Yes, an answer can be incorrect even if it looks reasonable
Explaining the statementYes, an answer can be incorrect even if it looks reasonable. This is because an answer might seem reasonable on the surface but may not be correct due to various reasons such as calculation errors, incorrect assumptions, or misinterpretation of the problem.
For instance, in a math problem that involves converting units of measurement, a student may have calculated the answer and arrived at a number that seems reasonable.
However, if the student used the wrong conversion factor or made an error in calculations, the answer would be incorrect despite appearing reasonable.
Similarly, in a word problem, an answer may seem reasonable but might not take into account all the given information, resulting in an incorrect solution.
Therefore, it is important to double-check answers and verify that they make sense in the context of the problem and that all the given information has been taken into account to ensure accuracy.
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Please help me show work
1.) m<A = 51°
AB = 17.5
BC = 13.6
How to calculate the missing side and angles of the given triangle?To calculate the missing part of the triangle, m <A ;
The sum of the interior triangle = 180°
That is , 180° = 90°+ 39° + m
make m the subject of formula;
m = 180 - 129
m <A = 51°
Using the formula from SOHCAHTOA;
Sin 39° = 11/AB
make AB the subject of formula;
AB = 11/0.629320391
= 17.5
Using the Pythagorean formula;
C² = a² + b²
C² = 17.5
a² = 11
b² = BC = ?
17.5² = 11² + b²
make b² the subject of formula;
b² = 17.5²-11²
b² = 306.25 - 121
b² = 185.25
b = √185.25
b = 13.60
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Plot -2 1/6 and 11/6 on the number line below.
The number line where we plotting -2 1/6 and 11/6 is attached
Plotting -2 1/6 and 11/6 on a number lineFrom the question, we have the following parameters that can be used in our computation:
-2 1/6 and 11/6
To start with, we convert both numbers to the same form
i.e. decimal or fraction
When converted to fractions, we have
-13/6 and 11/6
This means that we can plot -13/6 at -13 and 11/6 at point 11 where the difference in each interval is 1/6
Using the above as a guide, we have the following:
The number line is attached
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uppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 1600 bacteria selected from this population reached the size of 1838 bacteria in four hours. Find the hourly growth rate parameter.
Answer:
Below.
Step-by-step explanation:
Exponential growth equation is
Nt = No e^kt where No is initial quantity , Nt is quantity after time t and k is some constant.
Here we have:
1838 = 1600 e^4k
e^4k = 1838/1600 = 1.14875
4k = ln 1.14875 = 0.138674
k = 0.034669
sin(75°)= sqrt1-cos(150°)/2 true or false
[tex] \sqrt{ \frac{1 - cos(150)}{2} } = \sqrt{ \frac{1}{2} - \frac{cos(150)}{2} } = \sqrt{ \frac{1}{2} - \frac{ \frac{ - \sqrt{ 3}}{2} }{2} } = \sqrt{ \frac{2}{4} + \frac{ \sqrt{3} }{4} } = \sqrt{ \frac{2 + \sqrt{3} }{4} } [/tex]
[tex]= \frac{ \sqrt{6} + \sqrt{2} }{4} [/tex]
BTW:
[tex]sin(75) = \frac{ \sqrt{6} + \sqrt{2} }{4} [/tex]
[tex] = > sin(75) = \sqrt{ \frac{1 - cos(150)}{2} } [/tex]
Ans: True
Ok done. Thank to me >:33
A standardized exam consists of three parts: math, writing, and critical reading. Sample data showing the math and writing scores for a sample of 12 students who took the exam follow.
Student Math Writing
1 540 468
2 432 380
3 528 463
4 574 612
5 448 420
6 502 526
7 480 430
8 499 459
9 610 615
10 572 535
11 390 335
12 593 613
(a)
Use a 0.05 level of significance and test for a difference between the population mean for the math scores and the population mean for the writing scores. (Use math score − writing score.)
Formulate the hypotheses.
H0: d ≤ 0
Ha: d > 0
H0: d > 0
Ha: d ≤ 0
H0: d ≤ 0
Ha: d = 0
H0: d ≠ 0
Ha: d = 0
H0: d = 0
Ha: d ≠ 0
Correct: Your answer is correct.
Calculate the test statistic. (Round your answer to three decimal places.)
-1.044
Incorrect: Your answer is incorrect.
Calculate the p-value. (Round your answer to four decimal places.)
p-value =
What is your conclusion?
Reject H0. We can conclude that there is a significant difference between the population mean scores for the math test and the writing test.
Reject H0. We cannot conclude that there is a significant difference between the population mean scores for the math test and the writing test.
Do not reject H0. We cannot conclude that there is a significant difference between the population mean scores for the math test and the writing test.
Do not reject H0. We can conclude that there is a significant difference between the population mean scores for the math test and the writing test.
(b)
What is the point estimate of the difference between the mean scores for the two tests? (Use math score − writing score.)
What are the estimates of the population mean scores for the two tests?
Math
Writing
Which test reports the higher mean score?
The math test reports a
---Select---
mean score than the writing test.
The test statistic based on the information is given by 2.19.
How to calculate the valueThis evidence-based test has an available degree of freedom of 11 - being acquired by subtracting 1 from the overall 12. With 11 degrees of freedom in combination with a 0.05 margin of significance, an applicable t-distribution table states that the essential critical value is 1.796.
Seeing as our experimental statistic of 2.19 surpasses the critical value of 1.796, we must discount the null hypothesis. Consequently, sufficient proof signifies that the average math score population attains a higher mean than its writing counterpart when contemplating a 0.05 level of significance.
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if at least one child in a family with 2 children is a boy, what is the probability that both children are boys?
Answer:
The probability of both children being boys in a family with 2 children is
3
1
.
There are 3 possible outcomes for the gender of each child: boy, girl, or unknown. There are 2 children, so there are 3
2
=9 possible combinations of genders for the 2 children.
Of these 9 combinations, 3 of them have both children being boys: BB, BG, and GB. So the probability of both children being boys is
9
3
=
3
1
.
However, this is only the probability if we don't know the gender of the first child. If we know that the first child is a boy, then the probability of both children being boys is
2
1
. This is because there are only 2 possible outcomes for the gender of the second child: boy or girl. If the first child is a boy, then the second child must be a boy in order for both children to be boys. So the probability is
2
1
.
Step-by-step explanation:
Let's use the following notation for the children:
B: Boy G: Girl
There are 4 possible combinations for a family with 2 children:
1. BB (Both children are boys)
2. BG (First child is a boy, second child is a girl)
3. GB (First child is a girl, second child is a boy)
4. GG (Both children are girls)
Since we know that at least one child is a boy, we can eliminate the 4th combination (GG) as it doesn't meet the condition. Now we have 3 possible combinations left:
1. BB
2. BG
3. GB
Now, to find the probability that both children are boys (BB) from the remaining combinations, we can calculate it as follows:
Probability = (Number of favorable outcomes) / (Total possible outcomes)
Probability = 1 (BB) / 3 (BB, BG, GB)
Probability = 1/3
So, the probability that both children are boys is 1/3.
You invest $1800 in an account paying 6.3% interest compounded daily. What is the account's effective annual yield? You invest $1800 in an account paying 6.3% interest compounded daily. What is the account's effective annual yield?
The account's effective annual yield if you invest $1800 and it pays 6.3% interest compounded daily, is calculated as: 6.53%.
How to Find the Effective Annual Yield?In order to find the effective annual yield of an account, the formula to apply is expressed as:
Effective annual yield = (1 + r/n)^n - 1
where:
r represents the annual interest rate (as a decimal)
n represents the number of times the interest is compounded per year
In this case, we are given the following:
Annual interest rate = 6.3% = 0.063
The interest is compounded daily, so n = 365 (days in a year)
Plugging in the variables we have:
Effective annual yield = (1 + 0.063/365)^365 - 1
Effective annual yield = 0.0653 or 6.53%
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Find the value of x. Round to the nearest degree.
The missing sides of the triangle have been identified here.
How do we solve right triangle?Trigonometric ratios relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent. If you know the measure of one of the acute angles in the triangle and the length of one of the sides, you can use trigonometric ratios to solve for the length of another side.
1) Sin x = 5/14
x = Sin-1 (5/14)
x = 21°
2) Tan x = 8/5
x = Tan-1 (8/5)
x = 58°
3) Cos x = 9/13
x = Cos-1 (9/13)
x = 46°
4) Cos x = 3/5.8
x = Cos-(3/5.8)
x = 59°
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The missing sides of the triangle have been identified here.
How do we solve right triangle?Trigonometric ratios relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent. If you know the measure of one of the acute angles in the triangle and the length of one of the sides, you can use trigonometric ratios to solve for the length of another side.
1) Sin x = 5/14
x = Sin-1 (5/14)
x = 21°
2) Tan x = 8/5
x = Tan-1 (8/5)
x = 58°
3) Cos x = 9/13
x = Cos-1 (9/13)
x = 46°
4) Cos x = 3/5.8
x = Cos-(3/5.8)
x = 59°
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Total Time Slept
Individual Total Time Slept
(hours)
Individual Total Time Slept
(hours)
Mike 8
1
2
Gina 10
John 10 Elisabeth 9
Susan 8
1
2
Alexis 9
1
2
Linda 8
1
2
Drake 8
1
2
Frankie 6
1
2
Vincent 8
1
2
Bob 7
1
2
Herbert 9
Kim 7
1
2
John 10
Louie 9
1
2
Chrissy 7
1
2
Pamela 8
1
2
Liam 10
Heather 8 Julian 8
1
2
© 2017 Connections Education LLC. All rights reserved. 2
1. What was the most common amount of sleep?
2. Is there an outlier in the data? If so, what is it? Explain how you know.
3. What is the difference in hours between the longest night’s sleep and the
shortest night’s sleep?
4. How many people slept longer than 8 hours?
3
Part 2
Directions: The next day, Molly asked 5 more people how long they slept the night
before. Below is a chart of their answers. Add their times to the line plot you
created in Part 1.
Total Time Slept
Name Total Time Slept
(hours)
Zaria
7
LaDajia
12
Devonte
7
Leon
8
Kylie
7
1. Describe how the new data has changed the line plot.
2. Is there an outlier in the data? If so, is it the same as the outlier before the
new data was added? Explain.
3. How many total people slept less than 8 hours? How do you know?
The most common amount of sleep: is 8 hours (6 individuals).
Outlier: Frankie (slept for 6 hours), as there is a significant difference between his sleep time and the rest of the individuals in the dataset (range of 4 hours).
The predominant resting time among the subjects is 8 hours.
Nonetheless, it's worth noting that an outlier exists within the dataset; Frankie spent a mere 6 hours sleeping - which amounts to two hours less than the sleep duration recorded by the second least rested individual (8 hours).
This information can be extracted from analyzing the figures and noticing the conspicuous discrepancy between Frankie's slumbering span and that of the other participants in the pool of data and this is the outlier.
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What are the factors of m2 – 6m + 6m – 36?
Answer:
6 and -6
Step-by-step explanation:
M^2-6m+6m-36
m^2-36
(m-6)(m+6)
Δ XYZ, shown below, is a 30° - 60° - 90° triangle.
8). Which leg is the shorter leg?
9). In a 30° - 60° - 90° triangle, the shorter leg is always opposite the _____° angle.
10). Which leg is the longer leg?
11). In a 30° - 60° - 90° triangle, the longer leg is always opposite the ____° angle.
12). If YZ = 5, then XY = ____ and XZ = _______.
13). If YZ = 6, then XY = ____ and XZ = _______.
14). If XY = 8, then YZ = _____ and XZ = _______.
15). If XY = 6, then YZ = _____ and XZ = _______.
Answer:
8). YZ
9). 30°
10). XY
11). 90°
12). XY=10 and XZ=5√3
13). XY=12 and XZ=6√3
14). YZ=4 and XZ=4√3
15). YZ=3 and XZ=3√3
A statistics student believes that black cars are less likely to receive tickets for moving violations. Black cars make up 19% of all cars manufactured. The student randomly selects 70 moving violation records and finds that 10 of them involved black cars. The P-value for the test of the hypotheses, H 0: p = 0.19 and H alpha: p less-than 0.19, is 0.24. What is the correct interpretation of this value?
There is a 24% chance of a black car receiving a moving violation.
Assuming the true proportion of black cars that receive moving violations is 0.19, there is a 24% probability that the null hypothesis is true.
Assuming the true proportion of black cars that receive moving violations is 0.19, there is a 24% probability that the sample proportion would be 0.15 or less by chance alone.
Assuming the true proportion of black cars that receive moving violations is less than 0.19, there is a 24% probability that the sample proportion would be 0.15 or less by chance alone.
The correct interpretation of the P-value in this context is: Assuming the true proportion of black cars that receive moving violations is 0.19, there is a 24% probability that the sample proportion would be 0.15 or less by chance alone. So, the correct answer is C).
In other words, the P-value is the probability of obtaining a sample proportion of 0.15 or less (which corresponds to 10 black cars out of 70 total) if the true proportion of black cars that receive moving violations is actually 0.19.
Since the P-value is relatively high (larger than the significance level of 0.05), we fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim that black cars are less likely to receive tickets for moving violations.
So, the correct answer is C).
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Final Examination O
7
Consider the following information from a company's unadjusted trial balance at December 31, 2020. All accounts have normal balances.
Accounts Receivable.
Accounts Payable
Cash
Service Revenue
Common Stock
Equipment
Insurance Expense
Multiple Choice
$ 5,100
680
1,760
6,280
4,600
5,500
430
Land
Notes Payable, Due 2023
Notes Receivable, Matures 2021
Prepaid Insurance
Rent Expense
Retained Earnings, January 1, 2020
Salaries and Wages Expense
What is the total of the debit side of the unadjusted trial balance?
$18.790
4,400
4,600
1,260
430
Saved
1,430
7,910
3,760
The value of total of the debit side of the unadjusted trial balance is,
⇒ $24,350
We have to given that;
Consider the following information from a company's unadjusted trial balance at December 31, 2020.
Hence, We get;
The computation of the total of debit side is shown below;
= Accounts Receivable + Cash + Equipment + Insurance Expense + Land + Notes Receivable + Prepaid Insurance + Rent Expense + Salaries and Wages Expense
= 5100 + 680 + 1760 + 6280 + 4600 + 5500 + 430
= $24350
Thus, The value of total of the debit side of the unadjusted trial balance is,
⇒ $24,350
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what is the formula for finding the surface of a cone
Answer:
Formula for finding the surface area of a cone is shown below
[tex]\pi \: r {}^{2} + \pi \: rl \\ or \\ \pi(r + l)r[/tex]
The formula for finding the surface area of a cone is:
Surface area = πr² + πrl
Where:
π is the mathematical constant pi (approximately 3.14159) r is the radius of the base of the conel is the slant height of the cone, which can be calculated using the Pythagorean theorem (l² = r² + h²), where h is the height of the coneFind the length of the missing side
Answer: [tex]b=\sqrt{45}[/tex] or b=6.71 in.
Step-by-step explanation:
Use Pythagorean Theorem
[tex]a^2+b^2=c^2[/tex]
In this case, a=2in and c=7in, and we're solving for b.
[tex](2)^2+b^2= (7)^2\\4+b^2= 49\\b^2=45\\b=\sqrt{45}[/tex]
Therefore, b=6.71 in.
Identify the domain and range of the function. y=3√x
A. Domain: x≥3, Range: y≥3
B. Domain: All Real Numbers, Range: All Real Numbers
C. Domain: x≥0, Range: y≥0
D. Domain: x≤0, Range: y≤0
The domain and range of the function are C. Domain: x≥0, Range: y≥0
Identifying the domain and range of the functionThe domain of the function is the set of all possible input values (x) for which the function is defined.
In this case, the function y = 3√x is defined for non-negative real numbers, because the root of a negative number is not a real number.
Therefore, the domain of the function is:
Domain: {x | x ≥ 0}
The range of the function is the set of all possible output values (y) that the function can take.
Since the root of any positive number is also positive, the function y = 3√x will always return a positive number for any positive input value.
Therefore, the range of the function is:
Range: {y | y ≥ 0} or [0, ∞) in interval notation.
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Mrs. Brown records the rainfall in Seattle, Washington during each month of 2021. (8.75, 4.68, 2.61, 1.03, 1.12, 1.91, 0.00, 0.11, 3.02, 5.76, 10.62, 4.38} Mrs. Brown wants to use a graphical representation that will allow her students to see the overall shape of the data and provide enough information to determine the 5-number summary Which representations should Mrs. Brown consider? Select all that apply.
Answer:
Its line plot and box plot
Step-by-step explanation:
Cheese costs $4.40 per pound. Find the cost per kilogram. (1 kg ≈ 2.2 lb)
The cost per kilogram of cheese is found by dividing the cost per pound by the conversion factor 0.45359237 kilograms per pound. The result is $9.68 per kilogram.
Start with the given cost of cheese per pound: $4.40.
To convert from pounds to kilograms, we need to divide by the conversion factor 2.2 (since 1 kilogram is approximately equal to 2.2 pounds). So, we have
1 pound / 2.2 = 0.45359237 kilograms / 1 pound
Note that we can write this as a conversion factor with the pound unit cancelling out, leaving us with kilograms as the desired unit.
Now, we can multiply the cost per pound by the conversion factor to get the cost per kilogram
Cost per kilogram = Cost per pound * (1 pound / 0.45359237 kilograms)
= $4.40 * (1 / 0.45359237)
Evaluating this expression using a calculator gives us
Cost per kilogram = $9.68
So the cost of cheese per kilogram is approximately $9.68.
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HELP FAST PLEASE
Question
Does each equation represent exponential decay or exponential growth?
Drag and drop the choices into the boxes to correctly complete the table.
Note: If an equation is neither exponential growth nor exponential decay, do not drag it to the table.
All choices that have numbers like a/b are fractions.
Choices:
A= (0.97)^t
y= 3.7 (0.2)^t
y= 9/11 (4)^t
P= 7/9 (5/4)^t
V= 0.8 (9)^t
P= 0.9 (8.3)^t
g(x)= 2.1(x)
The exponential growth functions are,
[tex]y=\frac{9}{11}(4)^t[/tex]
[tex]V=0.8(9)^t[/tex]
[tex]P=0.9(8.3)^t[/tex]
[tex]P=\frac{7}{9}(\frac{5}{4})^t[/tex]
The exponential decay functions are,
[tex]A= (0.97)^t[/tex]
[tex]y= 3.7 (0.2)^t[/tex]
The function which is neither exponential growth nor exponential decay is,
g(x)=2.1(x).
What is exponential function?
A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.
If the base is larger than 1, it will be an exponential growth.
For example, [tex]3^2=9[/tex]
If the base is smaller than 1, it will be an exponential decay.
For example, [tex]0.5^2=0.25[/tex]
If the function does not have an exponent, that means there will be no exponential growth or decay.
Therefore the exponential growth functions are,
[tex]y=\frac{9}{11}(4)^t[/tex]
[tex]V=0.8(9)^t[/tex]
[tex]P=0.9(8.3)^t[/tex]
[tex]P=\frac{7}{9}(\frac{5}{4})^t[/tex]
The exponential decay functions are,
[tex]A= (0.97)^t[/tex]
[tex]y= 3.7 (0.2)^t[/tex]
The function which is neither exponential growth nor exponential decay is,
g(x)=2.1(x).
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Determine whether the graph of the quadratic function y = –2x^2 – 4x + 4 opens upward or downward. Explain.
The graph of the quadratic function [tex]y=-2x^2-4x+4[/tex] opens downward.
What is function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Here the given function is [tex]y=-2x^2-4x+4[/tex]
The general form of the quadratic function is y=[tex]ax^2+bx+c[/tex]
Then, a= -2
Which is negative value.
Then the graph is open downward.
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Find WX. Assume that segments that appear to be tangent are tangent.
WX =
(50 POINTs will give BRAINIEST FOR EFFORT)
Answer:
WX = 34 units---------------------
WX and YX are tangents drawn from point X to circle Z.
Tangent segments drawn to the same circle from the same point are equal:
WX = YXSubstitute values for side lengths and solve for x:
7x - 29 = 2x + 167x - 2x = 16 + 295x = 45x = 9Substitute 9 for x and find the length of tangent WX:
WX = 7*9 - 29 = 63 - 29 = 34Please answer question
The equation of line perpendicular to the tangent is found to be -
y = -2x + 7.
Give an explanation of the slope-intercept form:The equation for a line should be written in the slope-intercept form so that the y-intercept (where its line crosses a vertical y-axis) and slope (steepness) are immediately visible. The y = mx + b form is a common name for this form.
Given condition of digression line:
Comparing with the standard form: y = 1/2 x + 7 y = mx + c
m is the slant and c is the y block:
m = 1/2
Let the incline of the line opposite to the digression be M.
Then, at that point, connection between the inclines of opposite lines:
m. M = -1 equation of line perpendicular to the tangent.
y - 3 = M(x - 2)
y - 3 = -2(x - 2)
y = -2x + 4 + 3
y = -2x + 7
Thus, the equation of line perpendicular to the tangent is found to be -
y = -2x + 7.
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Complete question:The circle has the centre at (2,3). The equation of the tangent of the line on the circle : y = 1/2 x + 7. What is equation of line perpendicular to the tangent.
Suppose a worker makes $22,000 in wages per year. Find the percent increase in salary the worker can expect if he/she trains to be a teacher and can expect to earn a salary of $42,000.
The solution is, the percent increase in salary is: 90.9%
Here, we have,
given that,
Suppose a worker makes $22,000 in wages per year.
and, he/she trains to be a teacher and can expect to earn a salary of $42,000.
now, we have to find the percent increase in salary the worker can expect.
so, we have,
previous salary = $22,000
expected salary = $42,000.
so, increase = $ 20000
so, the percent increase in salary is:
20000/22000 * 100
=90.90
so, the percent increase in salary is: 90.9%
Hence, The solution is, the percent increase in salary is: 90.9%.
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Draw a pie chart to show the periods of sunshine cloudiness and darkness during the day
The procedure for creating a pie chart based on a given set of data involves a number of steps such as.
Create a circular shape with a non-specific measurement for its radius. Begin by drawing radii that correspond to the values of each respective component, using the horizontal radius as a starting point and ensuring that the central angles match. Apply the same procedure to all element of the given information.What is the pie chart?The Steps to draw a pie chart for weather conditions in Kaduna:
1. Draw a circle to represent 24-hour period.
2. Divide circle into sections for sunshine, cloudiness, and darkness.
Lastly, Use the weather duration to find section size.
Sunlight: 10/24 = 42% of circle. Cloudy for 3 hours = (3/24) or 12.5% of circle. 11 hours for darkness = (11/24) or 45.8% of circle.Thus, Label pie chart sections attached as "Sunshine", "Cloudiness", and "Darkness".
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See text below
b Discuss the performance with your teach During a 24-hour period in Kaduna, the sun shone for 10 hours, it was cloudy for 3 hours and it was dark for the remainder of the time. Draw a pie chart to show the periods of sunshi cloudiness and darkness during the day.
What is the slope of the line 9x+3y=11
Step-by-step explanation:
Arrange this equation into y = mx + b form.....m is the slope
9x+3y =11
3y = -9x + 11
y = -9/3 x + 11/3
y = -3 x + 11/3 m = slope = - 3
In a 300-m-tall building, the stairwells are no more than 20 stories high. A story is approximately 3 m high. What is the maximum pressure differential in a stairwell? What is the atmospheric pressure difference between the top of the building and street level? What is the difference in static water pressure between consecutive floors?
The maximum pressure differential in a stairwell is 58,860 Pa.
The atmospheric pressure difference between the top of the building and the street level is 2,943,000 Pa.
The difference in static water pressure between consecutive floors is 29,430 Pa.
We have,
Assuming a standard atmospheric pressure of 101.3 kPa.
Maximum pressure differential in a stairwell:
Since each stairwell is no more than 20 stories high and each story is approximately 3 m high, the maximum height difference between two floors in a stairwell is:
= 20 x 3
= 60 m
Using the formula for hydrostatic pressure, the maximum pressure differential in a stairwell is:
ΔP = ρgh
= (1000 kg/m³)(9.81 m/s²)(60 m)
= 58,860 Pa
The atmospheric pressure difference between the top of the building and street level:
The atmospheric pressure decreases with increasing altitude.
Using the formula for hydrostatic pressure, the pressure difference between the top of the building and the street level is:
ΔP = ρgh
= (1000 kg/m³)(9.81 m/s²)(300 m)
= 2,943,000 Pa
The difference in static water pressure between consecutive floors:
Assuming a standard density of water of 1000 kg/m³, the difference in static water pressure between consecutive floors is:
ΔP = ρgh = (1000 kg/m³)(9.81 m/s²)(3 m) = 29,430 Pa
Therefore,
The maximum pressure differential in a stairwell is 58,860 Pa.
The atmospheric pressure difference between the top of the building and the street level is 2,943,000 Pa.
The difference in static water pressure between consecutive floors is 29,430 Pa.
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Can you check if all these answers are correct?
Question 1: The side length c of the triangle is equal to: c 2 =a 2 +b 2 −2abcosC where a and b are the other two side lengths of the triangle, and C is the angle opposite side c. To solve for c, you can plug in the values of a, b, and C into the formula and solve for c. For example, if a=3, b=4, and C=60 ∘ , then you would plug in these values into the formula and solve for c as follows: c 2 =3 2 +4 2 −2⋅3⋅4cos60 ∘ c 2 =25 c= 25 =5 Therefore, the side length c of the triangle is equal to 5. Question 2: The angle C of the triangle is equal to: cosC= 2ab a 2 +b 2 −c 2 where a, b, and c are the other two side lengths of the triangle. To solve for C, you can plug in the values of a, b, and c into the formula and solve for C. For example, if a=3, b=4, and c=5, then you would plug these values into the formula and solve for C as follows: cosC= 2⋅3⋅4 3 2 +4 2 −5 2 =− 4 1 C=cos −1 (− 4 1 )≈109.47 ∘ Therefore, the angle C of the triangle is approximately 109.47 degrees. Question 3: The area of the triangle is equal to A= 2 1 absinC where a and b are the other two side lengths of the triangle, and C is the angle opposite side c. To solve for A, you can plug in the values of a, b, and C into the formula and solve for A. For example, if a=3, b=4, and C=60 ∘ , then you would plug in these values into the formula and solve for A as follows: A= 2 1 ⋅3⋅4sin60 ∘ =6 3 Therefore, the area of the triangle is equal to 6 3 . Question 4: The perimeter of the triangle is equal to: P=a+b+c where a, b, and c are the three side lengths of the triangle. To solve for P, you can simply add up the values of a, b, and c. For example, if a=3, b=4, and c=5, then you would add up these values to get P=12. Therefore, the perimeter of the triangle is equal to 12. Question 5: The centroid of the triangle is located at a point that is: One-third of the way from each vertex to the opposite side. Equidistant from all three vertices. On the medians of the triangle. To find the centroid of the triangle, you can use the following formula: G=( 3 a+b+c , 3 a+b+c , 3 a+b+c ) where (a,b,c) are the coordinates of the three vertices of the triangle.
Answer:
All of the answers appear to be correct based on the given formulas and values.
the day before Valentine's Day a store has 400 red roses and 200 boxes of chocolate. After the store opens at 9 a.m. half of the available roses are bought every 2 hours. 15% of the boxes are bought every hour. a. Find a formula that represents the number of red roses left t hours before the store opens. b. Find a formula that represents the number of box chocolates left t hours after the store opens. c. At what time will the number of roses be equal to the number of boxes of chocolates. d. How many boxes of chocolate are left at 12:30 in the afternoon? Round your answer to make sense in this context of the problem. e. Suppose you want to buy that special someone 36 red roses at the store. What is the latest you can arrive to successfully make your purchase?
Answer:
Step-by-step explanation:
a. The number of red roses left t hours before the store opens can be represented by the formula:
N(t) = 400 * (1/2)^(t/2)
Here, we're dividing the number of available roses by 2 every 2 hours, so the exponent t/2 represents the number of 2-hour intervals that have passed since the store opened.
b. The number of box chocolates left t hours after the store opens can be represented by the formula:
M(t) = 200 * (0.85)^t
Here, we're multiplying the number of available boxes by 0.85 every hour, so the exponent t represents the number of hours that have passed since the store opened.
c. We need to find the time t when the number of roses is equal to the number of boxes of chocolates:
400 * (1/2)^(t/2) = 200 * (0.85)^t
Dividing both sides by 200:
2 * (1/2)^(t/2) = 0.85^t
Taking the logarithm of both sides:
log(2) - (t/2) * log(2) = t * log(0.85)
Simplifying:
t * (log(0.85) + (log(2)/2)) = log(2)
t = log(2) / (log(0.85) + (log(2)/2))
Using a calculator, we get:
t ≈ 11.9 hours
Therefore, the number of roses will be equal to the number of boxes of chocolates approximately 11.9 hours before the store opens, or around 9 p.m. on the day before Valentine's Day.
d. To find the number of boxes of chocolate left at 12:30 p.m. (3.5 hours after the store opens), we can use the formula:
M(3.5) = 200 * (0.85)^3.5
M(3.5) ≈ 97.4
Therefore, there are approximately 97 boxes of chocolate left at 12:30 p.m.
e. To buy 36 red roses, we need to find the latest time we can arrive before the store runs out of roses. We can set N(t) equal to 36 and solve for t:
400 * (1/2)^(t/2) = 36
Dividing both sides by 400:
(1/2)^(t/2) = 0.09
Taking the logarithm of both sides:
t/2 * log(1/2) = log(0.09)
Simplifying:
t ≈ 5.2 hours
Therefore, the latest time we can arrive to successfully buy 36 red roses is approximately 5.2 hours before the store opens, or around 3:50 a.m. on the day before Valentine's Day.
TrianglePQR is shown.
A. What are the missing side lengths in TrianglePQR
B. Explain how you arrived at your answer.
The length of the two unknown sides of the triangle are: 12√2
How to find the missing lengths of the triangle?There are different methods of finding the missing sides of triangles such as:
Pythagoras Theorem
Law of sines or sine rule
Law of cosines or cosine rule
Now, we are given an Isosceles triangle with a base length and two equal base angles.
Thus, the two unknown sides will have equal side lengths.
∠D = 90°
Thus, using sine rule:
12/sin 90 = QR/sin 45
QR = 12 * 1/√2
Rationalizing the denominator gives:
QR = 12√2
Since the two unknown sides of the triangle are equal, then we say that:
PQ = 12√2
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Felix is purchasing a brownstone townhouse for $2,500,000. To obtain the mortgage, Felix is required to make a 18% down payment. Felix obtains a 30-year mortgage with an interest rate of 6.5%.
a) Determine the amount of the required down payment.
b) Determine the amount of the mortgage.
c) Determine the monthly payment for principal and interest.
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