V(t) = -$266.67t + $28,500 is the linear model that captures this situation.
What is a linear model?
In mathematics, a linear model is a mathematical function that has a constant rate of change between two variables. The general form of a linear model is given by:
y = mx + b
where "y" and "x" are variables, "m" is the slope of the line, and "b" is the y-intercept (the point where the line crosses the y-axis).
A line's slope is the ratio of change in y (vertical) to change in x. (horizontal). It denotes the pace at which y changes in relation to x. If the slope is upward, theIf the value is positive, the line ascends from left to right, while if it is negative, the line descends from left to right. A horizontal line has a slope of zero, but a vertical line has an indeterminate slope.
A line's y-intercept is the value of y when x is zero. It denotes the point at where the line intersects the y-axis.
We can build a linear model to characterise the car's value decline over time. Let V(t) be the car's worth t years after 2005. Then, using the two data points provided, we can construct two equations:
V(0) = $28,500 (the initial value in 2005)
V(3) = $27,700 (the value in 2008, 3 years later)
Because we are assuming
Because we have a straight line, we can write:
V(t) = mt + b
where m is the slope (annual rate of change) and b is the y-intercept (initial value).
We may use the two equations above to obtain the values of m and b:
V(0) = m(0) + b = $28,500 => b = $28,500
V(3) = m(3) + b = $27,700 = 3m + $28,500 = $27,700 = $27,700 = m = -$266.67/year
As a result, the linear model that best describes this circumstance is:
V(t) = -$266.67t + $28,500
This model reveals that the car's value depreciates at a rate of $266.67 per year, with a starting value of $28,500 in 2005. This methodology can be used to determine the worth of an automobile in any year after 2005.
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true or false? in the unit method of proportioning, the longest dimension of an object is set equal to one unit. the other units are then estimated as fractions of that unit.
The given statement "In the unit method of proportioning, the longest dimension of an object is set equal to one unit." is False because the unit method of proportioning does not require the longest dimension.
In the unit method of proportioning, a chosen dimension of an object is set equal to one unit, and then all other dimensions are expressed in terms of that unit, regardless of whether it is the longest dimension or not.
For example, if a rectangle has a width of 4 cm and a length of 6 cm, we could choose to set the length as the unit and express the width as a fraction of the unit: 4/6 or 2/3 of a unit.
Alternatively, we could choose to set the width as the unit and express the length as a fraction of the unit: 6/4. In either case, the longest dimension of the object is not necessarily the unit.
The unit method of proportioning is commonly used in art and design to help maintain consistent proportions between different elements of a composition. It allows for easy scaling and adjustment of proportions while preserving the overall relationships between the different elements.
Rather, any dimension can be chosen as the unit, and the other dimensions are expressed in terms of that unit.
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HELPPPPP DUE SOON!!!!
The distance between the points H (-9, 1), and K (-1, 8) in the coordinate plane, obtained using the distance formula is; Distance: 10.63
What is the distance formula?The distance formula is a formula that is used to find the distance between two points on the coordinate plane.
The specified points are; H = (-9, 1), and K = (-1, 8)
The distance formula can be used to calculate the distance between the points as follows;
The distance formula is; d = √((x₂ - x₁)² + (y₂ - y₁)²)
Where; (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
When, (x₁, y₁) = (-9, 1), and (x₂, y₂) = (-1, 8), we get;
d = √((-1 - (-9))² + (8 - 1)²) = √(8² + 7²) =
√(8² + 7²) = √(64 + 49) = √(113) ≈ 10.63 (rounded to the nearest hundredth)
The distance between the points is about 10.63 units
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annual starting salaries for college graduates with degrees in business administration are generally expected to be between $42,000 and $59,800. assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. (round your answers up to the nearest whole number.) what is the planning value for the population standard deviation? (a) how large a sample should be taken if the desired margin of error is $600? (b) how large a sample should be taken if the desired margin of error is $200?
The planning value for the population standard deviation ,a sample size of 677 graduates is needed to estimate the population mean starting salary with a margin of error of $200.
We need to use the range of the expected starting salaries, which is between $42,000 and $59,800. The formula for calculating the planning value is:
Planning value = (range of salaries) / (6)
Therefore, the planning value for the population standard deviation is:
Planning value =[tex]($59,800 - $42,000) / (6) = $2,967[/tex]
To determine the sample size needed for a desired margin of error, we need to use the following formula:
Sample size = (Z-score)^2 * (planning value)^2 / (margin of error)^2
For a margin of error of $600 and a 95% confidence level, the Z-score is 1.96. Plugging in the values, we get:
Sample size =[tex](1.96)^2 * ($2,967)^2 / ($600)^2 = 113[/tex]
Therefore, a sample size of 113 graduates is needed to estimate the population mean starting salary with a margin of error of $600.
For a margin of error of $200, the Z-score is still 1.96. Plugging in the new margin of error, we get:
Sample size =[tex](1.96)^2 * ($2,967)^2 / ($200)^2 = 677[/tex]
Therefore, a sample size of 677 graduates is needed to estimate the population mean starting salary with a margin of error of $200
In summary, the planning value for the population standard deviation is $2,967. The sample size needed for a margin of error of $600 is 113, while the sample size needed for a margin of error of $200 is 677. These calculations can help organizations determine the appropriate sample size needed to accurately estimate the starting salaries of business administration graduates.
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when a study sample shows representativeness, what can be concluded about the study? group of answer choices the study results show evidence of sampling bias the study used strict inclusion and exclusion criteria to limit the sample size the study is most likely not generalizable because the sample was obtained using specific inclusion criteria. the study is most likely generalizable, with results that can be applied to the target population
When a study sample is representative of the target population, it allows for the results to be generalizable, meaning they can be applied to the broader population.
This is an important aspect of research, as it ensures the study's findings are relevant and useful beyond the specific sample studied.
When a study sample shows representativeness, it means that the sample accurately reflects the characteristics of the target population.
In this case, the study is most likely generalizable, with results that can be applied to the target population.
To achieve representativeness, researchers often use random sampling techniques, which help minimize the potential for sampling bias.
Sampling bias occurs when certain groups within the target population are over- or under-represented in the sample, which can lead to inaccurate conclusions.
In contrast, if a study used strict inclusion and exclusion criteria to limit the sample size or relied on specific inclusion criteria, it could result in a sample that is not representative of the target population.
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the edges of a cube increase at a rate of 2 centimeters per second. how fast is the volume changing when the length of each cube edge is 50 centimeters ?
The required volume of the cube is increasing at a rate of 15,000 cubic centimeters per second when the length of each edge is 50 centimeters and the edges are increasing at a rate of 2 centimeters per second.
Let us consider V be the volume of the cube,
And s be the length of one edge of the cube.
Volume of a cube is equal to,
V = s^3
To find how fast the volume is changing with respect to time,
Use the chain rule of differentiation,
dV/dt = dV/ds × ds/dt
where dV/dt is the rate of change of volume with respect to time,
dV/ds is the rate of change of volume with respect to the length of one edge of the cube,
And ds/dt is the rate of change of the length of one edge of the cube with respect to time.
ds/dt = 2 cm/s,
find dV/dt when s = 50 cm.
First, find dV/ds,
dV/ds = 3s^2
Then, we can plug in s = 50 cm,
dV/ds = 3(50)^2
= 7500 cm^2
Finally, we can plug in the values we have to find dV/dt,
dV/dt = (dV/ds) × (ds/dt)
= 7500 cm^2/s × 2 cm/s
= 15,000 cm^3/s
Therefore, the volume of the cube is increasing at a rate of 15,000 cubic centimeters per second .
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what is the margin of error for a 95% confidence interval for the proportion of all employees at this firm who are dissatisfied
The margin of error for a 90% confidence interval for the proportion of all employees dissatisfied with their jobs, based on a survey of 200 employees where 44% reported dissatisfaction, is 0.068.
We can use the formula for the margin of error for a proportion:
ME = zsqrt((p_hat(1-p_hat))/n)
where z is the z-score associated with the desired level of confidence (90% in this case), p_hat is the sample proportion (0.44), n is the sample size (200), and sqrt is the square root.
From a standard normal distribution table, the z-score for a 90% confidence level is approximately 1.645.
Plugging in the values, we get:
ME = 1.645sqrt((0.44(1-0.44))/200)
ME ≈ 0.068
So the margin of error for a 90% confidence interval is approximately 0.068 or 0.068/1= 0.068 = 0.068 = 6.8% (rounded to 3 decimal places).
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--The given question is incomplete, the complete question is given
"A human resources consulting firm conducted a survey of 200 employees to determine how dissatisfed they were with their jobs. 44% of the employees said they were dissatisfied, what is the margin of error for a 90% confidence interval for the proportion of all employees that are dissatisfied with their jobs? Answer to 3 decimal places"--
Roxy has a box of pens. He has 11 black pens, 8 blue pens, and 6 red pens. He randomly selects a pen from the box. Describe the probability that the pen he selects is blue, using a number or a number range.
Step-by-step explanation:
The total number of pens in the box is:
Total number of pens = 11 black pens + 8 blue pens + 6 red pens
Total number of pens = 25 pens
The probability of Roxy selecting a blue pen can be expressed as the ratio of the number of blue pens to the total number of pens:
Probability of selecting a blue pen = Number of blue pens / Total number of pens
Probability of selecting a blue pen = 8 / 25
So, the probability that the pen Roxy selects is blue is 8/25 or approximately 0.32 (rounded to two decimal places).
Answer:8/25
Step-by-step explanation:
Mackenzie measured a line to be 5.3 inches long. If the actual length of the line is 5.4 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
The percent error of the measurement is 1.9%.
What is the percent error?
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error. Measurement mistakes or computation machine precision can generate an approximation error.
Here, we have
Given: Mackenzie measured a line to be 5.3 inches long. If the actual length of the line is 5.4 inches.
We have to find the percent error of the measurement.
If the actual length of the line is 5.4 inches
So, the difference in length of the line = 5.4-5.3
= 0.1
Now, the percent error = Difference in length of line/Actual length × 100
= 0.1/5.3 × 100
= 0.01887 × 100
= 1.9 %
Hence, the percent error of the measurement is 1.9%.
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suppose that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). consider a random sample of 200 shafts, and let x denote the number among these that are nonconforming and can be reworked. (round your answers to four decimal places.) (a) what is the (approximate) probability that x is at most 30? 0.9649 0.9726 (b) what is the (approximate) probability that x is less than 30? 0.9429 0.9550 (c) what is the (approximate) probability that x is between 15 and 25 (inclusive)?
The approximate probability that x is between 15 and 25 (inclusive) is 0.3026.
To solve this problem, we will use the binomial distribution, since we are dealing with a binary outcome (nonconforming vs. conforming) and a fixed sample size. Let p = 0.11 be the probability of a nonconforming shaft and q = 1 - p = 0.89 be the probability of a conforming shaft. Then, the probability mass function of x is given by:
P(X = x) = (200 choose x) * p^x * q^(200-x)
(a) To find the probability that x is at most 30, we can compute:
P(X ≤ 30) = Σ P(X = x) for x from 0 to 30
However, this is quite tiresome to tally by hand, so we can instead use a normal approximation to the binomial distribution. Specifically, if np and nq are both at least 10, then we can approximate the binomial distribution with a normal distribution with mean μ = np and standard deviation σ = sqrt(npq). In this case, we have np = 22 and nq = 178, both of which are at least 10.
Thus, we can approximate X with a normal distribution:
[tex]X ~ N(mu, σ^2) = N(22, 3.8004)[/tex]
Then, we can compute the probability that X is at most 30 by standardizing and using the standard normal distribution:
[tex]P(X ≤ 30) ≈ P(Z ≤ (30 - mu) / σ) = P(Z ≤ (30 - 22) / 1.9488) = P(Z ≤ 4.1142) = 0.9997[/tex]
(b) To find the probability that x is less than 30, we can use the same normal approximation and compute:
[tex]P(X < 30) ≈ P(Z < (30 - mu) / σ) = P(Z < (30 - 22) / 1.9488) = P(Z < 4.1142) = 0.9997[/tex]
(c) To find the probability that x is between 15 and 25 (inclusive), we can either use the binomial distribution directly or use the normal approximation as before:
P(15 ≤ X ≤ 25) = Σ P(X = x) for x from 15 to 25
However, we can use the normal approximation instead. Using the same approach as before, we get:
[tex]P(15 ≤ X ≤ 25) ≈ P((15 - μ) / σ ≤ Z ≤ (25 - μ) / σ) = P(-3.0806 ≤ Z ≤ -0.5145) = P(Z ≤ -0.5145) - P(Z ≤ -3.0806) = 0.3035 - 0.0009 = 0.3026[/tex]
Therefore, the approximate probability that x is between 15 and 25 (inclusive) is 0.3026.
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The scatter plot to the right shows the cost (y), in dollars, of orange trees based on their ages (x), in years. Based on the scatter plot, which equation represents the line of best fit for the cost of the orange trees?
A y=15.7x
B y=11.8x+29.2
C y=15.7+40.0
D y=11.8x
Answer:
The answer to your problem is, B. y=11.8x+29.2
Step-by-step explanation:
Determine the line of the best fit grpahically
Find the problem:
y = 11 x 8x + 29 x 2 B.
a robot spins the spinner shown twice. assume that the outcomes 1, 2, 3, and 4 are equally likely for each spin. what is the probability that the sum of the two outcomes will be 6?
The probability of rolling a six when spinning the spinner shown twice, assuming that the outcomes 1, 2, 3, and 4 are equally likely for each spin is 3/16.
A robot spins the spinner shown twice. Assume that the outcomes 1, 2, 3, and 4 are equally likely for each spin.
What is the probability that the sum of the two outcomes will be 6?
The probability that the sum of the two outcomes will be 6 when a robot spins the spinner shown twice, assuming that the outcomes 1, 2, 3, and 4 are equally likely for each spin, is 2/16 or 1/8.However, before determining the probability, we should first determine the possible outcomes of the spinner. When a spinner is spun twice, the possible outcomes are: 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, and 44.There are 16 possible outcomes. Of these 16 possible outcomes, only two add up to six. These two possible outcomes are: 33,24,42. Therefore, the probability of rolling a six is 3/16 .
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Help me please, how to find perimeter
it depends on the shape. There are yt videos you could watch that would explain how to solve the perimeters of that specific shape
OK what are you wanting to find the perimeter to?
Add up all the sides:
EX:
Square: 3+3+3+3
Rectangle: 4+2+4+2
Triangle [Equilateral]: 2+2+2
You get the gist?
Your parents allow you to have Internet access on your cell phone as long as you prepay the bill. If your bill is $19.60 per week, how much would you have to save per day to pay the bill? Describe the process you use to solve the problem.
PLS HURRY HTIS IS A PROJECT QUESTON
srry for spamming i need to get this done
After answering the presented question, we can conclude that To pay the $19.60 weekly cost for your cell phone Internet access, you would need to save $2.80 (or $2.86 if you round up) per day.
What is internet?The internet is a vast network of interconnected computers and devices that communicate with each other using a common set of protocols and technologies. It allows people to share information, communicate with each other, and access a wide range of digital services and resources. The internet is a global network that spans across the world, connecting people and businesses across different geographic locations and time zones. It has revolutionized the way people communicate and access information, enabling unprecedented levels of connectivity, collaboration, and innovation.
You can use the following steps to calculate how much you need to save per day to pay the bill:
Divide your weekly bill by the number of days in a week to see how much you need to save per day:
$19.60 ÷ 7 = $2.80
You can round up to the closest cent if you want to be more precise:
$19.60 divided by 7 equals $2.80 per day
$2.80 rounded up to $2.86
To pay the $19.60 weekly cost for your cell phone Internet access, you would need to save $2.80 (or $2.86 if you round up) per day.
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EXPANDING BRACKETS -
2 (3x + 7)
Answer:
[tex] \sf \: 6x + 14 [/tex]
Step-by-step explanation:
Now we have to,
→ Simplify the given expression.
The property we use,
→ Distributive property.
The expression is,
→ 2(3x + 7)
Let's simplify the expression,
→ 2(3x + 7)
→ 2(3x) + 2(7)
→ (2 × 3)x + 14
→ 6x + 14
Hence, the answer is 6x + 14.
A catalog of scientific equipment states that the lens of a particular telescope has a
circumference of 12.56 feet. What is the lens's diameter?
Use 3.14 for л. If necessary, round your answer to the nearest hundredth.
feet
The diameter of the lens of a particular telescope is approximately 4 feet.
What is circumference?The circumference of a circle is defined as the linear distance around it. In other words, if a circle is opened to form a straight line, then the length of that line will be the circle's circumference.
Equation:The circumference of a circle is given by the formula:
C = πd
where C is the circumference, d is the diameter, and π is approximately equal to 3.14.
In this case, we are given that the circumference of the lens is 12.56 feet. So we can plug in the values:
12.56 = 3.14d
To solve for d, we need to isolate it on one side of the equation. We can do this by dividing both sides by 3.14:
d = 12.56/3.14
Simplifying, we get:
d ≈ 4
Therefore, the diameter of the lens is approximately 4 feet
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Can someone help me ASAP it’s due tomorrow. I will give brainliest if it’s all done correctly. Show work.
Answer:
The last option/option D/2 over 7/(2/7)
Step-by-step explanation:
There are 3 $10 bills.
There are 4 $1 coins.
3/7=Pull out one $10 dollar bill
However, it is less likely to get the same answer twice.
A Root Graph (or what you like to call it):
As you can see, there are 3 instances where you wound up with 10 BOTH ROUNDS. There are also an additional 11 that DON'T wound up with 10 in both rounds. The ratio is 3/11. 3 divided by 11 is 0.27 (or 0.28). The last option, 2/7 is the one that I think is the answer. It is because 2 divided by 7=0.28...
Therefore our answer is the last option?
In how many years will the population of a colony be 92,610 from 80,000 at the population growth rate of 5% per annum? If the growth rate is 2% less than before, what would be the difference in population for the same time? Find it.
Answer:
To find the number of years it will take for the population of the colony to grow from 80,000 to 92,610 with a growth rate of 5% per annum, we can use the formula for compound interest:
Final Population = Initial Population * (1 + Growth Rate) ^ Number of Years
92,610 = 80,000 * (1 + 0.05) ^ t
Now, we can solve for t:
(92,610 / 80,000) = (1.05) ^ t
1.157625 = (1.05) ^ t
To find t, we can use logarithms:
t = log(1.157625) / log(1.05)
t ≈ 2.967
So, it will take approximately 2.967 years for the population to grow from 80,000 to 92,610 at a 5% growth rate.
Now, let's consider a 2% lower growth rate (5% - 2% = 3%). We can use the same formula to find the final population after the same time (2.967 years):
Final Population = Initial Population * (1 + Growth Rate) ^ Number of Years
Final Population = 80,000 * (1 + 0.03) ^ 2.967
Final Population ≈ 80,000 * 1.09364
Final Population ≈ 87,491.2
To find the difference in population for the same time, we can subtract the population with the lower growth rate from the population with the higher growth rate:
Difference in population = 92,610 - 87,491.2
Difference in population ≈ 5,118.8
So, the difference in population for the same time with a 2% lower growth rate would be approximately 5,118.8.
The school auditorium seats 350
students. There are 309
students already seated. Write
and solve an inequality that
represents the additional number
of students that can be seated.
As a result, more students than or equal to 41 can be added to the current student body by inequality.
what is inequality defined as?A mathematical statement known as an inequality compares two expressions using one of the following symbols:, >,, or.
For instance:
x + 2 < 5
2y - 3 > 7
3z ≤ 9
4w + 1 ≥ 13
Now,
The disparity that indicates the extra students who can be seated is as follows:
350 - 309 ≤ x
where x is the maximum number of extra pupils who can sit in a classroom.
When we simplify this inequality, we obtain:
41 ≤ x
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a classmate walks into class and states that he has an extra ticket to a festival on friday night. he asks everyone in the class to put their name on a piece of paper and put it in a basket. he plans to draw from the basket to choose the person who will attend the festival with him. if there are 22 other people in class that night, what is your chance of being chosen to attend the festival? round your answer to four decimal places, if necessary.
Your chance of being chosen to attend the festival is approximately: Probability = 1 / 23 ≈ 0.0435 or 4.35% when rounded to four decimal places.
To determine your chance of being chosen to attend the festival, you need to find the probability of your name being
drawn from the basket.
There are 22 other people in class, and each person, including you, will have their name on a piece of paper.
Total number of names in the basket = 22 (other people) + 1 (you) = 23
Since each person has an equal chance of being chosen, the probability of your name being drawn is:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Probability = 1 (your name) / 23 (total names)
So, your chance of being chosen to attend the festival is approximately:
Probability = 1 / 23 ≈ 0.0435 or 4.35% when rounded to four decimal places.
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PLEASE HELP!! 50 POINTS!! if you just take the points without actually helping you will be forever cursed within my mind and never forgiven.
Christopher borrows 7,500$ to build a garage. He agrees to pay 475$ a month for 24 months but pays off the loan after 18 months.
Part A: Determine the amount of unearned interest.
Part B: Determine the amount needed to repay the loan using the Rule of 78.
Part C: Show your work to support your answers to Part A and Part B.
To solve the problem, we can use the formula for the future value of an annuity:
FV = PMT * ( (1 + r)^n - 1 ) / r
where:
- PMT is the periodic payment
- r is the periodic interest rate
- n is the number of periods
In this case,
- PMT = $475 (the monthly payment)
- r = the monthly interest rate
- n = 24 (the number of months in the agreement)
We first need to calculate the monthly interest rate. We can find this by dividing the yearly interest rate by 12 months:
r = 18% / 12 months = 0.015
Now we can calculate the future value (FV) of the annuity using the above formula:
FV = $475 * ( (1 + 0.015)^24 - 1 ) / 0.015 = $13,237.19
This is the amount that Christopher would owe after 24 months if he made monthly payments of $475.
However, Christopher pays off the loan after 18 months. To find out how much he owes at this point, we can calculate the future value after 18 months:
FV = $475 * ( (1 + 0.015)^18 - 1 ) / 0.015 = $10,198.66
So, after 18 months, Christopher owes approximately $10,198.66.
Circle T is dilated to create circle T. The radius of circle T is 4 units, while the diameter of circle
Tis 10 units. Find the circumference and area of both figures measured to the nearest hun-
dredth. Use 3.14 for T. Use the correct units for all final answers.
Calculate the area of circle T': A
78.50 units²
O 157 units²
O100 units²
O 31.40 units²
Answer:
radius of circle T/smaller circle = 4 units
Diameter of larger circle is 10units
radius of larger circle = D/2
= 10/2 = 5units
CIRCUMFERENCE OF SMALLER CIRCLE =
2πr = 2 × 3.14 × 4
= 25.12 units
Area of smaller Circle =
πr² = 3.14 × 4 × 4
= 50.24 units²
CIRCUMFERENCE OF LARGER CIRCLE =
2πr = 2 × 3.14 × 5
= 31.4 units
Area of larger circle =
πr² = 3.14 × 5 × 5
= 78.5 units²
In ΔQRS, q = 940 cm, s = 720 cm and ∠S=45°. Find all possible values of ∠Q, to the nearest degree.
The measure of angle Q is equal to 40°.
What is triangle?A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry. In Geοmetry, triangles are the type οf pοlygοns, which have three sides and three vertices.
This is a twο-dimensiοnal figure with three straight sides. A triangle is cοnsidered a 3-sided pοlygοn. The sum οf all the three angles οf a triangle is equal tο 180°. The triangle is cοntained in a single plane. Based οn its sides and angle measurement, the triangle has six types.
Using Cos θ = adjacent/ Hypotenuse
Cos Q = 720/ 940
Cos Q = 36/47
Q = arccos 36/47
Q = 40.007793734°
Thus, The measure of angle Q is equal to 40°.
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A figure is drawn on the coordinate plane. Its points are located at D (-4, 4), E (4, 4), F (4, -2) and G (-4, -2). What is the difference between the perimeter and area of the figure.
The difference between the perimeter and area of the figure is -20 square units.
What is perimeter?In geometry, the perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape.
The figure is a rectangle with sides DE and FG measuring 8 units, and sides EF and GD measuring 6 units.
To find the perimeter of the figure, we can add up the lengths of all four sides:
Perimeter = DE + EF + FG + GD
Perimeter = 8 + 6 + 8 + 6
Perimeter = 28
To find the area of the figure, we can use the formula for the area of a rectangle:
Area = length * width
Area = DE * EF
Area = 8 * 6
Area = 48
Therefore, the difference between the perimeter and area of the figure is:
Perimeter - Area = 28 - 48
Perimeter - Area = -20
The difference between the perimeter and area of the figure is -20 square units.
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Simon and Luke shared a pizza. Simon ate of the pizza. Luke ate of the pizza. Which model is shaded to show the fraction of the pizza that both boys ate?
A 1/4
B 2/8
C 7/12
D 7/16
The model shaded to show the fraction of the pizza that both boys ate is option C, 7/12.
To find the fraction of the pizza that both boys ate, we need to find the intersection of the two fractions that represent the amount each boy ate.
We can represent each boy's portion of the pizza using the following models:
Simon = 3/12
Luke = 4/12
When these fractions are added, we have
Total = 3/12 + 4/12
Evaluate the sum
Total = 7/12
Hence, the model is 7/12
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will mark brainliest!!!!
Find the value of each variable.
x =
y =
(look at picture)
Check the picture below.
))
Which operation should be completed first to find the value of the expression
below?
6-3
12+ 30 (6-3) + 1
12+ 30
306
3+1
Don
Answer:
(6-3)
Step-by-step explanation:
Three numbers whose sum is 26 are in GP.If 5,9 and 5 are added to them respectively, then the three numbers are in AP. Find the numbers.
The three numbers are:
(-1 + √(97))/2, (-1 ± √(97))/2, (-1 ± 7√(97))/2
What is an arithmatic progression?
An arithmetic progression is a sequence of numbers in which each term after the first is obtained by adding a fixed constant to the preceding term. The fixed constant is called the common difference, denoted by d.
Let the three numbers in the GP be a/r, a, and ar, where a is the middle term.
Then we have:
a/r + a + ar = 26 (sum of GP)
(a/r + 5) + (a + 9) + (ar + 5) = 3(a + 4) (sum of AP)
Simplifying the second equation, we get:
a(r - 1) = 3
Substituting this into the first equation, we get:
a/r + a + ar = 26
1/r + 1 + r = 26/a
r^2 + r - 26/a = 0
Solving for r using the quadratic formula, we get:
r = (-1 ± √(1 + 104/a))/2
Since r > 0 (because the terms are in GP), we take the positive root:
r = (-1 + √(1 + 104/a))/2
Substituting this into the equation a(r - 1) = 3, we get:
a(-1 + √(1 + 104/a))/2 - a = 3
-a + a √(1 + 104/a) - 2 = 0
a √(1 + 104/a) = -a + 2
a² (1 + 104/a) = a² - 4a + 4
104a = 4a² - 4a + 4
a² - a + 1 = 26
(a - 1/2)² + 3/4 = 26
(a - 1/2)² = 97/4
a - 1/2 = ±√(97)/2
a = (1 ± √(97))/2
Since the terms are in GP, we can use the value of a to find the other two terms:
a/r = (1 ± √(97))/(2(-1 + √(1 + 104/a))/2) = (-1 ± √(97))/2
ar = (1 ± √(97))/(2(-1 - √(1 + 104/a))/2) = (-1 ± 7√(97))/2
Therefore, the three numbers are:
(-1 + √(97))/2, (-1 ± √(97))/2, (-1 ± 7√(97))/2
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suppose that 5% of teachers at a university attended a conference. if 4000 teachers are enrolled at the university, about how many teachers attended the conference?
Answer: 200 teachers attended the conference
Step-by-step explanation:
To answer this question, we will find 5% of 4,000. A percent divided by 100 becomes a decimal, and "of" means multiplication in mathematics.
5% / 100 = 0.05
4,000 * 0.05 = 200 teachers attended the conference
The answer is 200
If 5% of teachers at a university attended a conference and 4000 teachers are enrolled at the university, about 200 teachers attended the conference. What is the problem asking for? The problem is asking us to calculate how many teachers attended a conference given that 5% of the total number of teachers at a university attended the conference and that the university has 4000 teachers .What is the formula for percentage? The formula for percentage is given by:(Part/Whole)*100Let T be the total number of teachers at the university, and let x be the number of teachers that attended the conference. We know that 5% of teachers at a university attended a conference, therefore:(5/100)*T = x,. Given that there are 4000 teachers in the university, we can substitute this value into the equation: (5/100)*4000 = x. Simplifying the equation, we get: x = 0.05 * 4000x = 200.
Therefore, about 200 teachers attended the conference.
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help with this problem
Answer:
PQ = 165.60m
Step-by-step explanation:
Since triangles are similar
PQ/70 + 210 = 124.2/210
PQ = 124.2 (70 + 210)/210 = 165.60m
Naomi's bedroom is 6 meters long and 4 meters wide. Starting at the far left corner, Naomi walks down the length, across the width, and then diagonally back to the far left corner. How far does Naomi walk? If necessary, round to the nearest tenth.
Naomi walks a total of 6 + 4 + 7.2 ≈ 17.2 meters.
How to calculate?
Naomi walks the length of the room, which is 6 meters, then across the width, which is 4 meters.
Using the Pythagorean theorem, the length of the diagonal can be found:
diagonal = √(6²2 + 4²2)
diagonal = √(36 + 16)
diagonal = √52
diagonal ≈ 7.2 meters
Therefore, Naomi walks a total of 6 + 4 + 7.2 ≈ 17.2 meters.
The Pythagorean theorem is a fundamental concept in mathematics that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
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