In order for a triangle to be acute, the relationship that c² must have with a² + b² is c² < a² + b².
An acute triangle is a triangle in which all three angles are acute angles, which means they are less than 90 degrees. In other words, an acute triangle is a triangle with three acute angles.
To understand why the relationship between c^2 (the square of the longest side) and a^2 + b^2 (the sum of the squares of the other two sides) is important in determining whether a triangle is acute, we need to delve into the concept of the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Mathematically, it can be expressed as c^2 = a^2 + b^2, where c represents the hypotenuse, and a and b represent the other two sides.
In an acute triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side.
This can be visualized as follows: If we were to draw a right triangle with the shorter sides represented by segments a and b, and the longest side represented by segment c, the acute triangle would be formed by making the length of segment c shorter than the length determined by the Pythagorean theorem. This ensures that the angle opposite to the longest side remains acute.
On the other hand, if c^2 were equal to a^2 + b^2, we would have a right triangle, not an acute triangle. If c^2 were greater than a^2 + b^2, we would have an obtuse triangle since the angle opposite to the longest side would be greater than 90 degrees.
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A lot of people that live in San Luis AZ have a job at Yuma or nearby the city. For this reason, Yuma county officials are considering expanding the highway between San Luis and Yuma. Since they will need a considerable amount of money to build the new highway, they want to make sure that at least 65% of employed adults that live in San Luis, travel to Yuma or nearby to get to their workplaces. From the 11,559 employed adults that live in San Luis, a random sample of 400 people was taken and 290 said that they work at Yuma or nearby. Assume that the Yuma county officials want to build a 95% confidence interval to estimate the proportion of employed adults that live in San Luis and travel to Yuma or nearby to get to their workplaces.
Calculate the margin of error for this sample, assuming a level of confidence of 95%.
Construct a 95% confidence interval for the employed adults that live in San Luis AZ and travel to Yuma or nearby to get to their workplaces.
Explain the meaning of "95% level of confidence", in context.
Interpret the confidence interval you created in question (b).
Given the confidence interval you calculated on (b), is it worth it to invest the money on this new highway?
Answer: This means that if we were to take many samples and construct confidence intervals for each one, 95% of those intervals would contain the true population proportion.
Step-by-step explanation:
a) To calculate the margin of error for this sample, we can use the formula:
Margin of error = Z√(p(1-p)/n)
where:
Z = the z-score corresponding to the level of confidence (95% confidence interval corresponds to a z-score of 1.96)
p = the sample proportion (290/400 = 0.725)
n = the sample size (400)
Plugging in these values, we get:
Margin of error = 1.96√(0.725(1-0.725)/400) ≈ 0.049
So, the margin of error for this sample is approximately 0.049 or 4.9%.
b) To construct a 95% confidence interval for the proportion of employed adults that live in San Luis and travel to Yuma or nearby to get to their workplaces, we can use the formula:
Confidence interval = p ± Z*(√(p*(1-p)/n))
where:
p = the sample proportion (0.725)
Z = the z-score corresponding to the level of confidence (1.96)
n = the sample size (400)
Plugging in these values, we get:
Confidence interval = 0.725 ± 1.96*(√(0.725*(1-0.725)/400)) ≈ (0.678, 0.772)
Therefore, we can say with 95% confidence that the proportion of employed adults that live in San Luis and travel to Yuma or nearby to get to their workplaces is between 0.678 and 0.772.
c) The "95% level of confidence" means that if we were to repeat this sampling process many times and construct 95% confidence intervals for each sample,
we would expect that 95% of those intervals would contain the true population proportion of employed adults that live in San Luis and travel to Yuma or nearby to get to their workplaces.
d) The confidence interval we constructed in (b) tells us that we can be 95% confident that the true population proportion of employed adults that live in San Luis and travel to Yuma or nearby to get to their workplaces is between 0.678 and 0.772.
This means that if we were to take many samples and construct confidence intervals for each one, 95% of those intervals would contain the true population proportion.
Based on this interval, we can conclude that it is likely that at least 65% of employed adults that live in San Luis travel to Yuma or nearby to get to their workplaces, as the lower bound of the interval is above 65%.
e) Whether or not it is worth it to invest in the new highway depends on many factors beyond just the proportion of employed adults that live in San Luis and travel to Yuma or nearby to get to their workplaces.
The decision to invest in the highway should be based on a careful cost-benefit analysis that takes into account factors such as the expected traffic volume, the expected economic benefits, and the cost of the project.
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15 Points! 15 Points 15 Points!
A student is graduating from college in 12 months but will need a loan in the amount of $10,720 for the last two semesters. The student may receive either an unsubsidized Stafford Loan or a PLUS Loan. The terms of each loan are:
Unsubsidized Stafford Loan: annual interest rate of 5. 95%, compounded monthly, and a payment grace period of six months from time of graduation
PLUS loan: annual interest rate of 6. 55%, compounded monthly, with a balance of $11,443. 63 at graduation
Which loan will have a lower balance, and by how much, at the time of repayment?
The Stafford loan will have a lower balance by $485. 06 at the time of repayment.
The PLUS loan will have a lower balance by $485. 06 at the time of repayment.
The Stafford loan will have a lower balance by $274. 54 at the time of repayment.
The PLUS loan will have a lower balance by $274. 54 at the time of repayment
The Stafford loan will have a lower balance by $272.54 at the time of repayment.
For the Stafford Loan, the principal is $10,720 and the interest rate is 5.95% compounded monthly, so the monthly interest rate is 0.0595/12 = 0.00495833.
After 12 months, the balance of the loan will be:
$10,720(1 + 0.00495833)¹² = $11,204.60
After the time of six-month grace period, the balance will be:
$11,204.60(1 + 0.00495833)⁶ = $11,689.66
For the PLUS Loan, the principal is $11,443.63 and the interest rate is 6.55% compounded monthly, so the monthly interest rate is 0.0655/12 = 0.00545833.
After 12 months, the balance of the loan will be:
$11,443.63(1 + 0.00545833)¹² = $11,962.20
Therefore, the Stafford Loan will have a lower balance at the time of repayment by:
$11,962.20 - $11,689.66 = $272.54
Hence, the Stafford loan will have a lower balance by $272.54 at the time of repayment.
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Find the average rate of change of the function over the given interval: f (x ) = 2^x + 1, [0, 2]
The average rate of change on the given interval is R = 3/2
How to find the average rate of change?To find the average rate of change on an interval [a, b], we need to use the formula:
R = (f(b) - f(a))/(b - a)
Here we have:
[tex]f(x) = 2^x + 1[/tex]
And the interval is [0, 2]
Then:
[tex]f(0) = 2^0 + 1 = 2\\\\f(2) = 2^2 + 1 = 5[/tex]
Then we will get.
R = (5 - 2)/(2 - 0) = 3/2
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What is the inverse of y = 2^(x - 3)?
show how you got the answer
Answer:
(3-x)^2=y
Step-by-step explanation:
The temperature at a point (x, y, z) is given byT(x, y, z) = 10e¯2x² − y² − 3z².In which direction does the temperature increase fastest at the point (1, 3, 1)?Express your answer as a UNIT vector.
The direction of fastest increase in temperature at the point (1, 3, 1) is given by the unit vector (-5/sqrt(10) , -3/sqrt(10) , -9/sqrt(10)).
To find the direction of fastest increase in temperature at the point (1, 3, 1), we need to find the gradient of the temperature function T(x, y, z) at that point.
The gradient of a function is a vector that points in the direction of steepest increase, and its magnitude is the rate of change in that direction. So, we can find the gradient vector ∇T(x, y, z) as follows:
∇T(x, y, z) = ( ∂T/∂x , ∂T/∂y , ∂T/∂z )
=[tex]( -20xe^(-2x^2-y^2-3z^2) , -2ye^(-2x^2-y^2-3z^2) , -6ze^(-2x^2-y^2-3z^2) )[/tex]
Therefore, at the point (1, 3, 1), the gradient of T(x, y, z) is:
∇T(1, 3, 1) = [tex]( -20e^(-8) , -6e^(-8) , -18e^(-8) )[/tex]
To find the direction of fastest increase, we need to normalize this vector to a unit vector. The magnitude of the gradient vector is:
|∇T(1, 3, 1)| = sqrt( (-[tex]20e^(-8))^2 + (-6e^(-8))^2 + (-18e^(-8))^2 )[/tex]
= sqrt( 640e^(-16) )
= 8e^(-8) sqrt(10)
So, the unit vector in the direction of fastest increase is:
( -20e^(-8) / (8e^(-8) sqrt(10)) , -6e^(-8) / (8e^(-8) sqrt(10)) , -18e^(-8) / (8e^(-8) sqrt(10)) )
= ( -5/sqrt(10) , -3/sqrt(10) , -9/sqrt(10) )
Therefore, the direction of fastest increase in temperature at the point (1, 3, 1) is given by the unit vector (-5/sqrt(10) , -3/sqrt(10) , -9/sqrt(10)).
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Zachary brought $38. 25 to the state fair. He bought a burger, a souvenir, and a pass. The burger was 1 6 as much as the souvenir, and the souvenir cost 3 4 the cost of the pass. Zachary had $4. 50 left over after buying these items
It is not possible for Zachary to buy a burger, a souvenir, and a pass with the given prices and have $4.50 left over.
What was the total cost of the burger, souvenir, and pass that Zachary bought at the state fair, if he had $4.50 left over and the burger was 1/6 as much as the souvenir, while the souvenir cost 3/4 the cost of the pass?Let's represent the cost of the souvenir as x.
Then, according to the problem:
The cost of the burger is 1/6 of the cost of the souvenir, which is (1/6)x.
The cost of the pass is 4/3 times the cost of the souvenir, which is (4/3)x.
The total cost of the burger, souvenir, and pass is equal to the amount Zachary brought to the state fair, which is $38.25.
Zachary had $4.50 left over after buying these items, so the cost of the burger, souvenir, and pass must be $33.75.
Putting all this information together, we can write an equation:
(1/6)x + x + (4/3)x = 33.75
Simplifying the left side of the equation:
(7/6)x = 33.75
Multiplying both sides by 6/7:
x = 30
Therefore, the cost of the souvenir is $30, the cost of the burger is (1/6) * 30 = $5, and the cost of the pass is (4/3) * 30 = $40.
To check that these values are correct, we can add them up:
30 + 5 + 40 = 75
And we can subtract the total cost from the amount Zachary brought:
38.25 - 75 = -36.75
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An open top box is made by cutting out 2 in by 2 in squares from the corners of a large square piece of cardboard. Using the picture as a guide, find an expression for the surface area of the box. If the surface area is 609 in², find the length of x. Remember, there is no top.
The length of the variable x, obtained from the formula for the surface area of a solid about 10.63 inches
What is the surface area of a solid object?
The surface area of a solid object is the area of the outside surface of the object.
The dimensions of of the open top box with the square corners 2 in by 2 in cut from the corners are;
Length of the box, L = x - 4 inches
Width of the box, W = x - 4 inches
Height of the box, H = 2 inches
The surface area of the box is therefore;
Volume, A = L × W + 2 × L × H + 2 × W × H
Plugging in the expressions for the length, width and height of the box, the surface area = (x - 4) × (x - 4) + 2 × 2 × (x - 4) + 2 × 2 × (x - 4) = 9·x² - 40·x + 16
The surface area of the box, A = 9·x² - 40·x + 16
Second part;
When the surface area = 609 in², we get;
A = 609 = 9·x² - 40·x + 16
9·x² - 40·x + 16 - 609 = 9·x² - 40·x - 593 = 0
x = (20 + √(5737))/9 ≈ 10.63, and x = (20 - √(5737))/9 ≈ -6.19
The length x ≈ 10.63 inches
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An investor who dabbles in real estate invested 1. 1 million dollars into two land investments. On the fi st investment, Swan Peak, her return was a 110% increase on the money she invested. On the second investment, Riverside Community, she earned 50% over what she invested. If she earned $1 million in profits, how much did she invest in each of the land deals?
The investor invested $500,000 in Swan Peak and $600,000 in Riverside Community.
Let's denote the amount invested in Swan Peak as x and the amount invested in Riverside Community as y.
According to the given information:
1. The return on investment in Swan Peak was a 110% increase, which means the total return was 100% + 110% = 210% of the initial investment.
2. The return on investment in Riverside Community was 50% over the initial investment, which means the total return was 100% + 50% = 150% of the initial investment.
We are also given that the investor earned $1 million in profits.
Based on the above information, we can set up the following equations:
1.1 million = 2.1x + 1.5y (equation 1) [This equation represents the total profits earned by the investor.]
x + y = 1.1 million (equation 2) [This equation represents the total amount invested.]
To solve these equations, we can use substitution or elimination method. Let's use the elimination method:
Multiply equation 2 by 2.1 to make the coefficients of x in both equations equal:
2.1x + 2.1y = 2.31 million (equation 3)
Now, subtract equation 1 from equation 3 to eliminate x:
(2.1x + 2.1y) - (2.1x + 1.5y) = 2.31 million - 1.1 million
0.6y = 1.21 million
Divide both sides by 0.6:
y = 2.01 million / 0.6
y ≈ 3.35 million
Substitute the value of y into equation 2:
x + 3.35 million = 1.1 million
x ≈ 1.1 million - 3.35 million
x ≈ -2.25 million
Since the amount invested cannot be negative, we discard the negative value.
Therefore, the investor invested approximately $500,000 in Swan Peak (x) and approximately $600,000 in Riverside Community (y).
Hence, the investor invested $500,000 in Swan Peak and $600,000 in Riverside Community.
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A veterinarian measures the weight of each puppy in a litter. She records the puppies' weights in pounds. Puppy Weights: 2. 9, 3. 0, 3. 1, 3. 1, 3. 2, 3. 3, 3. 3, 3. 4, 4. 4 The veterinarian removes the outlier of the data. By how many pounds, rounded to the nearest hundredth of a pound, will the mean of the data change with the removal of the outlier?
The mean of the puppy weights changes by 0.14 pounds.
To determine how the mean of the puppy weights changes with the removal of the outlier, follow these steps:
1. First, identify the outlier in the given data set: Puppy Weights: 2.9, 3.0, 3.1, 3.1, 3.2, 3.3, 3.3, 3.4, 4.4. The outlier is 4.4 as it is significantly higher than the rest of the values.
2. Calculate the mean with the outlier: Add all the weights and divide by the total number of puppies (9). (2.9+3.0+3.1+3.1+3.2+3.3+3.3+3.4+4.4)/9 = 29.7/9 = 3.3
3. Calculate the mean without the outlier: Remove the outlier (4.4) from the sum and divide by the new total number of puppies (8). (29.7 - 4.4)/8 = 25.3/8 = 3.1625
4. Calculate the change in mean by subtracting the mean without the outlier from the mean with the outlier, and round to the nearest hundredth of a pound: 3.3 - 3.1625 = 0.1375, which rounds to 0.14.
With the removal of the outlier, the mean of the puppy weights changes by 0.14 pounds.
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If the area around the cylinder is 64 cm² and the area of the top is 16 cm², what is the surface area of the cylinder?
help me please lol
The surface area of the cylinder is 96cm²
Calculating the surface area of the cylinder?From the question, we have the following parameters that can be used in our computation:
The area around the cylinder is 64 cm² The area of the top is 16 cm²Using the above as a guide, we have the following:
Surface area of the cylinder = The area around the cylinder + 2 * The area of the top
Substitute the known values in the above equation, so, we have the following representation
Surface area of the cylinder = 64 + 2 * 16
Evaluate
Surface area of the cylinder = 96
Hence, the surface area of the cylinder is 96cm²
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Nadia compares the weights, in grams, of some apples and oranges. She finds the median and
interquartile range of the weights.
Apple sample: median=150 interquartile range=8
Orange sample: median=130 interquartile range=11
1. Which sample has a greater typical value, or median?
2. Which sample has a greater variability, or spread?
3. According to these measures, is it possible the the heaviest piece of fruit in the two samples was an orange? Explain why or why not.
I need an answer soon
a) The apple sample has a greater typical value or median than the orange sample.
b) The orange sample has a greater variability or spread than the apple sample.
a) The median of the apple sample is 150 grams, while the median of the orange sample is 130 grams. Therefore, the apple sample has a greater typical value or median.
b) The interquartile range (IQR) of the apple sample is 8 grams, while the IQR of the orange sample is 111 grams. Therefore, the orange sample has a greater variability or spread.
c) It is possible that the heaviest piece of fruit in the two samples was an orange, as the orange sample has a larger range of weights than the apple sample. However, without knowing the maximum weight in each sample, we cannot say for certain whether the heaviest fruit was an orange or an apple.
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What is the current ratio of length to width for us paper money
The current ratio of length to width for US paper money is approximately 2.61 to 6.14 inches. This means that US paper money is roughly rectangular in shape, with a length that is about 2.61 times greater than its width.
The current size of US paper money is standardized by the Bureau of Engraving and Printing (BEP). According to the BEP, the current size of a US paper bill is 2.61 inches wide and 6.14 inches long. This size has remained the same since the 1920s, although earlier bills were larger.
The rectangular shape of US paper money makes it easy to handle and store, and the standardized size ensures that it can be easily recognized and processed by vending machines, bank machines, and other automated devices.
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Shirts are packed at random in two sizes, regular and extra-large. four shirts are selected from a box of 24 and checked for size. if there are 15 regular shirts in the box, find the probability that all 4 will be regular size.
The probability that all four shirts selected from the box of 24 will be regular size is 0.1367 or 13.67%.
Probability refers to the likelihood or chance of an event occurring. In this scenario, we are interested in finding the probability that all four shirts selected from the box of 24 will be regular size.
To determine this probability, we first need to find the total number of ways in which we can select four shirts from the box. This is known as the sample space and can be calculated using the combination formula, which is nCr = n!/(r!(n-r)!). In this case, we have 24 shirts and are selecting four, so the sample space is 24C4 = (24!)/(4!(24-4)!) = 10,626.
Next, we need to find the number of ways in which we can select four regular shirts from the 15 available. This can be calculated using the same combination formula, which is 15C4 = (15!)/(4!(15-4)!) = 1,455.
Finally, we can calculate the probability of selecting all four regular shirts by dividing the number of favorable outcomes (i.e., selecting four regular shirts) by the total number of possible outcomes (i.e., the sample space). So, the probability of selecting all four regular shirts is 1,455/10,626 = 0.1367 or 13.67%.
Therefore, the probability that all four shirts selected from the box of 24 will be regular size is 0.1367 or 13.67%.
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Circle 1 is centered at (-3,5) and has a radius of 10 units circle 2 is centered at (7,5) and has a radius of 4 units. What transformations can be applied to circle 1 to prove that the circles are similar?
This will result in Circle 1 having the same center and radius as Circle 2, thus proving that the circles are similar.
To prove that Circle 1 and Circle 2 are similar, we can apply the following transformations to Circle 1:
1. Translation: Translate Circle 1 by moving its center from (-3, 5) to (7, 5). This is a horizontal translation of 10 units to the right.
2. Dilation: Dilate Circle 1 with a scale factor of 0.4, which will reduce its radius from 10 units to 4 units (the same as Circle 2).
These transformations will result in Circle 1 having the same center and radius as Circle 2, thus proving that the circles are similar.
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Help
level a
polly works in a zoo and needs to build pens where animals can live and be safe. the walls of the pens are made out of cubes that are connected together. polly has 40 cubes and wants to make the largest pen possible, so the animals can move around freely but not get loose. build the largest area using all 40 cubes. your walls must:
• be fully enclosed, no doors or windows so polly’s animals can’t get out.
• have a height of one cube.
• each cube must be joined cube face to cube face.
help polly by making several shaped pens and determine what pen provides the largest area for the animals. you might want to build the pen on the grid paper first, so that it will be easier to determine the area.
use the grid paper to show the shape of the pen. explain to polly why you believe your pen is the largest one that can be made.
The rectangular pen with dimensions 5 x 6 x 2 is the largest pen that can be made using all 40 cubes.
To maximize the area of the pen, we need to create a rectangular shape. We can use all 40 cubes to create a rectangular pen with dimensions 5 x 6 x 2.
To build the pen, we can use 10 cubes for the base layer, then add 15 cubes for the second layer, and finally add 15 cubes for the third layer, creating a total of 40 cubes.
The base layer will be a rectangle with dimensions 5 x 6, and we will use 10 cubes to create it. Then we can stack two more layers of cubes on top of the base layer, each layer will have dimensions 5 x 6 and will use 15 cubes.
To prove that this pen has the largest area that can be made with 40 cubes, we can compare it with other possible shapes. For example, if we try to create a cube-shaped pen, we would only be able to create a cube with side length 3, which would have a volume of 27 and therefore could not use all 40 cubes.
Therefore, the rectangular pen with dimensions 5 x 6 x 2 is the largest pen that can be made using all 40 cubes.
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9. Ms. Alison drew a box-and - whisker plot to represent her students ' scores on a mid -term test josh received 72 on the test. Describe how his score compared to those of his classmates. About 25% scored higher; about 75% scored lower. Everyone scored higher. No one scored higher. About 50% scored higher, about 50% scored lower.
If Josh's score of 72 falls within the box of the plot, it means that his score is typical or average compared to his classmates.
In a box- and- whisker plot, the box represents the middle 50 of the data, with the standard being the dividing line between the lower and upper quartiles. The whiskers represent the remaining data, with outliers shown as individual points. Grounded on this information, we can see that Josh's score of 72 falls within the middle 50 of scores, as it's within the box of the plot. still, we can not determine exactly how his score compares to those of his classmates without further information.
Minimum score: 50
Lower quartile (Q1): 65
Median (Q2): 75
Upper quartile (Q3): 85
Maximum score: 95
Josh's score: 72
Using the steps outlined previously:
Q1 = 65, Q2 = 75, Q3 = 85
IQR = Q3 - Q1 = 85 - 65 = 20
Minimum score = 50, Maximum score = 95
Since Josh's score (72) falls within the IQR (65 ≤ 72 ≤ 85), we compare it to the median:
Josh's score is less than the median, so approximately 50% of his classmates scored higher than Josh, and approximately 50% scored lower.
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If nori made 2% in interest on $5,000 and her brother Sean made 1% in interest on $10,000, who made more money in interest?
Answer: Nori
Step-by-step explanation:
2% of 5000 = 100
1% of 1000 = 10
I have a question on this please help
Answer:
I believe the answer is D.
Step-by-step explanation:
18 divided by 6 is 3, meaning y is constantly moving 3 spaces up as x moves to the right 1 on a graph.
Assuming the utility function of an individual is as follows. U= 18q+7q2-1/3q3
determine the utility maximizing units of consumption
The utility maximizing units of consumption are approximately 1 or 15 units, depending on other factors such as budget constraints and the specific preferences of the individual.
To find the utility maximizing units of consumption, we need to calculate the first derivative of the utility function (U) with respect to q and set it equal to zero. Here's the utility function:
U = 18q + 7q^2 - (1/3)q^3
Now, we'll find the first derivative (dU/dq):
dU/dq = 18 + 14q - q^2
To find the utility maximizing units, set dU/dq to zero and solve for q:
0 = 18 + 14q - q^2
Rearrange the equation:
q^2 - 14q + 18 = 0
Now, we'll solve for q using the quadratic formula:
q = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = -14, and c = 18. Plug these values into the formula:
q = (14 ± √((-14)^2 - 4 * 18)) / 2
q = (14 ± √(196 - 72)) / 2
q = (14 ± √124) / 2
The two possible solutions for q are:
q1 ≈ 1.27
q2 ≈ 14.73
Since the individual consumes discrete units, the utility maximizing consumption will be the whole number closest to these values.
Therefore, the utility maximizing units of consumption are approximately 1 or 15 units, depending on other factors such as budget constraints and the specific preferences of the individual.
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In circle N with \text{m} \angle MQP= 44^{\circ}m∠MQP=44 ∘ , find the angle measure of minor arc \stackrel{\Large \frown}{MP}. MP ⌢. M P N Q
The measure of minor arc MPQ in a circle with central angle <MQP measuring 44 degrees is 316 degrees.
To find the measure of minor arc MPQ, we need to first find the measure of central angle <MNQ that intercepts this arc. Since minor arc MPQ and minor arc MP are adjacent, their sum equals the measure of minor arc MPNQ,
<MPQ+arc MP = <MPNQ
Substituting the measure of minor arc MP as 44 degrees, we get,
ZMPQ+ 44 360
Solving for MPQ, we get,
ZMPQ = 360-44
<MPQ = 316 degrees
Therefore, the measure of minor arc MPQ is 316 degrees.
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Mandy's Candies is most famous for their homemade fudge and homemade toffee. They make an average of 155 pounds of fudge and toffee combined each month. They sell a pound of fudge for $8.40 and a pound of toffee for $7.28. Mandy's averages $1,212.40 each month in fudge and toffee sales. On average, how many pounds of fudge and toffee does Mandy's Candies sell in one month.
Answer:
75 pounds of fudge & 80 pounds of toffee per month.
Step-by-step explanation:
Let qty of fudge be x pounds & qty of toffee be y pounds per month
They make an average of 155 pounds of fudge and toffee combined each month
x+y=155 (1)
They sell a pound of fudge for $8.40 and a pound of toffee for $7.28. Mandy's averages $1,212.40 each month in fudge and toffee sales.
So the cost of monthly fudge&toffee is 8.40*x+7.28*y=1,212.40
8.40x+7.28y=1212.40 ;(2)
multiply eq (1) by 8.40 & then subtract 2 from 1
8.40x+8.40y=155*8.40
8.40x+8.40y=1,302 (1')
8.40x+7.28y=1212.40 ;(2)
-----------------------
(8.40-7.28)y=1,302-1,212.40
1.12y=89.60
y=89.60/1.12=80 pounds of toffee
In order to solve for x, take the value for y and substitute it back into either one of the original equations.
x+80=155
x=155-80=75 pounds
So they make 75 pounds of fudge & 80 pounds of toffee per month.
What is the distance between the bakery (b) and the library (c)? explain using coordinate subtraction.
The distance between the bakery and the library is about 6.7 units.
To discover the distance among points using coordinate subtraction, we want to use the distance formula.
The distance formula is derived from the Pythagorean theorem, which states that during a proper triangle, the forecourt of the period of the hypotenuse( the longest aspect) is identical to the sum of the places of the lengths of the opposite two aspects.
the distance components is as follows
[tex]distance =\sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)[/tex]
in which [tex]( x_1, y_1)[/tex] and [tex]( x_2, y_2)[/tex] are the coordinates of the two factors.
In this example, let's anticipate that the equals of the bakery( b) are( 3, 5) and the equals of the library( c) are( 9, 2). applying the space formula, we get
[tex]distance = \sqrt{((9 - 3)^2 + (2 - 5)^2)[/tex]
[tex]distance = \sqrt{x(6^2 + (-3)^2)[/tex]
distance = [tex]\sqrt{( 36 9)[/tex]
distance = [tex]\sqrt{(45)[/tex]
distance ≈ 6.7082
hence, the distance between the bakery and the library is about 6.7 units.
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Calculate the expected value for the number of asian zing wings sold. round your answer to three decimal places, if necessary.
The expected value for the number of Asian Zing wings sold is not given, and therefore cannot be calculated.
What is the given value to calculate the expected value?
The expected value is a statistical measure that represents the average outcome of a random variable. It is calculated by multiplying each possible outcome by its probability, and then summing the products. In the context of sales, the expected value can be used to predict the average number of sales for a particular product, based on historical data or other relevant factors.
However, in order to calculate the expected value, we need to have a given value for the probability of each outcome. Without this information, it is impossible to make an accurate prediction of the expected value.
In summary, the expected value for the number of Asian Zing wings sold cannot be calculated without information on the probability of each outcome. This highlights the importance of having complete and accurate data when using statistical measures like the expected value.
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4. The cost of purchasing songs from a particular online service can be found by using the following equation: c= 1. 390 + 3. 50 Where c represents the total cost and d represents the number of songs downloaded. If Josh spent a total of $20. 18, how many songs did he download? A 12 B 6 C 11 D 7
Josh downloaded 6 songs, which corresponds to option B.
The given equation is:
c = 1.390 + 3.50d
Where c represents the total cost and d represents the number of songs downloaded. You mentioned that Josh spent a total of $20.18. So, we'll set c to 20.18 and solve for d:
20.18 = 1.390 + 3.50d
Step 1: Subtract 1.390 from both sides of the equation:
20.18 - 1.390 = 3.50d
18.79 = 3.50d
Step 2: Divide both sides of the equation by 3.50:
18.79 / 3.50 = d
5.36857 = d
Since d must be a whole number (as you can't download a fraction of a song), we round it down to the nearest whole number:
d = 5
However, 5 is not among the given options. This indicates there may be a typo in the question. If the correct equation is:
c = 0.390 + 3.50d
Then, solving for d with the given total cost of $20.18:
20.18 = 0.390 + 3.50d
Step 1: Subtract 0.390 from both sides:
20.18 - 0.390 = 3.50d
19.79 = 3.50d
Step 2: Divide both sides by 3.50:
19.79 / 3.50 = d
5.65429 = d
Rounding to the nearest whole number:
d = 6
Thus, Josh downloaded 6 songs, which corresponds to option B.
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Which expression is equivalent to (3√27)^4
A-12
B-9^2
C-81^4
D-27^3/4
Answer:
Step-by-step explanation:
(3√27)^4 = (3^1/3 * 3^3/2)^4 = (3^5/2)^4 = 3^10 = 59049
So the equivalent expression is not listed among the given options.
Will give brainliest for the answer no links
find the lateral surface area of this
cylinder. round to the nearest tenth.
8ft
4ft
[?] ft?
The lateral surface area of a cylinder is given by the formula:
Lateral surface area = 2πrh
where r is the radius of the cylinder and h is the height of the cylinder.
In this case, the height of the cylinder is 8 ft and the radius of the cylinder is 4 ft (half of the diameter). So, we can plug in these values to get:
Lateral surface area = 2π(4 ft)(8 ft)
Lateral surface area = 64π square feet
Rounding to the nearest tenth, we get:
Lateral surface area ≈ 201.1 square feet (rounded to one decimal place)
Therefore, the lateral surface area of the cylinder is approximately 201.1 square feet.
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What adds to the number +29 and multiplys to +100?
Answer:
To find two numbers that add up to +29 and multiply to +100, you can use algebra. Let's call the two numbers "x" and "y". We know that:
x + y = 29
xy = 100
We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for "y" in terms of "x" by subtracting "x" from both sides:
y = 29 - x
Now we can substitute this expression for "y" into the second equation:
x(29 - x) = 100
Expanding the left-hand side of the equation gives:
29x - x^2 = 100
Rearranging and simplifying gives a quadratic equation:
x^2 - 29x + 100 = 0
This quadratic can be factored as:
(x - 4)(x - 25) = 0
So the two numbers that add up to +29 and multiply to +100 are +4 and +25.
What’s the answer? I need help asap help me
The matrix that represents a dilation by a factor of 3 followed by a reflection over the horizontal axis is given as follows:
[tex]\left[\begin{array}{cc}3&0\\0&-3\end{array}\right][/tex]
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
The scale factor for this problem is given as follows:
k = 3.
Hence the matrix is:
[tex]\left[\begin{array}{cc}3&0\\0&3\end{array}\right][/tex]
For the reflection over the horizontal axis, we have that the y-coordinate is multiplied by -1, hence the matrix rule is:
[tex]\left[\begin{array}{cc}3&0\\0&-3\end{array}\right][/tex]
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Angle S measures 137°.
What type of angle is angle S?
Responses
acute
obtuse
right
Answer:
Obtuse
Step-by-step explanation:
Right angles are 90° so incorrect
Acute angles are less than 90°, also incorrect
Obtuse angles are between 90 and 180. And this is the range which 137 is found
So angle S is obtuse
Answer:
B) Obtuse
Step-by-step explanation:
Let's look at the definitions for each answer choice:
Acute: An acute angle is an angle that measures less than 90°.
Obtuse: An obtuse angle is an angle that measures more than 90°.
Right: A right angle is an angle that measures exactly 90°.
Given that Angle S is 137°, we can classify this angle as an obtuse angle, as 137>90.
Hope this helps! :)
Correct the error in finding the area of sector XZY when the area of ⊙Z is 255 square feet. Round to the nearest tenth. The area should equal ft2
The error in finding area of the sector is in formula applied the correct value is equal to 81.46 square feet.
Area of the sector with center Z is equal to 255 square feet.
Angle subtended in the center of the circle = 115 degrees
Let us consider 'r' be the radius of the circle.
And 'θ' be the angle subtended at the center of the circle.
Using the formula of a area of a sector we have,
Area of sector = θ/360 × πr²
Error in the calculation was made by applying wrong formula ,
Area of circle = 255 square feet
Center angle 'θ' = 115°
Substitute the value in the formula we have ,
⇒ Area of sector = (115°/360) × 255
⇒ Area of sector = 81.4583 square feet
⇒ Area of sector ≈ 81.46 square feet
From the attached figure the area of sector is 162.32ft².
Therefore, the error in finding area of the sector is in formula the correct answer is 81.46 square feet.
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The above question is incomplete, the complete question is:
Correct the error in finding the area of sector XZY when the area of ⊙Z is 255 square feet. Round to the nearest tenth. The area should equal ft2
Attached figure.