You start at (-3, 5). You move right 3 units and down 7 units. Where do you end?
Answers
Answer:
(0,-2)
Step-by-step explanation:
-3 plus 3 equals 0 and 5 minus 7 equals -2, so (0,-2).
Related Questions
Solve: log 3x = log 2 + log (x - 1) O a. -2 O b. 2. Oc. - 2/5 O d. 1/2
Answers
The solution to the equation is (a) -2.
What is the value of x that satisfies the given equation?To solve the equation log(3x) = log(2) + log(x - 1), we can use the properties of logarithms.
According to the logarithmic property log(a) + log(b) = log(ab), we can rewrite the equation as:
log(3x) = log(2(x - 1))
Since the logarithm function is one-to-one, we can equate the expressions inside the logarithms:
3x = 2(x - 1)
Expanding the equation:
3x = 2x - 2
Bringing all terms to one side:
3x - 2x = -2
x = -2
Therefore, the solution to the equation is x = -2.
The correct answer is (a) -2.
Learn more about logarithmic equations
brainly.com/question/29197804
#SPJ11
if a regular polygon has exterior angles that measure 40 each how many sides tdoes the polygon have
Answers
If you have exterior angles that are 40° each, then you can see how many times it goes into 360° to find your number of sides.
360° / 40° = 9 sides
Hope this helps!
Yes or no question plz help
Answers
Simplify the expression 2/3 divided by (-4) - (1/6 - 8/6)
Answers
Answer:
2/3 divided by -17/6
Step-by-step explanation:
2/3 divided by (-4) - (1/6 - 8/6)
2/3 divided by (-24/6) - (-7/6) <---- ( I had to find the common denominator )
2/3 divided by -17/6 <---- ( Then I had to subtract (-24/6) - (-7/6) )
Answer: correct answer is 1
Step-by-step explanation:
Noah borrowed $0.80 from his friend John five days last week to buy chips. how much does Noah owe John?
Answers
Answer:
$0.80
Step-by-step explanation:
Answer:
So Noah owes John $4.00
Step-by-step explanation:
Since Noah borrowed 80 cents from John for 5 days, you'd simply multiply 0.80 (remember to include the decimal) by 5, and you'd get 4.
Hope this helps you :)
The price of the original shirt is $45, it is reduced to $32.50. Calculate the percentage decrease. Show your workings.
Answers
Answer:
The percent decrease in the price of shirt is 27.78%
Step-by-step explanation:
The percent decrease is the decrease in the price of a product or good.
Given
Original Price = $45
Decreased price = $32.50
Percentage decrease is calculated by using the formula
\(Percentage\ decrease = \frac{decrease}{Original\ price} *100\\\)
And the decrease is calculated as:
\(Decrease = Original\ price - Reduced\ price\)
So,
\(Decrease = 45-32.50 = 12.5\)
Putting the values in the formula for percent decrease
\(Percent\ decrease = \frac{12.50}{45} *100\\=0.2777..*100\\= 27.77..\)
Rounding off to nearest hundredth: 27.78%
Hence
The percent decrease in the price of shirt is 27.78%
1 , 3 , 6 , 10 , 15
1) What is the nth term of the sequence?
2) Use the nth term to work out the 21st term of the sequence.
Please help :) will award brainliest.
Answers
As we can see that common difference is increasing to one more digit after every term
so it means
a21 = 231
Answer:
1. a_n = a_(n-1) + n where a_1 is 1 or a_n = n(n+1)/2
2. 231
Step-by-step explanation:
Notice that from 1 to 3, you add 2; from 3 to 6, you add 3; from 6 to 10, you add 4, etc. The pattern here is add 2, add 3, add 4, add 5, etc.
1. Let the nth term be a_n. The recursive equation can be written as a_n = a_(n-1) + n where a_1 = 1 (Use this because they most likely teach you this in schools)
Here is it written in an arithmetic equation (most likely not taught in school):
We can write an arithmetic expression using the summation formula because it is basically the sum of the numbers from 1 to n, so a_n = n(n+1)/2
2. Using the recursive, we would need to constantly add until you get up to a_21, which would take a while. Using the arithmetic equation, we can simply get:
21(21+1)/2 = 21(11) = 231
I hope this helps! :)
Weekly wages at a certain factory are normally distributed with a mean of $400 and a standard deviation of $50. Find the probability that a worker selected at random makes between $350 and $400. ?%
Answers
The probability that a worker selected at random makes between $350 and $400 is given as follows:
0.34 = 34%.
How to obtain a probability using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for the salaries in this problem are given as follows:
\(\mu = 400, \sigma = 50\)
The probability that a worker selected at random makes between $350 and $400 is the p-value of Z when X = 400 subtracted by the p-value of Z when X = 350, hence:
X = 400:
\(Z = \frac{X - \mu}{\sigma}\)
Z = (400 - 400)/50
Z = 0
Z = 0 has a p-value of 0.5.
X = 350:
\(Z = \frac{X - \mu}{\sigma}\)
Z = (350 - 400)/50
Z = -1
Z = -1 has a p-value of 0.16.
Hence the probability is given as follows:
0.5 - 0.16 = 0.34 = 34%.
More can be learned about the normal distribution at https://brainly.com/question/25800303
#SPJ1
Find an equation for the perpendicular bisector of the line segment whose endpoints are ( − 7 , − 3 ) and ( − 3 , 7 )
Answers
Answer:
-0.4x + y = 2
Step-by-step explanation:
To find an equation for the perpendicular bisector of the line segment whose endpoints are (-7, -3) and (-3, 7), you can start by finding the midpoint of the line segment. The midpoint is the point on the line segment that is exactly halfway between the two endpoints.
To find the midpoint of the line segment, you can average the x-coordinates and y-coordinates of the two endpoints:
Midpoint: ((-7 + -3)/2, (-3 + 7)/2)
= (-5, 2)
Then, you can find the slope of the line segment by using the formula:
slope = (y2 - y1)/(x2 - x1)
= (7 - (-3))/(-3 - (-7))
= 10/4
= 2.5
The slope of the perpendicular bisector will be the negative reciprocal of the slope of the line segment. To find the slope of the perpendicular bisector, you can take the negative reciprocal of the slope of the line segment:
Perpendicular slope = -1/slope
= -1/(2.5)
= -0.4
Then, you can use the midpoint and the slope of the perpendicular bisector to find the equation of the perpendicular bisector. The equation of a line in slope-intercept form is:
y = mx + b
Where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.
To find the y-intercept of the perpendicular bisector, you can substitute the coordinates of the midpoint and the slope into the equation:
y = (-0.4)x + b
2 = (-0.4)(-5) + b
2 = 2 + b
b = 0
Therefore, the equation of the perpendicular bisector in slope-intercept form is:
y = (-0.4)x + 0
= (-0.4)x
Alternatively, you can write the equation in standard form, which is:
Ax + By = C
Where A, B, and C are constants and x and y are variables. To find the equation of the perpendicular bisector in standard form, you can substitute the slope and the coordinates of the midpoint into the standard form equation:
(-0.4)x + y - 2 = 0
-0.4x + y = 2
Therefore, the equation of the perpendicular bisector in standard form is:
-0.4x + y = 2
Answer:
Step-by-step explanation:
Since it is a perpendicular bisector, hence point M is the midpoint
∴ Midpoint (AB)=[
2
7+3
,
2
5+1
]=[
2
10
,
2
6
]=M[5,3]
Slope (AB)m
1
=
5−1
3−7
=
4
−4
=−1
m
1
×m
2
=−1
−1×m
2
=−1
m
2
=1
Equation of perpendicular bisector.
=(y−3)=1(x−5)
y−3=x−5
x−y−2=0
The exact Value of the sine, cosine, and tangent about of the angle
Answers
Answer:
Below are the exact values of sine, cosine, and tangent of the given angle -11π/12.
\(sin(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{4}\)\(cos(-\frac{11\pi}{12})=\frac{-\sqrt{6}-\sqrt{2}}{4}\)\(tan(-\frac{11\pi}{12})=\frac{sin(-\frac{11\pi}{12})}{cos(-\frac{11\pi}{12})}=2-\sqrt{3}\)Explanation:
We can use the following trigonometric identities to solve the exact value of the given angle.
\(\begin{gathered} sin(x+y)=sin\text{ }x\text{ }cos\text{ }y+cos\text{ }x\text{ }sin\text{ }y \\ cos(x+y)=cos\text{ }x\text{ }cos\text{ }y-sin\text{ }x\text{ }sin\text{ }y \end{gathered}\)For sine function, we have:
\(\begin{gathered} sin(-\frac{11\pi}{12})=sin(\frac{\pi}{4}-\frac{7\pi}{6}) \\ sin(\frac{\pi}{4}-\frac{7\pi}{6})=sin\text{ }\frac{\pi}{4}cos(-\frac{7\pi}{6})+cos\text{ }\frac{\pi}{4}sin(-\frac{7\pi}{6}) \end{gathered}\)Simplify.
\(\begin{gathered} sin(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{\sqrt{2}}{2}(-\frac{\sqrt{3}}{2})+\frac{\sqrt{2}}{2}(\frac{1}{2}) \\ sin(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{-\sqrt{6}}{4}+\frac{\sqrt{2}}{4} \\ sin(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{-\sqrt{6}+\sqrt{2}}{4} \\ sin(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{4} \end{gathered}\)For cosine function, we have:
\(\begin{gathered} cos(-\frac{11\pi}{12})=cos(\frac{\pi}{4}-\frac{7\pi}{6}) \\ cos(\frac{\pi}{4}-\frac{7\pi}{6})=cos\frac{\pi}{4}cos(-\frac{7\pi}{6})-sin\frac{\pi}{4}sin(-\frac{7\pi}{6}) \end{gathered}\)Simplify.
\(\begin{gathered} cos(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{\sqrt{2}}{2}(-\frac{\sqrt{3}}{2})-(\frac{\sqrt{2}}{2})(\frac{1}{2}) \\ cos(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{-\sqrt{6}}{4}-\frac{\sqrt{2}}{4} \\ cos(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{-\sqrt{6}-\sqrt{2}}{4} \\ cos(-\frac{11\pi}{12})=\frac{-\sqrt{6}-\sqrt{2}}{4} \end{gathered}\)Lastly, for tangent function, it is the ratio between sine and cosine function.
\(tan(-\frac{11\pi}{12})=\frac{sin(-\frac{11\pi}{12})}{cos(-\frac{11\pi}{12})}\)Applying the division rule, we get the reciprocal of the denominator and multiply it to the numerator. The equation becomes:
\(tan(-\frac{11\pi}{12})=sin(-\frac{11\pi}{12})\times\frac{1}{cos(-\frac{11\pi}{12})}\)Now, let's replace the sine and cosine value that we have calculated above.
\(tan(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{4}\times\frac{4}{-\sqrt{6}-\sqrt{2}}\)Since 4 is a common factor on both numerator and denominator, we can cancel it out. The equation then becomes,
\(tan(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{-\sqrt{6}-\sqrt{2}}\)To further simplify the function, let's remove the radicals in the denominator by rationalization.
\(\begin{gathered} tan(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{-\sqrt{6}-\sqrt{2}}\times\frac{-\sqrt{6}+\sqrt{2}}{-\sqrt{6}+\sqrt{2}} \\ tan(-\frac{11\pi}{12})=\frac{6-\sqrt{12}-\sqrt{12}+2}{6-\sqrt{12}+\sqrt{12}-2} \end{gathered}\)\(\begin{gathered} tan(-\frac{11\pi}{12})=\frac{8-2\sqrt{12}}{4} \\ tan(-\frac{11\pi}{12})=\frac{8-2\sqrt{4\times3}}{4} \\ tan(-\frac{11\pi}{12})=\frac{8-(2\times2\sqrt{3})}{4} \\ tan(-\frac{11\pi}{12})=\frac{8-4\sqrt{3}}{4} \\ Factor\text{ }4\text{ }in\text{ }the\text{ }numerator. \\ tan(-\frac{11\pi}{12})=\frac{4(2-\sqrt{3})}{4} \\ Cancel\text{ }4. \\ tan(-\frac{11\pi}{12})=2-\sqrt{3} \end{gathered}\)I WIL NAME YOU THE BRAINLIEST IF YOU HELP! PLEASE HURRY!
IT IS IN THE PHOTO!
Answers
The base is Bethany wants to build a wooden deck on her patio, which is in the shape of a parallelogram. The area of the patio is 580 ft². The base is 30ft. The correct option is c.
What is the area?Like the formula for the area of a rectangle, the formula for the area of a parallelogram is base times height.
Area = 580 ft².
Height = 3x
Base = 5x
The area of the parallelogram A can be written as;
Area = base × height
A = b×h
Substituting the values of Area, base, and height.
580 = 5x × 3x
580 = 15x²
x² = 580/15
x = √(580/15)
Since the base = 5x ;
Substituting the value of x.
Base = 5x = 5(√(580/15))
x = 5(√(580/15)) = 30ft.
Therefore, the base is 30ft. The correct option is c.
To learn more about the area, visit here:
https://brainly.com/question/19187448
#SPJ1
How many solutions does this equation have? –9h + 9h = 0
Answers
Answer:
Infinite
Step-by-step explanation:
Let's assume that h=2
-9(2)+9(2)=0
-18+18=0
And if we assumed that h=9
Then: - 9(9)+9(9)=0
- 81+81=0
Thus, h can be any number
−2 + x ≤ −16 a closed or open circle?
Answers
Answer:
Closed circle
Step-by-step explanation:
If the sign is less than or equal too/greater than or equal too the circle will be closed
Answer:
closed
Step-by-step explanation:
use an open circle for "less than" or "greater than", and a closed circle for "less than or equal to" or "greater than or equal to".
Kono divides The numerator and the denominator of 4872 by the greatest common factor to simplify the fraction in one step by what number does he divide
Answers
Complete question:
Kono divides The numerator and the denominator of 48 over 72 by the greatest common factor to simplify the fraction in one step by what number does he divide
Answer:
2/3
Step-by-step explanation:
Given the number : 48 / 72
Obtain the greatest common factor of 48 and 72
- - - - 48 - - - - 72
- 2-- 24 - - - - 36
- 2 - 12 - - - - - 18
- 2 - 6 - - - - - - 9
- 3 - 2 - - - - - - 3
The greatest common factor of 48 and 72 is hence (2 * 2 * 2 * 3) = 24
Hence, divide both the numerator and denominator by 24 ;
Numerator = 48/24 = 2
Denominator = 72 / 24 = 3
= 2/3
Ayden's monthly bank statement showed the following deposits and withdrawals:
-−$21.78, -−$26.26, -−$91.08, $63.64, $100.54
If Ayden's balance in the account was $40.85 at the beginning of the month, what was the account balance at the end of the month?
Answers
Given XY←→ and point Z below, find the equation of the line in slope-intercept form, through Z that is parallel to XY←→
Answers
The equation of the line in slope-intercept form, through Z that is parallel to XY is: C. y = 2/3(x) + 1
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of line XY;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (4 - 2)/(8 - 5)
Slope (m) = 2/3
At data point Z (6, 5) and a slope of 2/3, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 5 = 2/3(x - 6)
y = 2/3(x) - 4 + 5
y = 2/3(x) + 1
Read more on point-slope here: brainly.com/question/24907633
#SPJ1
A cost that changes in total as output changes is a variable cost. a. True b. False
Answers
Answer:
a. True
Step-by-step explanation:
a. True
A cost that changes in total as output changes is indeed a variable cost. Variable costs are expenses that vary in direct proportion to the level of production or business activity. As output increases, variable costs increase, and as output decreases, variable costs decrease. Examples of variable costs include direct labor, raw materials, and sales commissions.
Can someone please help me with this?
Answers
Answer:
the answer is c
Step-by-step explanation:
5). Susan wants to make a tent in the shape of
a square pyramid. If the base is made up of a
square that is 5 feet in length and the
triangular sides have a height of 6 feet, how
much material will she need to make the tent?
Answers
If Susan wants to make a tent in the shape of a square pyramid. The material she will need to make the tent is 85 square feet.
What is the material needed?First step is to find the area of triangle using this formula
Area of triangle =1/2 × base × height
Let plug in the formula
Area of triangle = 1/2 × 5 feet × 6 feet
Area of triangle = 15 square feet
Each four triangular sides has an area of 15 square feet for a total surface area of 60 square feet calculated as (4 × 15).
Now let find the material she need
Material needed = 25 + 60
Material needed = 85 square feet
Therefore she need 85 square feet.
Learn more about material needed here:https://brainly.com/question/18684769
#SPJ1
they are 8,756 students that attend middle schools in the city of Johnson. Of the students, 3,252 are picked up by car, 2,549 ride the bus home, and 2,955 students walk home. How many students leave school by bus or car?
Answers
The number of students that leave by bus or car is given as follows:
5801 students.
How to obtain the union and intersection set of the two sets?The union and intersection sets of multiple sets are defined as follows:
The union set is composed by the elements that belong to at least one of the sets.The intersection set is composed by the elements that belong to at all the sets.The or operation is equivalent to the union operation, meaning that we add the number of students that leave by bus to the number of students that leave by car.
Hence the number of students that leave by bus or car is given as follows:
3232 + 2549 = 5801 students.
More can be learned about union and intersection at brainly.com/question/4699996
#SPJ1
I need help with this ASAP
Answers
Answer:
hope this will help you........
1/2 * 6 * 4 * 10
= 120cm (cubed)
Which of the following situations are equal to 30%? Select all that apply A) 27 out of 90 B) 12 out of 36 C) 50 out of 80 D) 9 out of 30 E) 6 out of 24
Answers
Answer:
27 out of 90; 9 out of 30
Kelly and Greta are asked to write an equation for the scenario below. "One person was able to plant 4 trees in the same amount of time that 5 people working together were able to plant 20 trees." The girls agree that x represents the number of people working and y represents the number of trees planted. Kelly wrote the equation y = one-fourth x, and Greta wrote the equation y = 4 x. Which person is correct, and why?
Answers
Answer:
Greta is correct. The answer is y = 4x
Step-by-step explanation:
This is because one person is able to plant four trees and five people are able to plant 20 in the same amount of time which means 4 trees is to 1 person. In other words if you substitute the values into the equation you will see that x = 1 in the first scenario and x = 5 in second scenario.I will work out the second scenario below.
y = 4x (where y = 20)
20 = 4(x)
\(\frac{20}{4} = \frac{4x}{4}\)
5 = x
OR
y = 4x (where x = 5)
y = 4 * 5
y = 20
The equation which represents the number of trees planted y for the x number of people will be y = 4x thus Greta will be right.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
An equation is a set of variables that are constrained through a situation or case.
As per the given,
1 person plants 4 trees.
x = 1 and y = 4
y/x = 4
5 people plant 20 trees
x = 5 and y = 20
y/x = 20/5 = 4
y = 4x
Thus, y = 4x will be correct.
Hence "The equation which represents the number of trees planted y for the x number of people will be y = 4x thus Greta will be right".
For more about the equation,
https://brainly.com/question/10413253
#SPJ5
How many pairs of parallel lines are in the flipped shape
Answers
Answer: 5
Step-by-step explanation:
The scale factor of two similar polygons is given. Find the ratio of their perimeters and the ratios of their areas.
1) 3:1
2) 7/4
Answers
The ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.
Given the scale factor of two similar polygons, we need to find the ratio of their perimeters and the ratios of their areas,
To find the ratio of the perimeters of two similar polygons, we can simply write the scale factor as it is because the ratio of the perimeter is equal to the ration of the corresponding lengths.
1) So, perimeter = 3:1
The ratio of areas between two similar polygons is equal to the square of the scale factor.
Since the scale factor is 3:1, the ratio of their areas is:
(Ratio of areas) = (Scale factor)² = 9/1 = 9:1
Similarly,
2) Perimeter = 7:4
Area = 49/16
Hence the ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.
Learn more about scale factors click;
https://brainly.com/question/29464385
#SPJ1
i’m so gonna fail math
Use the information given to write an equation in standard form.
6. Slope is 3, and (1. 4) is on the line.
7. Slope is -2, and (4,3) is on the line.
10. Slope is , and (1, 3) is on the line.
11. Slope - , and (2, 3) is on the line
Answers
6. 3x-y=-1
In slope intercept form this equation has a slope of 3 and point 1,4 is included on the graphed line: y=3x+1 is slope intercept form.
7. 2x+y=11
In slope intercept form this equation has a slope of -2 and point 4,3 is included on the graphed line: y=-2x+11 is slope intercept form
10. 4x-7y=-17
In slope intercept form this equation has a slope of 4/7 and point 1,3 is included on the graphed line: y=4/7x+17/7 is slope intercept form
11. 3x+2y=12
In slope intercept form this equation has a slope of -3/2 and point 2,3 is included on the graphed line: y=-3/2x+6 is slope intercept form
You basically just find the slope intercept form of each question then convert the intercept form over to standard form then graph in intercept form to see if the point lies on the line :)
Question in picture. Pls answer soon 30 points!
Answers
Answer: 25.13cm
Step-by-step explanation:
Answer:
31.4 cm
Step-by-step explanation:
C=2πr
Plug in numbers: C= 2 * 3.14 * 5
Review Questions
1. Cindy is a baker and runs a large cupcake shop. She has already
a. How many workers will the firm hire if the market wage rate is
hired 11 employees and is thinking of hiring a 12th. Cindy esti- $27.95 ? \$19.95? Explain why the firm will not hire a larger or mates that a 12 th worker would cost her $100 per day in wages $ smaller number of units of labor at each of these wage rates. and benefits while increasing her total revenue from $2,600per. day to $2,750 per day. Should Cindy hire a 12 th worker? b. Show this firm Explain. L016.2 c. Now again determine the firm's demand curve for labor. Complete the following labor demand table for a firm that is assuming that it is selling in an imperfectly competitive marhiring labor competitively and selling its product in a competiket and that, although it can sell 17 units at $2.20 per unit, it tive market. L016.2 ginal product of each successive labor unit. Compare this demand curve with that derived in part b. Which curve is more elastic? Explain. 3. Alice runs a shoemaking factory that uses both labor and capital to make shoes. Which of the following would shift the factory's demand for capital? You can select one or more correct answers from the choices shown. LO16.3 a. Many consumers decide to walk barefoot all the time. b. New shoemaking machines are twice as efficient as older machines. c. The wages that the factory has to pay its workers rise due to an economywide labor shortage.
Answers
Cindy should hire the 12th worker as it would result in a net increase in profit, with additional revenue exceeding the cost of hiring. Insufficient information is provided to determine the demand curve for labor or compare its elasticity. Events that would shift the factory's demand for capital include new, more efficient machines and rising wages due to a labor shortage.
a. To determine whether Cindy should hire a 12th worker, we need to compare the additional revenue generated with the additional cost incurred. Hiring the 12th worker would increase total revenue by $150 ($2,750 - $2,600) per day, but it would also increase costs by $100. Therefore, the net increase in total profit would be $50 ($150 - $100). Since the net increase in profit is positive, Cindy should hire the 12th worker.
b. By hiring the 12th worker, Cindy can increase her total revenue from $2,600 per day to $2,750 per day. The additional revenue generated by the 12th worker exceeds the cost of hiring that worker, resulting in a net increase in profit.
c. To determine the firm's demand curve for labor, we need information about the marginal product of labor (MPL) and the wage rates. Unfortunately, this information is not provided, so we cannot complete the labor demand table or derive the demand curve for labor.
Without specific data or information about changes in the quantity of labor demanded and wage rates, we cannot determine which demand curve (from part b or c) is more elastic. The elasticity of the demand curve depends on the responsiveness of the quantity of labor demanded to changes in the wage rate.
The events that would shift the factory's demand for capital are:
a. New shoemaking machines being twice as efficient as older machines would increase the productivity of capital. This would lead to an increase in the demand for capital as the factory would require more capital to produce the same quantity of shoes.
b. The wages that the factory has to pay its workers rising due to an economy-wide labor shortage would increase the cost of labor relative to capital. This would make capital relatively more attractive and lead to an increase in the demand for capital as the factory may substitute capital for labor to maintain production efficiency.
The event "Many consumers decide to walk barefoot all the time" would not directly impact the demand for capital as it is related to changes in consumer behavior rather than the production process of the shoemaking factory.
Learn more about the demand curve at:
brainly.com/question/1139186
#SPJ11
For 0 ≤ x ≤ 2pi, solve the equation:tanx = 4sec^2x-4
Answers
Given the equation;
\(\tan x=4\sec ^2x-4\)We start by moving all terms to the left side of the equation;
\(\tan x-4\sec ^2x+4=0\)Now we re-write this using trig identities;
\(4+\tan x-4\sec ^2x=0\)Note that;
\(\sec ^2x=\tan ^2x+1\)Input this into the last equation and we'll have;
\(4+\tan x-4(\tan ^2x+1)=0\)Simplify the parenthesis;
\(\begin{gathered} -4(\tan ^2x+1) \\ =-4\tan ^2x-4 \end{gathered}\)We now refine the last equation;
\(\begin{gathered} 4+\tan x-4\tan ^2x-4 \\ =4-4+\tan x-4\tan ^2x \\ =\tan x-4\tan ^2x \end{gathered}\)The equation now becomes;
\(\tan x-4\tan ^2x=0\)We now represent tan x by letter a.
That means;
\(a-4a^2=0\)We shall apply the rule;
\(\begin{gathered} \text{If} \\ ab=0 \\ \text{Then} \\ a=0,b=0 \end{gathered}\)Therefore;
\(\begin{gathered} a-4a^2=0 \\ \text{Factorize;} \\ a(1-4a)=0 \end{gathered}\)At this point the solutions are;
\(\begin{gathered} a=0 \\ \text{Also;} \\ 1-4a=0 \\ 1=4a \\ \frac{1}{4}=a \end{gathered}\)If we now substitute a = tan x back into the equation, we would have;
\(\begin{gathered} \tan x-4\tan ^2x=0 \\ \tan x=0,\tan x=\frac{1}{4} \end{gathered}\)Where tan x = 0;
\(\begin{gathered} \tan x=0 \\ x=\pi \end{gathered}\)Where tan x = 1/4;
\(\begin{gathered} \tan x=\frac{1}{4} \\ x=\arctan (\frac{1}{4}) \\ x=0.24497\ldots \end{gathered}\)ANSWER:
\(\begin{gathered} x=\pi \\ x=0.245 \end{gathered}\)F(x)=|-3x|=-30 solve this equation
Answers
Answer:
no solution
Step-by-step explanation:
|-3x|=-30
Absolute value means take the non negative
An absolute value cannot be negative
There is no solution.