a) 72 cm^2
(b) 9 cm^2
(c) 9 cm^2
(d) 54 cm^2
Step-by-step explanation:
(a):
Area of a rectangle = Length * Width
12 * 6 = 72 cm^2
(b):
Area of a triangle = (Length * Width) / 2
(3 * 6) / 2 = 9 cm^2
(c):
Triangle B = Triangle A
9 cm^2
(d):
The parallelogram is the remaining area of the rectangle when the two triangles are removed. Therefore, using the answers from the previous three questions:
72 - 9 - 9 = 54 cm^2
NEED HELP ASAP!!! 50 POINTS!!! WILL MARK BRAINLIEST
2. The following triangle, ∆, has angle measures as shown.
Step 1: What is the measure of angle C? Show your work.
Step 2: What is the value of x? Show your work.
Answer:
x=29. Angle C= 93
Step-by-step explanation:
3(x+2)= 3x+6.
3x+6+52+35= 3x+93.
180-93=87.
87/3= 29. So that means x=29.
for proof you can do 3(29)+93 and you'll get 180.
For angle C; 3(29+2)= 3x31. 31x3= 93.
Angle C= 93 degrees.
You are given the prices of a particular stock over a period of n days. Let the price per share of the stock on day i be denoted by pį. Our question is the following: How should we choose a day i on which to buy the stock and a later day j > i on which to sell it, if we want to maximize the profit per share (pj – pi)? (If there is no way to make money during the n days, we should conclude that.) Give a O(n) algorithm for the above problem, using dynamic programming.
The Algorithm for a time complexity of O(n) is given at the end.
The algorithm with a time complexity of O(n) to solve the problem:
1. Initialize two variables: "min_price" to store the minimum price encountered so far and "max_profit" to store the maximum profit found so far. Set both variables to infinity or a very large number.
2. Iterate through the given prices from left to right, for each day i:
- Update min_price as the minimum between min_price and prices[i].
- Calculate the potential profit as prices[i] - min_price.
- Update max_profit as the maximum between max_profit and the potential profit.
3. After the iteration, max_profit will contain the maximum profit that can be obtained by buying on one day and selling on a later day.
4. In this case, return a suitable message indicating that there is no profitable opportunity.
5. If max_profit is positive, it represents the maximum profit that can be obtained. To find the specific days i and j, iterate through the prices again and find the day i where the profit is equal to max_profit. Then, continue iterating from day i+1 to find the day j where the price achieves the maximum profit (prices[j] - prices[i]). Return the pair of days (i, j).
The Python code implementing the algorithm:
def find_optimal_days(prices):
n = len(prices)
min_price = float('inf')
max_profit = 0
buy_day = 0
sell_day = 0
for i in range(n):
min_price = min(min_price, prices[i])
potential_profit = prices[i] - min_price
max_profit = max(max_profit, potential_profit)
if potential_profit == max_profit:
sell_day = i
if max_profit <= 0:
return "No profitable opportunity."
for i in range(sell_day):
if prices[sell_day] - prices[i] == max_profit:
buy_day = i
break
return buy_day, sell_day
# Example usage:
prices = [7, 1, 5, 3, 6, 4]
result = find_optimal_days(prices)
print(result)
This algorithm has a time complexity of O(n), where n is the number of days (length of the prices list). It iterates through the prices list twice, but the overall complexity is linear.
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Two opposite angles of a parallelogram are 3x+4 and 5x-2 find measure of all angles of parallelogram
Answer:
=The opposite angles of a parallelogram are equal
=(3x+4)
=(5x-2)
=-2x=-6
=x=6+2
=x=3=
1st angle=3x+4=13
3rd angle=5x-2=13
=sum of adjacent side of angle is 180°
=Let the adjacent (2nd angle ) be y=
y+13°=180°
=y=180°-13°
=y=167°=
2nd angle=4th angle
=2nd angle=167°
=4th angle=167°
Step-by-step explanation:
This might be confusing, but I hope it helps <3
I just Failed my Spanish final exam what do I do now?
Answer:u can advance or pray u god u ain’t getting whipped
Step-by-step explanation:
How does the graph of y = 3^xcompare to the graph of y = 3^-x?
A. The graphs are the same.
B.The graphs are reflected across the x-axis.
C. The graphs are reflected across the y-axis.
Answer:
C
Step-by-step explanation:
The graphs are reflected across the y-axis.
80+45+12x+7=180
Someone help please
Multiply
(Thank You if you help)
(3x-4)^2
the answer is on the picture
Complete the intro by adding in the appropriate statistical vocabulary in the blanks. Watch your spelling! This study was conducted to explore whether perception of money by preschool age children is influenced by their family wealth. This was investigated by testing how the children would recall the size of a coin, with the assumption that the size recalled related to the value placed on the coin To conduct the study, three local thy-care facilities specializing in preschool age children were randomly selected. Consent forms were sent home to the parents of the kids. which also asked parents for their average yearly household income. Since everyone from the three selected facilities was used in the study, this is random ___________sampling. The income data collected was what type of data (categorical or quantitative)? _________
From the parents who consented. the children were divided into two groups: those whose family income was greater than $40.000. and those whose family income was less than $40.000. Each child was asked to draw a nickel. The resulting circle diameter was then measured. When the shape drawn was not a perfect circle, the largest and smallest diameters were averaged. If the researcher found the mean of all the coin diameter data. would that be a statistic or a parameter? _________
The gender of each child was also collected. The gender data was what type of data? _____________
Since we are not imposing an intervention or treatment on the children. This is not an _________.
It is hypothesized that children from lower income families would draw larger coins than children from higher income families.
Here, is filling the blanks.
1. Random cluster sampling.
2. The income data collected was what type of data (categorical or quantitative)? Quantitative.
3. If the researcher found the mean of all the coin diameter data, would that be a statistic or a parameter? Statistic.
4. The gender of each child was also collected. The gender data was what type of data? Categorical.
5. Since we are not imposing an intervention or treatment on the children, this is not an experiment.
This study was conducted to explore whether perception of money by preschool-age children is influenced by their family wealth. This was investigated by testing how the children would recall the size of a coin, with the assumption that the size recalled related to the value placed on the coin. To conduct the study, three local daycare facilities specializing in preschool-age children were randomly selected. Consent forms were sent home to the parents of the kids, which also asked parents for their average yearly household income. Since everyone from the three selected facilities was used in the study, this is random cluster sampling. The income data collected was what type of data (categorical or quantitative)? Quantitative.
From the parents who consented, the children were divided into two groups: those whose family income was greater than $40,000, and those whose family income was less than $40,000. Each child was asked to draw a nickel. The resulting circle diameter was then measured. When the shape drawn was not a perfect circle, the largest and smallest diameters were averaged. If the researcher found the mean of all the coin diameter data, would that be a statistic or a parameter? Statistic.
The gender of each child was also collected. The gender data was what type of data? Categorical.
Since we are not imposing an intervention or treatment on the children, this is not an experiment.
It is hypothesized that children from lower income families would draw larger coins than children from higher income families.
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Grace and her brother Sid want to raise money to go to band camp. Their parents have agreed to help them earn up to $400 by paying them $25 when one of them mows the lawn and $10 for each hour that one of them babysits their younger brother. They will have to do a combination of both chores in order to earn the money. Select the equation that represents the number of lawns they can mow, m, and hours they can babysit, b, to earn $400.
Answer:
25m + 10b = 400
Step-by-step explanation:
Total amount that can be earned = $ 400
Amount earned on mowing a lawn = $ 25
Amount earned per hour on babysitting = $10
Amount earned for mowing one lawn is $ 25, so amount earned for mowing m lawns will be $ 25m
Amount earned for one hour of babysitting is $ 10, so amount earned for babysitting for b hours will be $ 10b
Using the values from above, we can set up the equation as:
400 = 25m + 10b
or
25m + 10b = 400
This equation represents the number of lawns they can mow, m, and hours they can babysit, b, to earn $400.
Hope this helps have a good day
plot four different points whose -coordinates are half their -coordinates. do these points lie on a line?
The four points with y-coordinates half their x-coordinates are (0,0), (2,1), (4,2), and (6,3). These points do lie on a line, as they all satisfy the linear equation y = x/2.
To plot four points whose y-coordinates are half their x-coordinates, we can choose any four values of x and then compute the corresponding values of y using the equation y = x/2. For example
If x = 0, then y = 0/2 = 0, so the first point is (0,0).
If x = 2, then y = 2/2 = 1, so the second point is (2,1).
If x = 4, then y = 4/2 = 2, so the third point is (4,2).
If x = 6, then y = 6/2 = 3, so the fourth point is (6,3).
We can plot these points on a coordinate plane
As we can see from the plot, the four points do lie on a straight line. This is because the equation y = x/2 is the equation of a linear function with slope 1/2 and y-intercept 0. Therefore, any two points on this line will have a constant slope between them, and thus the four points will be collinear.
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Which angle is formed by EA−→
and EG−→−?
Select all that apply.
Answer:
Step-by-step explanation:
\(\angle 2,\angle AEG, \angle GEB\)
Vishal and Christina went to Greenwood Bakery on Liberty Avenue on Monday to buy desserts. Vishal bought 3 packages of cupcakes and 2 packages of brownies for $19. Christina bought 2 packages of cupcakes and 4 packages of brownies for $24. Part One: Write a system of equations that describes the given situation. Part Two: Solve the system of linear equations algebraically to determine the cost of one cupcake and one brownie at Greenwood Bakery on Liberty Avenue.
Using a system of equations, it is found that one cupcake costs $2.50 and one brownie costs $4.25.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Cost of one cupcake.Variable y: Cost of one brownie.Vishal bought 3 packages of cupcakes and 2 packages of brownies for $19, hence:
3x + 2y = 19
Christina bought 2 packages of cupcakes and 4 packages of brownies for $24, hence:
2x + 4y = 24
Simplifying by 2
x + 2y = 12
x = 12 - 2y
Replacing on the first equation:
3x + 2y = 19
3(12 - 2y) + 2y = 19
4y = 17
y = 4.25
x = 12 - 2y = 12 - 2(4.25) = 2.50
One cupcake costs $2.50 and one brownie costs $4.25.
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What is the simplified value of the expression below?
Negative 2.6 + 5.8
–8.4
–3.2
3.2
8.4
Answer:
i did that quiz the answer is 3.2
Step-by-step explanation:
your welcome
Answer:
3.2
Step-by-step explanation:
The day you were born your parents invested $5,000 in CD account (Certificate of Deposit).
The account pays 0.88% annual interest rate. How much money will be in your account by
your high school graduation (18 years)?
Plz help. I need an answer and explanation step by step plz
Answer:
You will have $5,792 in your account by your high school graduation
Step-by-step explanation:
Simple Interest
Interest calculated on the original principal only of a loan or on the balance of an account.
Unlike compound interest where the interest earned in the compounding periods is added to the new principal, simple interest only considers the principal to calculate the interest.
The interest earned is calculated as follows:
I=P.r.t
Where:
I = Interest
P = initial principal balance
r = interest rate
t = time
The parents invested P = $5,000 in CD account that pays r=0.88% annual interest rate. The rate must be converted to decimal, thus r=0.88/100 =0.0088.
We are required to calculate the total money in the account after t=18 years.
First, we calculate the interest:
I = $5,000 * 0.0088 * 18
I = $792
Adding interest to the principal, we have the future balance in the account:
A = $5,000 + $792 = $5,792
You will have $5,792 in your account by your high school graduation
PLEASE HELP ME ITS DUE RIGHT NOW :(
An image of a rhombus is shown.
a rhombus with a base of 18 centimeters and a height of 15.5 centimeters
What is the area of the rhombus?
16.75 cm2
33.5 cm2
139.5 cm2
279 cm2
Answer:279 cm2
Step-by-step explanation:
The area of a rhombus is calculated by multiplying the length of the base by the height.
The base of the rhombus is 18 cm and the height is 15.5 cm.
Therefore, the area of the rhombus is:
18 cm × 15.5 cm = 279 cm²
So the answer is 279 cm².
A proton's mass is estimated to be 1.6726 x 10^-24 and the mass of an electron is estimated to be 9.1093 x 10^-28. How many times larger is the mass of a proton compared to the mass of an electron?
A proton has a mass of \($$1.6726 * 10^{-24}\) g corresponds to 1.0072766 Atomic Mass Unit
A proton exists 1836.096 times heavier than an electron.
Proton Mass = 938.2720813 \($$MeV/c_2\)
Electron = 0.5109989461 \($$MeV/c_2\)
E : P Ratio = 1 : 1836.15267
What is a proton's mass in AMU?
\($$m_{p\) = mass of a proton (1.007277 AMU)
\($$m_n\) = mass of a neutron (1.008665 AMU)
\($$m_e\) = mass of an electron (0.000548597 AMU)
\($$m_{atom}\) = mass of nuclide (AMU)
A proton has a mass of \($$1.6726 * 10^{-24}\) g corresponds to 1.0072766 Atomic Mass Unit
[AMU, Atomic Mass Unit exists utilized to describe atomic and molecular weights, equivalent to one-twelfth of the mass of an atom of carbon-12].
Whereas, the Electron exists at \($$9.1093 * 10^{-28}\) equaling 0.000548597 AMU.
Electron to Proton Ratio = 1: (0.000548597 / 1.0072766)
= 1836.096
A proton exists 1836.096 times heavier than an electron.
Proton Mass = 938.2720813 \($$MeV/c_2\) (MeV= Mega Electron Volt)
(As per Mass - the energy equivalence principle, energy exists proportional to mass whereby, an electron volt exists also as a unit of Mass. Energy can be converted to Momentum and Mass)
Electron = 0.5109989461 \($$MeV/c_2\)
E : P Ratio = 1 : 1836.15267
Therefore, the correct answer is E : P Ratio = 1: 1836.15267.
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a line is reflected. Which of these could be the result? Pls help
Answer:
A
Step-by-step explanation:
Answer:
The answer is A.
Step-by-step explanation:
AP EX
The solid below is made from 1 yard cubes. Find its surface area.
Answer:
Surface area = 80yd
Step-by-step explanation:
4x3 + 4x4 + 4x3 + 4x4 + 4x3 + 4x3 = 80
hope this helped :D
Thu has the same amount of money automatically deposited into a new savings account each week. After 2 weeks, she has $14. After 5 weeks, she has $35. The unit rate is measured in dollars per week. What is the constant of proportionality?
For the given data of saving account, unit rate is measured in dollars per week then constant of proportionality is equal to $7.
As given in the question,
For the saving account,
Amount deposited is directly proportional to the number of weeks
Let y be the amount deposited and x be the number of weeks
y ∝ x
y = kx
'k' is the constant of proportionality
As per data unit rate is measured in dollars per week
For y = $14 then x = 2 weeks
14 = 2k
⇒ k = $7
For y = $35 then x = 5weeks
35 =5k
⇒ k = $7
Therefore, for the given data of saving account, unit rate is measured in dollars per week then constant of proportionality is equal to $7.
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Graph the inequality in the coordinate plane. x < -7
For the given inequality x < -7 we draw a straight line at the point -7. The inequality is not strict, hence the line is dotted.
What is inequality?A mathematical statement called an inequality compares two numbers or expressions, typically by employing a symbol. Inequalities show that two quantities are not equal and that one is more than or less than the other.
Number lines can be used to visualise inequality conditions. Depending on whether the endpoint is part of the solution set or not, numbers that meet the inequality are shaded in or denoted by an open or closed circle. A number line would, for instance, show the inequality x > 2 with an open circle at 2 and shading to the right to show all values higher than 2.
In many areas of mathematics as well as in other disciplines like economics and social sciences, inequality is used.
For the given inequality x < -7 we draw a straight line at the point -7.
The inequality is not strict, hence the line is dotted.
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