Point (-4, -5) is located which quadrant?
A) Quadrant I
B) Quadrant II
C) Quadrant IV
D) Quadrant III
Btw, This is a question from USATestPrep:)

Answers

Answer 1

Answer:

D) Quadrant III

Step-by-step explanation:

The point (-4, -5) is located in the 3rd quadrant, in which both the x axis and the y axis are negative.

Point (-4, -5) Is Located Which Quadrant?A) Quadrant IB) Quadrant IIC) Quadrant IVD) Quadrant IIIBtw,

Related Questions

Simplify 11 square root 1215

Answers

Answer:

35

Step-by-step explanation:

Its 34.85685 but simplifies to 35.

Answer:

\(99\sqrt{15} \thickapprox \:383.42535\)

Step-by-step explanation:

\(11\sqrt{1215}\)

Factor \(1215\) \(=9^{2} \times 15\). Rewrite the square root of the product \(\sqrt{9^{2} } \sqrt{15}\), than take the square root of \(9^{2}\).

\(11\times 9\sqrt{15}\)

Multiply 11 and 9 which will give you 99.

\(99\sqrt{15}\)

_________________________

What is the answer to the 1/5 - 1/3 = ? Pls help if I fail I could be on punishment for months

Answers

Okay so I think it may be -2/15
What is the answer to the 1/5 - 1/3 = ? Pls help if I fail I could be on punishment for months

Answer:

-2/15

Step-by-step explanation:

1. Change the denominator.

1/5 = 3/15

3/15 = 5/15

3/15 - 5/15 = -2/15

A square stepping stone has a side length of 10 1/4 inches.

What is the area of the stepping stone?

Answers

Area=2.5

Step-by-step explanation:

area

\(area = length \times width\)

\(area = 10 \times \frac{1}{4} \)

Area of square = 4*length of one side
If one side = 10 1/4 inches = 10.25 inch
Then
Area = 4* 10.25 = 41 inches^2

999f=4,131

Solve for f.

Answers

Answer:

4.135

Step-by-step explanation:

f = 4131/999

f = 4131 ÷ 999

4131 ÷ 999 = 4.1351351351

Answer:

4.135

Step-by-step explanation:

f = 4131 / 999 = 4.135

helpppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp

helpppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp

Answers

Answer:

its B

Step-by-step explanation:

pls do not listen to the other person

you have to add the tax so multiplying the two together instead of just adding them would get the same number

(also x+0.05x is literally 1.05x anyway)

hope this helps <3

I need to know how to know the answer and how to solve this

I need to know how to know the answer and how to solve this

Answers

Answer:

the line equals 180 degrees...

(4q-1)+117= 180

-117 -117

4q-1=63

+1 +1

4q= 64

/4 /4

q= 16 degrees

Step-by-step explanation:








Q6: Find the inverse of the function y=x³+2 Q7: Solve the equation e5-3x = 10

Answers


To find the inverse of the function y = x³ + 2, we can follow a step-by-step process. First, we express the function in terms of x instead of y. Then, we swap the variables x and y to interchange their roles. Next, we solve the equation for y to obtain the inverse function. The inverse of y = x³ + 2 is given by x = (y - 2)^(1/3).


To find the inverse of a function, we start with the equation y = x³ + 2. To express the function in terms of x, we rewrite the equation as x³ = y - 2. Next, we swap the roles of x and y by replacing x with y and y with x: y³ = x - 2.

To solve for y, we take the cube root of both sides: y = (x - 2)^(1/3). This equation represents the inverse of the original function. Therefore, the inverse of y = x³ + 2 is x = (y - 2)^(1/3).

In the inverse function, the input x becomes the output y, and the output y becomes the input x. The inverse function undoes the operation of the original function, so if we apply the inverse function to the output of the original function, we obtain the original input.

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Find the radius of convergence, R, of the series. [infinity] n 5n (x + 5)n n = 1 R =

Answers

The given series is as follows:[infinity] n 5n (x + 5)n n = 1Now let's find the radius of convergence (R) of the given series.

Radius of convergence is the distance between the center of the circle and the point at which the graph becomes infinite. Here, the center of the circle is x = -5. We will apply the ratio test to find the radius of convergence.Ratio Test is as follows: If the limit lim┬(n → ∞)⁡〖|a[n+1]/a[n]|〗 exists then the series is absolutely convergent if lim┬(n → ∞)⁡〖|a[n+1]/a[n]|〗 < 1 and it is divergent if lim┬(n → ∞)⁡〖|a[n+1]/a[n]|〗 > 1 and the test is inconclusive if lim┬(n → ∞)⁡〖|a[n+1]/a[n]|〗 = 1.By applying the ratio test we get:r = lim┬(n → ∞)⁡〖|a[n+1]/a[n]|〗= lim┬(n → ∞)⁡〖5(n+1)(x+5)^(n+1)/5n(x+5)n〗= lim┬(n → ∞)⁡5(x+5) = 5|x+5|

Hence, the radius of convergence is R = 5, so the given series converges absolutely for |x+5| < 5 and diverges for |x+5| > 5. The end points x = -10 and x = 0 are excluded because the series diverges for these values of x. Thus, the interval of convergence is (-10, -5) ∪ (-5, 0).Long answer with step-by-step explanation has been provided.

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A nurse provides a back massage as a palliative care measure to a client who is unconscious, grimacing, and restless. Which of the following findings should the nurse identify as indicating a therapeutic response? (Select all that apply.)
A. the shoulders droop
B. the facial muscles relax
C. the RR increases
D. the pulse is within the expected range
E. the client draws his legs into a fetal position

Answers

A nurse provides a back massage as a palliative care measure to a client who is unconscious, grimacing, and restless.

The therapeutic response that the nurse should identify in the client after a back massage includes relaxing of facial muscles and the pulse remaining within the expected range.
Massage is a fundamental nursing measure that is often utilized as part of palliative care for patients. The purpose of back massage is to promote relaxation, improve blood circulation, reduce muscle tension, and alleviate pain, stress, and anxiety. The nursing assessment of the patient before and after the massage is essential to determine its effectiveness as a therapeutic intervention for the patient.
When providing back massage as a palliative care measure to an unconscious, grimacing, and restless client, the nurse should identify several therapeutic responses as follows;
The shoulders droop: The nurse should expect the shoulders of the client to relax during massage therapy. If this occurs, it is a sign that the patient is experiencing relaxation and tension relief.
The facial muscles relax: Relaxation of the facial muscles is a common therapeutic response during back massage. The nurse should observe the patient's face for any signs of relaxation, which may include softening of facial lines, eyelids drooping, or a general expression of peacefulness.
The respiratory rate (RR) decreases: The nurse should expect the client's respiratory rate to decrease during a back massage. This is because relaxation stimulates the parasympathetic nervous system, resulting in decreased respiratory rate, heart rate, and blood pressure.
The pulse is within the expected range: The nurse should expect the client's pulse to remain within the expected range during a back massage. A normal pulse rate is between 60-100 beats per minute for adults. If the pulse remains within this range, it is a sign that the patient is responding positively to the massage therapy.

In conclusion, providing back massage as a palliative care measure to an unconscious, grimacing, and restless client can help to promote relaxation, improve blood circulation, reduce muscle tension, and alleviate pain, stress, and anxiety. The nurse should identify therapeutic responses in the patient during the massage therapy, which may include relaxation of the shoulders, facial muscles, decreased respiratory rate, and pulse remaining within the expected range.

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HELPPPPPPPPPPPPPP!!!!!!!!!

HELPPPPPPPPPPPPPP!!!!!!!!!

Answers

Middle one I think or bottom left

Answer:

The top right and the middle one.

Step-by-step explanation:

For a repeated-measures study comparing two treatments with 12 scores in each treatment, what is the df value for the t statistic?

Answers

The degree of freedom for t statistic is 11.

According to the given question.

For a repeated-measure study, comparing two treatments with 12 scores in each treatment .

So, we can say that sample size, n = 12.

We know that, when you have a sample and estimate the mean, we have

n – 1 degrees of freedom, where n is the sample size.

Therefore,

The degree of freedom for the given sample test will be

d.f = n -1

⇒ d.f = 12 - 1

⇒ d.f = 11

Hence, the degree of freedom for t statistic is 11.

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SOLVE. |y - z| when y=7, z= 11


please help I am super confused and im in the middle of the test

Answers

Answer:

\(y - z \\ = 7 - 11 \\ = - 4\)

A local supermarket has sodas on sale this week. If you buy fewer than three packs of soda, then each pack costs $3.99. If you buy 3 or more packs of soda, then each pack is $2.50. Which function represents this sale? Question 7 options:

A local supermarket has sodas on sale this week. If you buy fewer than three packs of soda, then each
A local supermarket has sodas on sale this week. If you buy fewer than three packs of soda, then each
A local supermarket has sodas on sale this week. If you buy fewer than three packs of soda, then each
A local supermarket has sodas on sale this week. If you buy fewer than three packs of soda, then each

Answers

Answer:

$5.95 is the answer I think

Suppose a survey of found that more than ought. which part of the survey represents the descriptive branch of statistics? make an inference based on the results of the survey.

Answers

The majority of business owners avoid flood insurance.

Inferential statistics enables you to draw conclusions ("inferences") from descriptive statistics, which describes data (such as a chart or graph). Using inferential statistics, you can draw conclusions about a population using data from samples. Using inferential statistics, you can try to discover whether the sample data from a tiny sample of people can forecast whether the medication will be effective for everybody (i.e. the population). There are several techniques to accomplish this, including post-hoc (advanced) testing and generating a z-score, which shows where your data would fall in a normal distribution.

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The average height of susan's 8th grade class is 56 inches. however, the height of any student in the class can vary by up to 4 in
from the average. which inequality shows all the possible heights (h) for any given student in the class?

Answers

Answer:

\(52 \leqslant h \leqslant 60\)

Step-by-step explanation:

Add and subtract 4 to and from 56

Calculate the first and second
differences for the function f(x)=
3x² +5
xy First Differences
Second
Differences
05
18
217
332
453

Answers

Answer:

Hi,

Step-by-step explanation:

\(\begin{array}{|c|c|c|c|}x&3x^2+5&\Delta_1x&\Delta_2x\\--&--&--&--\\0&5&-&-\\1&8&3&-\\2&17&9&6\\3&32&15&6\\4&53&21&6\\--&--&--&--\\\end{array}\)

Write an equation to relate the flow of water from the 8-inch pipe (1600) to the flow of water from the 4-inch pipe (2400). enter your answer in simplest form.

Answers

The equation to relate the flow of water from the 8-inch pipe (1600) to the flow of water from the 4-inch pipe (2400) is 2400.

To relate the flow of water from the 8-inch pipe to the flow of water from the 4-inch pipe, we can use the equation of continuity, which states that the product of the cross-sectional area of a pipe and the velocity of the fluid is constant.

Let's assume that the velocity of water flowing through the 8-inch pipe is V1 and the velocity of water flowing through the 4-inch pipe is V2. The cross-sectional area of the 8-inch pipe is A1 = π\((8/2)^2\) = 64π square inches, and the cross-sectional area of the 4-inch pipe is A2 = π\((4/2)^2\) = 4π square inches.

According to the equation of continuity, A1 * V1 = A2 * V2.

Substituting the given values, we have:

64π * V1 = 4π * V2

Simplifying, we get:

16V1 = V2

So, the equation to relate the flow of water from the 8-inch pipe (1600) to the flow of water from the 4-inch pipe (2400) is:

1600 * 16 = 2400

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I need help yall lol​

I need help yall lol

Answers

Answer:

C: Triangles A,B, and C

They are all similar

Step-by-step explanation:

All of the triangles are just different sizes, and are flipped differently, meaning they are all similar.

Hope this helped and sorry if wrong

How many terms are in the polynomial?
6-7x² + 3x
Enter only a number.

Answers

The sum of terms with the notation kxn, where k is any number and n is a positive integer, is referred to as a polynomial.

What number of terms makes up the polynomial?

The following expressions are polynomials:

A. 6y^2 + 5x

D. (7y^2 + 9x) / 4

Describe polynomials.

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers.

Any polynomial must have variable exponents that are non-negative integers.

Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

These expressions are now:

A. 6y^2 + 5x

B. (7x^2 + 8) / 4x

C. (y^2 + 3x ^1/3) / 4

D. (7y^2 + 9x) / 4

Here, we can observe that there are just two polynomial expressions.

A. 6y^2 + 5x

D. (7y^2 + 9x) / 4

The non-polynomial expressions include,

B. (7x2 + 8/ 4x) contains a variable in the numerator.

C. (y2 + 3x 1/3) / 4 - This exponent has a fractional exponent.

Consequently, the polynomial expressions are,

A. 6y^2 + 5x

D. (7y^2 + 9x) / 4

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What is 7,230,000,000 in scientific notation
What is 0.0000865 in scientific notation

Answers

Answer:

7,230,000,000 = 7.23 x 10 to the 9th power. 0.0000865 = 8.65 x 10 to the negative 5th power.

Step-by-step explanation:

Answer:

7.23 times 10^9                        8.65 times 10^-5

The order of the differential equation d 2 y dx2 4x dy dx = d 3 (cos 2x) dx3 is:_________

Answers

The order of the differential equation d²y/dx² + 4x(dy/dx) = d³(cos(2x))/dx³ is 3.

The order of a differential equation is determined by the highest derivative present in the equation. In the given differential equation, the highest derivative is the third derivative, d³(cos(2x))/dx³. Since this is the highest derivative and there are no higher-order derivatives present, the order of the differential equation is 3. This means that the equation involves up to the third derivative of the dependent variable y with respect to the independent variable x.

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The position of a ball after it is kicked can be determined by using the function f left parenthesis x right parenthesis equals negative 0.11 x squared plus 2.2 x plus 1f(x)=−0.11x2+2.2x+1​, where​ f(x) is the​ height, in​ feet, above the ground and x is the horizontal​ distance, in​ feet, of the ball from the point at which it was kicked. What is the height of the ball when it is​ kicked? What is the highest point of the ball in the​ air?

Answers

Answer:

When kicked, the height of the ball is 1 feet. The highest point for the ball's trajectory is 12 feet.

Step-by-step explanation:

We are given that the height is given by \(f(x)=-0.11x^2+2.2x+1\). The distance between the ball to the point where it was kicked is 0 right at the moment the ball was kicked. So, the height of the ball, when it was kicked is f(0) = -0.11*0 + 2.2*0 +1  = 1.

To determine the highest point, we will proceed as follows. Given a parabola of the form x^2+bx + c, we can complete the square by adding and substracting the factor b^2/4. So, we get that

\( x^2+bx+c = x^2+bx+\frac{b^2}{4} - \frac{b^2}{4} +c = (x+\frac{b}{2})^2+c-\frac{b^2}{4}\).

In this scenario, the highest/lowest points is \(c-\frac{b^2}{4}[/tex} (It depends on the coefficient that multiplies x^2. If it is positive, then it is the lowest point, and it is the highest otherwise).

Then, we can proceed as follows.

\( f(x) = -0.11x^2+2.2x+1 = -0.11(x^2-20x)+1\)

We will complete the square for \(x^2-20x\). In this case b=-20, so

\( f(x) = -0.11(x^2-20x+\frac{400}{4}-\frac{400}{4})+1 = -0.11(x^2-20x+100-100)+1\)

We can distribute -0.11 to the number -100, so we can take it out of the parenthesis, then

\( f(x) = -0.11(x^2-20x+100)+1+100*0.11 = -0.11(x^2-20x+100)+1+11 = -0.11(x-10)^2+12\)

So, the highest point in the ball's trajectory is 12 feet.

Answer:

Initial height = 1ft

Heighest height = 12ft

Step-by-step explanation:

In order to solve this problem, we can start by graphing the given height function. This will help us visualize the problem better and even directly finding the answers, since if you graph it correctly, you can directly find the desired values on the graph. (See attached picture)

So, the initical height happens when the x-value is equal to zero (starting point) so all we need to do there is substitute every x for zero so we get:

\(f(x)=-0.11x^{2}+2.2x+1\)

\(f(0)=-0.11(0)^{2}+2.2(0)+1\)

which yields:

\(f(0)=1 \)

so the height of the ball when it is kicked is 1 ft.

In order to find the highest point of the ball in the air, we must determine the x-value where this will happen and that can be found by calculating the vertex of the parabola. (see the graph)

the vertex is found by using the following formula:

\(x=-\frac{b}{2a}\)

in order to find "a" and "b" we must compare the given function with the standard form of a quadratic function:

\(f(x)=ax^{2}+bx+c\)

\(f(x)=-0.11x^{2}+2.2x+1\)

so:

a=-0.11

b=2.2

c=1

so the vertex formula will be:

\(x=-\frac{b}{2a}\)

\(x=-\frac{2.2}{2(-0.11)}\)

so we get that the highest point will happen when x=10ft

so the highest point will be:

\(f(10)=-0.11(10)^{2}+2.2(10)+1\)

f(10)=12ft

so the highes point of the ball in the air will be (10,12) which means that the highest the ball will get is 12 ft.

The position of a ball after it is kicked can be determined by using the function f left parenthesis

Jenna alone takes x days to finish a project kelly alone takes 3 days more than jenna alone to finish the project. if they together take 2 days to finish the project, find the value of x.

Answers

The value of x is 3 days.

Here,

Jenna alone takes x days to finish a project.

Kelly alone takes 3 days more than Jenna alone to finish the project.

They together take 2 days to finish the project.

We have to find the value of x.

What is Mathematical expression?

Mathematical expression is a way where calculations and analytical processes should be observed.

Now,

Jenna alone takes x days to finish a project.

Hence, Jenna complete work in 1 day = 1/x work

Kelly alone takes 3 days more than Jenna alone to finish the project.

That is, x + 3 days.

Hence, Kelly complete work in 1 day = \(\frac{1}{x+3}\) work

They together take 2 days to finish the project.

Hence, They together complete a work in 1 day = 1/2 work.

To find the value of x we use the formula of work word problem as;

\(\frac{1}{x} + \frac{1}{x+3} = \frac{1}{2} \\\\\frac{(x+3)+x}{x(x+3)} = \frac{1}{2}\\\\2(2x+3) = x (x+3)\\\\4x + 6 = x^{2} + 3x\\\\x^{2} -x-6=0\\\\x^{2} -3x+2x-6=0\\\\x (x-3) +2(x-3)=0\\\\(x+2) (x-3) = 0\\\\x = -2, x = 3\)

Since, The value of x = -2 is not possible (because days are not shown in negative sign).

Hence, The value of x is 3 days.

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Can someone help me with this Question.

Can someone help me with this Question.

Answers

The formula we need to use is given above. In this formula, we will substitute the desired values. Let's start.

\(P=3W+D\)

A) First, we can start by analyzing the first premise. The team has \(8\) wins and \(5\) losses. It earned \(8 \times 3 = 24\) points in total from the matches it won and \(1\times5=5\) points in total from the matches it drew. Therefore, it earned \(24+5=29\) points.

B) After \(39\) matches, the team managed to earn \(54\) points in total. \(12\) of these matches have ended in draws. Therefore, this team has won and lost a total of \(39-12=27\) matches. This number includes all matches won and lost. In total, the team earned \(12\times1=12\) points from the \(12\) matches that ended in a draw.

\(54-12=42\) points is the points earned after \(27\) matches. By dividing \(42\) by \(3\) ( because \(3\) points is the score obtained as a result of the matches won), we find how many matches team won. \(42\div3=14\) matches won.

That leaves \(27-14=13\) matches. These represent the matches team lost.

Finally, the answers are below.

\(A)29\)
\(B)13\)

Answer:

  a) 29 points

  b) 13 losses

Step-by-step explanation:

You want to know points and losses for different teams using the formula P = 3W +D, where W is wins and D is draws.

A 8 wins, 5 draws

The number of points the team has is ...

  P = 3W +D

  P = 3(8) +(5) = 29

The team has 29 points.

B 54 points

You want the number of losses the team has if it has 54 points and 12 draws after 39 games.

The number of wins is given by ...

  P = 3W +D

  54 = 3W +12

  42 = 3W

  14 = W

Then the number of losses is ...

  W +D +L = 39

  14 +12 +L = 39 . . . substitute the known values

  L = 13 . . . . . . . . . . subtract 26 from both sides

The team lost 13 games.

__

Additional comment

In part B, we can solve for the number of losses directly, using 39-12-x as the number of wins when there are x losses. Simplifying 3W +D -P = 0 can make it easy to solve for x. (In the attached, we let the calculator do the simplification.)

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Can someone help me with this Question.

helppppppppppp mee plssss

helppppppppppp mee plssss

Answers

Answer:

4.  4:3 = 20:15

5.  5:9 = 40:72

7.   7:9 = 21:27

8.  1:9 = 8:72

9.   6:1 = 12:2

10.  49:84 =7:12

11.  12:5 = 72 : 30

12.  5:35 = 1:7

13.  5:4  = 20:16

14. 2:9 = 12:54

15. 10:1 = 30:3

16.  3:5 = 21:35

17.  21:6 = 7:2

18.  5:1 = 35:7

19.  5:6 = 35:42

20. 55:60 = 11:12

Step-by-step explanation:


Match the correct corresponding parts. Make sure your letters are in the correct order!!
SAT~GRE

Match the correct corresponding parts. Make sure your letters are in the correct order!!SAT~GRE

Answers

Answer:

Step-by-step explanation:

Match the correct corresponding parts. Make sure your letters are in the correct order!!SAT~GRE

What is 9 in roman numerals?

Answers

The Roman numeral for the number 9 is IX.

Roman numerals are a numeral system that originated in ancient Rome and were used throughout the Roman Empire. Instead of using a base 10 system like the one we use today, Roman numerals use a combination of letters to represent numbers. The basic symbols in Roman numerals are I, V, X, L, C, D and M.

The numeral I represents the number 1, and the numeral X represents the number 10. To represent 9, we can represent 1 before 10 which is I before X.

It's important to note that Roman numerals have a strict set of rules for how to use the symbols correctly. For example, a numeral can only be repeated up to three times in a row, and numerals can only be subtracted from the next highest numeral that is at least 10 times larger.

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In a recent poll, 370 people were asked if they liked dogs, and 18% said they did. Find the margin of error of this poll, at the 95% confidence level. Give your answer to three decimals

Answers

The margin of error for the poll is 3.327% at the 95% confidence level.

To calculate the margin of error, we need to consider the sample size and the proportion of people who said they liked dogs in the poll. The margin of error represents the maximum likely difference between the poll results and the true population value.

Given that 370 people were surveyed and 18% of them said they liked dogs, we can calculate the sample proportion as 0.18 (18% expressed as a decimal).

To find the margin of error, we use the formula:

Margin of Error = Critical Value * Standard Error

At the 95% confidence level, the critical value for a two-tailed test is approximately 1.96. The standard error is calculated using the formula:

Standard Error = sqrt((p * (1-p)) / n)

Where p is the sample proportion and n is the sample size.

Substituting the values into the formula, we have:

Standard Error = sqrt((0.18 * (1-0.18)) / 370)

Standard Error ≈ 0.019

Margin of Error = 1.96 * 0.019

Margin of Error ≈ 0.037

Rounded to three decimals, the margin of error for this poll is approximately 0.037 or 3.327%. This means that we can be 95% confident that the true proportion of people who like dogs in the population falls within a range of 14.673% to 21.327%.

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Question One Assume there is a toll bridge in your city. Suppose that if the toll is abolished and crossing the bridge becomes free, there will be 30,000 vehicles crossing the bridge each year; with $1 of price increase, the number of vehicles crossing the bridge will drop by 100 each year. On the other hand, the city claims that maintenance of the bridge is costly. If there is no toll charge, the city would allow no cars to use the bridge; with $1 of price increase, the number of vehicles that the city would allow to use the bridge increases by 100 . a) Use the given information to write down the demand and supply functions of the bridge usage. (4 Marks) b) Solve for the equilibrium price and quantity of the bridge usage. (4 Marks) c) Suppose due to the decrease in transportation needs, the demand for the bridge usage decreased by 10% this year. Calculate the new equilibrium price and quantity of the bridge usage. (6 Marks) d) Assume the government enforces a toll charge of $100. Use the demand function derived in Part c) and the original given supply function to check if there will be an excess demand or excess supply with the government enforcement. If there is, what is the amount? (5 Marks) e) Suppose the toll bridge needs maintenance and repairs, and the supply of the bridge decreases by a half. What is the new supply function? Combine this new supply function with the demand function derived in Part c) to calculate a new set of equilibrium price and quantity of the bridge usage. (6 Marks)

Answers

a) Demand function: Qd = 30,000 - 100P, Supply function: Qs = -P b) Equilibrium price: $303.03, Equilibrium quantity: 27,697 vehicles. c) New equilibrium price: $333.33, New equilibrium quantity: 24,000 vehicles. d) Excess demand of 417 vehicles. e) New equilibrium price: $250, New equilibrium quantity: 24,750 vehicles.

a) The demand function for the bridge usage can be written as:

Qd = 30,000 - 100P

Where Qd represents the quantity demanded (number of vehicles crossing the bridge) and P represents the toll price.

The supply function for the bridge usage can be written as:

Qs = -P

Where Qs represents the quantity supplied (number of vehicles allowed to use the bridge by the city) and P represents the toll price.

b) To find the equilibrium price and quantity, we set the quantity demanded equal to the quantity supplied:

30,000 - 100P = -P

Simplifying the equation, we get:

30,000 = 99P

P = 303.03

Substituting the value of P back into either the demand or supply function, we find:

Qd = 30,000 - 100(303.03)

Qd = 27,697

Therefore, the equilibrium price is $303.03 and the equilibrium quantity is 27,697 vehicles.

c) If the demand for the bridge usage decreases by 10%, the new demand function becomes:

Qd = 0.9(30,000 - 100P)

Setting the new demand equal to the supply function:

0.9(30,000 - 100P) = -P

Solving the equation, we find:

P = 333.33

Substituting the value of P back into the demand or supply function, we get:

Qd = 0.9(30,000 - 100(333.33))

Qd = 24,000

Therefore, the new equilibrium price is $333.33 and the new equilibrium quantity is 24,000 vehicles.

d) With a toll charge of $100, we use the demand function from part c) and the original supply function:

0.9(30,000 - 100P) = -100

Solving the equation, we find:

P = 305.56

Substituting the value of P back into the demand or supply function, we get:

Qd = 0.9(30,000 - 100(305.56))

Qd = 24,417

Since the quantity demanded is greater than the quantity supplied, there is an excess demand of 24,417 - 24,000 = 417 vehicles.

e) If the supply of the bridge usage decreases by half, the new supply function becomes:

Qs = -0.5P

Setting the new supply equal to the demand function from part c):

0.9(30,000 - 100P) = -0.5P

Solving the equation, we find:

P = 250

Substituting the value of P back into the demand or supply function, we get:

Qd = 0.9(30,000 - 100(250))

Qd = 24,750

Therefore, the new equilibrium price is $250 and the new equilibrium quantity is 24,750 vehicles.

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Janet enjoys reading books, and reads an average of 4 books a month. Janet's younger brother, Alex waited for a month before deciding he liked reading, and also reads at an average of 4 books a month. If m represents the number of months Janet has been reading books, the equation 4m=4(m−1) represents the situation where Alex and Janet have read the same number of books.

Solve the equation to find the number of months it will take for Alex and Janet to have read the same number of books. Show your work.

Answers

Answer:

No solution

Step-by-step explanation:

4m = 4(m - 1)

Distribute;

4m = 4m - 4

Subtract 4m from both sides;

0 ≠ -4

No months because Alex cannot catch up to Janet since they both read the same amount of books per month.

Answer: They will never have read the same number of books

Step-by-step explanation:

4(m-1) will always be less than 4m no matter what.

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