original equations: S(p) = -200 + 50p and D(p) = 1060 - 55p
please find the equilibrium price and quantity of the two equations. I think I already set up the equation for the equilibrium price here, though no guarantee that I did it right.
Qd = 1060 - 55p = Qs = -200 + 50p​

Answers

Answer 1

The equilibrium price is 12 and the equilibrium quantity is 400.

How to find the equilibrium price and quantity?

It should be noted that on order to fund equilibrium price and quantity, we've to equate the quantity supplied and demanded. This will be:

Qd = 1060 - 55p

Qs = -200 + 50p

Qd = Qs

1060 - 55p = -200 + 50p

Collect like terms

-55p - 50p = -200 - 1060

-105p = -1260

Divide

p = 1260 / 105

p = 12

The equilibrium price is 12

Equilibrium quantity = -200 + 50p

= -200 + 50(12)

= -200 + 600

= 400

Learn more about equilibrium on:

brainly.com/question/26075805

#SPJ1


Related Questions

Identify the type of angle shown

A. Corresponding angles
B. Same side interior angles
C. Alternate exterior angles
D. Alternate interior angles

Help!!!

Answers

Answer:

A. Corresponding Angles

Step-by-step explanation:

They are both the same angle, and on the same side

Answer:

A. Corresponding angles

Step-by-step explanation:

Corresponding angles hold the same relative position as another angle somewhere else in the triangle. They have the same degree too. So answer is A

how many one-to-one functions are there from a set containing 5 elements to a set containing 6 elements?

Answers

There are 5x6=30 one-to-one functions from a set containing 5 elements to a set containing 6 elements.

A one-to-one (or injective) function is a type of mathematical function that maps each element of one set to one, and only one, element of another set. In other words, a one-to-one function is a function that has a unique output for each input. To calculate the number of one-to-one functions from a set containing 5 elements to a set containing 6 elements, we can use the formula f(x)=y, where x is the number of elements in the original set and y is the number of elements in the target set. In this case, x = 5 and y = 6, so f(x) = 6. Since each element in the original set must be mapped to a unique element in the target set, the total number of one-to-one functions is equal to the product of x and y, or 5 x 6 = 30.

Learn more about function here

https://brainly.com/question/29633660

#SPJ4

Identify how many and what type of solutions for each graph:

1). 1 non-real number
2). 3 real numbers
3). 2 real numbers
4). 1 real number
5). 2 nonreal Number

Answers

The quadratic equation has 2 non-real numbers as solutions.

How many solutions the quadratic equation has?

Here we have the graph of a quadratic equation of the form:

y = a*x^2 + b*x + c

And the solutions of the quadratic equation are the values of x such that:

0 =  a*x^2 + b*x + c

To identify these values, we need to see the values of x such that the graph intercepts the x-axis. But here we can see that the graph never intercepts the x-axis.

Then the solutions are complex numbers, and because it is a quadratic, there are two.

So the correct option is the 5th one, 2 non-real numbers.

Learn more about quadratic equations:

https://brainly.com/question/1214333

#SPJ1

Please help 100 points!!

Answers

Answer:

i think ur answer is c

Step-by-step explanation:

being timed, urgent question!!

Answers

1) 5
2) 6
3) 8
4) 1
5) 4
6) 7
7) 2
8) 3

Mary deposits $260.00 into a new savings account.
The account earns 2.5% simple interest per year. No
money is added or removed from the account for
5 years. What is the total amount of money in her
savings account at the end of the 5 years?
A) $292.50
C) $65.00
D) $325.00
B) $32.50

Answers

Answer:

A

Step-by-step explanation:

To solve this problem, we need to first find out how much interest the account earns each year. If the account earns 2.5% simple interest per year, and it starts with an initial balance of $260, then the interest earned each year is 0.025 * $260 = $6.50.

Over 5 years, the account will earn a total of 5 * $6.50 = $<<5*6.5=32.50>>32.50 in interest.

To find the total amount of money in the account at the end of the 5 years, we need to add the interest earned to the initial balance of the account. The total amount of money in the account will be $260 + $32.50 = $<<260+32.5=292.50>>292.50.

Therefore, the total amount of money in the account at the end of the 5 years is $292.50.

Answer:

A)  $292.50

Step-by-step explanation:

Simple Interest Formula

A = P(1 + rt)

where:

A = Final amountP = Principal amountr = Interest rate (in decimal form)t = Time (in years)

Given:

P = $260.00r = 2.5% = 0.025t = 5 years

Substitute the given values into the formula and solve for A:

⇒ A = 260(1 + 0.025 · 5)

⇒ A = 260(1 + 0.125)

⇒ A = 260(1.125)

⇒ A = 292.50

Therefore, the total amount of money in her savings account at the end of 5 years is $292.50.

The graph shown here is the graph of which of the following rational functions?

Answers

C. Because vertical asymptotes are determined by setting the denominator to 0, and since the vertical asymptotes are at x = -2 and x = 5, the denominator would have to be (x+2) and (x-5), and C has the only function with that denominator.

Let A(0, 1) and B(-4 ,3) be two fixed points. find the locus of point P such that PA^2 PB^2 = 16​

Answers

The locus of point P such that PA²+PB² = 16 is [tex]x^{2} +y^{2} + 4x - 4y + 5 =0[/tex]

What is the locus?

A locus is the collection of all points that satisfy a condition, typically forming a curve or surface. For instance, the set of points in three-space that are equally spaced out from a given point is a sphere, and the locus of points in the plane that are equally spaced apart from a given point is a circle.

Calculation:

Given that A and B are two fixed points on a plane locus of P such that PA²+PB² =16

Let point P be (x,y) then [tex]{(x-0)^{2} +(y-1)^{2} }+{(x-(-4))^{2}+(y-3)^{2} } = 16[/tex]

is the Locus of the given point P

On simplyfying we  get

[tex]{x^{2}+(y-1)^{2} } +{(x+4)^{2}+(y-3)^{2} } = 16[/tex]

[tex]2x^{2} +2y^{2} +8x-8y+10=0\\x^{2} +y^{2} + 4x - 4y + 5 =0[/tex]

This is the Locus of point P where PA²+PB²  = 16.

The locus of point P such that PA²+PB² = 16 is [tex]x^{2} +y^{2} + 4x - 4y + 5 =0[/tex]

To know more about Locus, visit:

https://brainly.com/question/19578071

#SPJ1

What are the equations of the asymptotes of the hyperbola?

(y+4)^2. (x-6)^2
——— - ———. =. 1
36. 49


Enter your answer in a point-slope form by filling in the boxes. Enter the slope as a simplified fraction.


y= ……= +…..(x…..)

Answers

The equations of the asymptotes of the hyperbola is 6y = -7x,

Define Asymptotes of the hyperbola.

There are two asymptotes on each hyperbola. A hyperbola with a horizontal transverse axis and centre at (h, k) contains one asymptote with equation y = k + (x - h) and the other with equation y = k - (x - h). A straight line that continuously approaches a certain curve without ever meeting it is an asymptote. In other words, an asymptote is a line that a curve travels towards as it approaches infinity. The two vertices, the two focus points, and the centre are all on the same horizontal line and equally spaced from one another. This is a horizontal hyperbola because of this. Our graph of the hyperbola follows the lines of the asymptotes.

Given,

Equations of hyperbola,

(y+4)². (x-6)²

——— - ———. =. 1

36. 49

a² = 36

a = 6

b² = 49

b = 7

Asymptotes of the hyperbola:

y = ±b/a × x

y = 7/6x

6y = 7x

y = -7/6 x

6y = -7x

To learn more about Asymptotes of the hyperbola, visit:

https://brainly.com/question/12601454

#SPJ1

help me asap i need the full answer please

Answers

Answer:

dont get it

Step-by-step explanation:

a least squares linear trend line is just a simple regression line with the years recoded. group of answer choices true false

Answers

a least squares linear trend line is just a simple regression line with the years recoded  then it is a true statement

The simple linear regression model is;

y = mx + c

Where,

y = dependent variable

m is the slope

x is the independent variable

c is the y- intercept

The long-term trend only Least-Squares Regression Model also follows the same format except y becomes Yt and x becomes t.

The long-term trend only Least-Squares Regression Model is therefore the same as a simple linear regression only with different variable terms.

learn more about of square here

https://brainly.com/question/19595237

#SPJ4


Plot the given parabola on the axes. Plot the roots, the vertex and two other points.
y = 29x² - 174x - 203

Answers

The graph of the parabola is shown with a vertex, while the root of the equation is x = 7 and -1.

What is a parabola?

A parabola is a cross-section cut out of the cone and represented by an equation

Here,
y = 29x² - 174x - 203
Roots the equation,
29x² - 174x - 203 = 0
x² - 6x - 7 = 0
(x - 7)(x + 1) = 0

Roots are x = 7 and -1
Now illustrating the graph of the parabola,

Thus the graph of the parabola is shown with a vertex, while the root of the equation is x = 7 and -1.

Learn more about parabola here:

brainly.com/question/4074088

#SPJ1

Please help me raise my grade!

Answers

We need to use the concept of Percentile Rank. The Percentile Rank for score 71 is   33.33   and the score of Viktor is   84.

What is Percentile Rank?

According to the pupils in the particular norm group, a student's performance is shown by their percentile rank. Let's try to put the percentile rank in a tidy mathematical equation now that you are clearer on what it actually is. A collection of values A = x1, x2, x3,..., xn with N values will be used in our attempt to calculate the percentile rank of the data point xm. In this scenario:

PR = L / N × 100 where:

PR stands for percentile rank and has a range of 0 to 100;

L is the quantity of values in set A that are less than or equal to the value of your data, xm; and

The entire collection of values in A has a total of N values.

Calculation:

Given some of the test scores. Arrange the test Scores in ascending order.

A={58,64,66,70,71,75,77,80,84,85,87,90,93,95,96}

N=15

Now find out the values in the set which are less than or equal to 71.

L=5

Apply, PR=L/N ×100

⇒PR=5/15 × 100

PR=33.33 is the Percentile Rank of score 71.

Viktor is in 60th percentile, so find out L.

⇒60=L/15 ×100

⇒L=60×15/100

L=9.

So 84 is Viktor Score.

We need to use the concept of Percentile Rank. The Percentile Rank for score 71 is   33.33   and the score of Viktor is   84.

To refer more about Percentile Rank, visit:

https://brainly.com/question/24245405

#SPJ1

the midpoint of AB is M=(1,3). one endpoint is A=(4,1). find the coordinates of the other endpoint, b.

Answers

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +4}{2}~~~ ,~~~ \cfrac{ y +1}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(1~~,~~3)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +4}{2}=1\implies x+4=2\implies \boxed{x=-2} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +1}{2}=3\implies y+1=6\implies \boxed{y=5}[/tex]

2+2:
NNEED THOROUGH EXPLANATION

Answers

The mathematical expression 2+2 has a value of 4. This is because when two numbers are added together, their values are combined to produce a new value. In the case of 2+2, the value of 2 is added to the value of 2, resulting in a new value of 4.

In mathematical notation, the plus sign (+) is used to indicate addition. When a plus sign appears between two numbers, it indicates that the numbers should be added together to produce a new value. In the expression 2+2, the plus sign indicates that the values of 2 and 2 should be added together to produce a new value.

In order to evaluate the expression 2+2, we can follow the order of operations, which is a set of rules that dictate the sequence in which mathematical operations should be performed. The order of operations specifies that addition should be performed before any other operation, so in the expression 2+2, we would first perform the addition of 2 and 2 to produce a new value of 4.

Therefore, the value of the expression 2+2 is 4.

Answer:

Step-by-step explanation:

take your fingers, raise 2 of them now raise 2 more how many do you see? 4.

to display the distribution of grades (a, b, c, d, f) in a course, it would be correct to use

Answers

In order to display the distribution of grades (a, b, c, d, f) in a course, it would be correct to use a bar chart.

To create a bar chart to display the distribution of grades in a course, you would first need to gather the data on the number of students who received each grade. Once you have gathered this data, you can use a computer software tool or graph paper and a pencil to create the bar chart.

When creating the chart, you would label the x-axis with the different grades (a, b, c, d, f) and the y-axis with the number of students. Then, you would draw a bar for each grade, with the height of the bar representing the number of students who received that grade. You can also add a legend to the chart to provide more information about the data, such as the percentage of students who received each grade.

Thus, a bar chart would be the best to use for dispaying the distribution of grades.

Learn more about bar chart by visiting the link below:

brainly.com/question/15507084

#SPJ4


Spent $650
Spent $842
Earned $522
Earned $650
Part A - Write an integer to represent the positive or negative value for each transaction. Make sure to include your signs!
Part B - Spending $650 and earning $650 are opposite transactions but they have the same absolute value.
Why? Explain what makes these values opposites AND how their absolute value is the same

Answers

-$650, Spent -$842, Earned +$522 and Earned +$650 are required integers and Spending $650 and earning $650 are opposite transactions but they have the same absolute value.

What is Number system?

A number system is defined as a system of writing to express numbers.

Spent $650

Spent $842

Earned $522

Earned $650

Spent -$650, Spent -$842, Earned +$522 and Earned +$650.

Spending $650 and earning $650 are opposite transactions but they have the same absolute value because the absolute value of a number n is written as |n|.

The absolute value of 0 is 0. Two numbers are opposites if they have the same absolute value but different signs. Opposites are the same distance from 0 on a number line, and they are on opposite sides of 0.

Hence, -$650, Spent -$842, Earned +$522 and Earned +$650 are required integers and Spending $650 and earning $650 are opposite transactions but they have the same absolute value.

To learn more on Number system click:

https://brainly.com/question/22046046

#SPJ1

Find the measure of angle <1

A. 45
B. 120
C. 180
D. 60

Please help!!!

Answers

Answer:

D. 60

Step-by-step explanation:

A triangle has 180 degree

We know that the three angles of this triangle are corresponding, which means all three angles are equal to each other.

Take 180 divided by 3 = 60 degree

So, the answer is D

Answer:

D, 60°

Step-by-step explanation:

These lines on all angles of the triangle mean all of the angles are equal to each other!

Remember, ALL triangles equal 180°

There are 3 angles that share 180° degrees!

Let's divide 180° by 3 to see what EACH ANGLE equals

180 ÷ 3 = 60

All of these angles are equal to 60°

Or, in other words, angle 1 = 60°

These tables of ordered pairs represent some points on the
graphs of lines p and r.
Which system of equations is represented by lines p and r?

Answers

Answer:

y=2x+8 and y=-2x+7

Step-by-step explanation:

The attached graphic shows the steps.  Two distinctive features of a straight line in the form of y=mx+b are its slope, m, and its y-intercept, b.  A quick look at the equations reveals that their slopes form unique pairs.  The slopes in the first option are 2 and -2.  The other slope pairs are b)  4 and -2, c) -3 and 3, and d)  -2,-6.  This means that if we calculate the slopes of lines p and r from the given points, there should only be one result that matches the combinations provided.

Set up a table for the points (see worksheet) and then pick any two points for each line to calculate slope.  The slope is the Rise/Run of the line:  the change in y for a change in x.  The table uses the first and last points for each line, but any two points will work (for a straight line).  

Lines p and r are found to have slopes of 2 and -2, respectively.  That means their equations will take the form of:

p:  y = 2x + b

r:   y= -2x + b

We could (and will) work further to find the y-intercepts (b), but just looking at the answer options, it is clear that the first set of equations match the slope calculations exactly.

 y = 2x+8, and y = -2x+7

None of the others come close.  This is the answer.  If this is a test, or you are missing a more interesting activity, stop here.  But just to insure we are doing the work correctly, and that the ideas are understood, lets plot the two given equations and add the points, as shown on the worksheet.  It is satisfying to find that the graph confirms our choice.  The points all fall on the two lines.  Another useful check is to find the y-intercepts (the value of y when x=0).  Those are noted on the graph (0,7) for r, and (0,8) for p, and lend further confimration to our choice.  Add these intercepts to the first equations that contain the y-intercept as b.  b for line p is 8,  b for line r is 7:

p:  y = 2x + b

r:   y= -2x + b

p:  y = 2x + 8

r:   y= -2x + 7

A perfect match to our selection.  Calculating b is not needed based on the options presented, but a tougher question may require finding the y-intercept before making a choice.

which two numbers whose product is -10 and whose sum is 10 ?

Answers

By solving a system of equations we can find the two numbers:

y = 5 + √15

x = 5 - √15

How to find two numbers?

We can define the two numbers as x and y, and we know that:

x*y = -10

x  + y = 10

So we have a little system of equations here.

We can isolate x on the second equation to get:

x = 10 - y

And now replace it on the first equation to get:

(10 - y)*y = -10

10y - y^2 = 10

Then we have a quadratic equation:

y^2 - 10y + 10 = 0

The solutions are given by:

[tex]y = \frac{10 \pm \sqrt{(-10)^2 - 4*10*1} }{2} \\\\y = \frac{10 \pm \sqrt{60} }{2}\\\\y = 5 \pm \sqrt{15}[/tex]

So the two numbers are:

y = 5 + √15

x = 5 - √15

Learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

Click the arrows to choose an answer from each menu.
One circled number equals Choose... . Another circled number equals
The sum of those numbers is the third number because
Choose...
Choose...

Answers

One circled number equals 10. Another circled number equals 30. The sum of those numbers is the third number because 10 + 30 is equal to 40.

What is a numerical data?

In Mathematics, a numerical data is sometimes referred to as a number and it can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data simply refers to a data set consisting of numbers rather than words.

Based on the information provided in the multiplication table, we can logically deduce the following three (3) numbers that are circled:

First circled number = 10

Second circled number = 30

Third circled number = 40

In this context, the sum of the first circled number and the second circled number is equal to the third circled number;

Third circled number = 10 + 30

Third circled number = 40.

Read more on numbers here: brainly.com/question/24654699

#SPJ1

Complete Question:

Three numbers are circled in the multiplication table. Use the drop-down menus to explain why the sum of two of the numbers is the third number.

Click the arrows to choose an answer from each menu.

One circled number equals ____. Another circled number equals _____. The sum of those numbers is the third number because ____.

Write a system of linear inequalities represented by the graph.
Inequality 1:
Inequality 2:
(Please explain, thanks!)

Answers

The system of equations  presented in the graph is written as

y > -2x/3 + 2y = x

How to write the inequalities

Linear function in the slope intercept formula is written in the form

y = mx + c

definition of variable

y = output variable

m = slope

x = input variable

c = y intercept

The dashed line represents inequality without "equal to" hence less than or greater then only. shading above the line is greater than

the line passed through points (0, 2) and (3, 0)

the slope, m is = (2 - 0) / (0 - 3) = -2/3

the y intercept = 2

y > -2x/3 + 2

The solid line means the inequality has equal to hence it either greater than or equal to OR less than or equal to. no shading means it is only equal to

the line passed through points (0, 0) and (2, 2)

the slope, m is = (0 - 2) / (0 - 2) = 1

the y intercept = 0

y = x

The equation of the graph is

y > -2x/3 + 2

y = x

Learn more about linear functions at:

https://brainly.com/question/29213643

#SPJ1

O{-4, -1, 15, 18}
O{-4, -1, 1, 4, 7, 8, 15, 18}
{-1, 4, 8, 18)
O{-4, 1, 7, 15}
-1.
4-
8-
18
-4
7
-15

Answers

What’s the question? Is it asking for Domain or Range?

Which expression is equivalent to 4(−4.3y − 13.6)?

−17.2y − 13.6
−17.2y − 54.4
−0.3y − 9.6
−0.3y − 13.6

Answers

Answer:

[tex]-17.2y-54.4[/tex]

Step-by-step explanation:

Use the distributive property.

Answer:

A

Step-by-step explanation:

The correct answer is A. −17.2y − 13.6.

To find the equivalent expression, we can first distribute the 4 to the terms inside the parentheses:

4(−4.3y − 13.6) = −17.2y − 54.4

Then, we can combine like terms to simplify the expression:

−17.2y − 54.4 = −17.2y − 13.6

Therefore, the equivalent expression is −17.2y − 13.6.

You receive $8 for raking leaves for 2 hours. what is the expression?

Answers

Answer:

8x2

Step-by-step explanation:

Find the area and perimeter of these shapes

Answers

Answer:

what the shapes mg me down..

Simplify : a) 2(x 2 + y 2 ) + 3 ( x 2 − y 2 )

Answers

Answer:

8x2−8y2+6x−6y

Step-by-step explanation:

x2 means x squared

Please help me, write it in numbers please, not letters. It's due tonight and I need help with everything!

Answers

Answer:

1) 4 1/4, 2) 10 22/35, 3) 9 11/15, 4) 7 1/3, 5) 11 1/24

-------------------------------------------

See the steps below, they should be self-explanatory.

Let me know if anything is unclear.

Question 11 1/2 + 2 3/4 = 1 + 2 + 1/2 + 3/4 = 3 + 2/4 + 3/4 = 3 + 5/4 = 3 + 1 1/4 = 4 1/4

Question 24 3/7 + 6 1/5 = 4 + 6 + 3/7 + 1/5 = 10 + 3*5/35 + 1*7/35 = 10 + 22/35 = 10 22/35

Question 34 2/5 + 5 2/6 = 4 + 5 + 2/5 + 1/3 = 9 + 2*3/5 + 1*5/15 = 9 + 11/15 = 9 11/15

Question 43 7/7 + 3 1/3 = 3 + 1 + 3 1/3 = 4 + 3 1/3 = 7 1/3

Question 51 4/6 + 9 3/8 = 1 + 9 + 2/3 + 3/8 = 10 + 2*8/24 + 3*3/24 = 10 + 25/24 = 10 + 1 1/24 = 11 1/24

A basketball team had a mean score of 66 points per game. The total number of points they scored is 924. How many games have they played?

Answers

Answer:

the team played a total of 14 games

Step-by-step explanation:

To find the number of games the team played, you can divide the total number of points they scored by the mean number of points they scored per game. In this case, you would divide 924 by 66 to get:

[tex]924 / 66 = < < 924/66=14 > > 14 games[/tex]

So, the team played a total of 14 games.

How many solutions does each system of equations have? Part A: {3x−y=13y+3=9x

Answers

The system of equations have Unique solution.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The system of equation is,

⇒ 3x - y = 13

⇒ y + 3 = 9x

Now,

Since, The system of equation is,

⇒ 3x - y = 13

⇒ y + 3 = 9x

It can be written as,

⇒ 3x - y = 13

⇒ 9x - y = 3

Clearly, We have;

⇒ 3/9 = - 1 / - 1

⇒ 1/3 ≠ 1

Thus, It has Unique solution.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

Other Questions
describe what happens in the embryonic stage of development. describe what happens in the fetal stage of development. an object is placed just inside the focal point of a converging lens. describe the image (mark all that apply). You are going send Christmas cards to 100 of your friends. Each box ofChristmas cards contains 15 cards and the cost per box is $17.00. You are going to purchase enough Foreverstamps from the post office to mail 100 cards. How much will it cost in total? Simplify the expression.14+(-4)-6/7j-3/7j+7 6x-3y= -214x=3y-9Help Babak Industries is a division of a major corporation. Last year the division had total sales of $21,360,000, net operating income of $1,895,760, and average operating assets of $7,800,000.The division's turnover is closest to:Multiple Choice2.740.241.9611.27 The question is "What does the y-intercept of the line of best fit tell you about the situation below?" Lucy wants to but a new car but needs money for the down payment. Her parents agree to lend her money at an annual rate of 5%, charged as simple interest. They lend her $4000 for 2 years. She makes no payments except the one at the end of that time.Answer the following questions:How much total interest will Lucy have to pay?What will the total repayment amount be (including interest) which of the following impacts on political participation has resulted from the decrease in barriers to publishing on the internet? The average age of ceo's is 56 years. Assume the random variable is normally distributed. If the standard deviation is 4 years, find the probability that the age of a ceo is between 50 and 56 years old. the degrees of freedom for a chi-square test of independence for the following data is 5. group of answer choices true false In the accompanying diagram of right triangle ABC,altitude BD is drawn to hypotenuse AC.Which statement must always be true?1) AD/AB = BC/AC2) AD/AB = AB/AC3) BD/BC = AB/AD4) AB/BC = BD/AC A farmer wants to find the best conditions for growing carrots. Previous research indicates that they grow best in partial sunlight. Which factor is the best choice for an independent variable for the farmer's experiment?A.Type of vegetableB. Amount of sunlightC. Type of fertilizerD. Mass of carrot simplify (10x-5/6)-x+4/3 it has been shown that in the absence of taxes and other market imperfections firm value will be unaffected by dividend policy. explain the logic behind this conclusion Let X be a binomial random variable with n trials and probability p of success. A.What is the generalized likelihood ratio for testing H_0: p = .5 versus H_A: p notequalto .5? B.Show that the test rejects for large values of |X - n/2|. C.Using the null distribution of X, show how the significance level corresponding to a rejection region |X - n/2| > k can be determined. D.If n = 10 and k = 2, what is the significance level of the test? E.Use the normal approximation to the binomial distribution to find the significance level if n = 100 and k = 10. Please help me!I need to deliver it tomorrow. MODELING REAL LIFE An obstacle course needs anew piece made in the shape of a triangular prismwith an equilateral triangle for a base. The side lengthx (in feet) of the base and the height y (in feet) of theprism are related by the inequality y> x + 1. Thepiece has the following additional constraints. The height must be no more than 7 feet greater thanthe side length of the base. The side length of the base must be at least 1 foot.Write and graph a system that represents the situation.Give one example of a height and side length that theobstacle course can use. based on the above chart, approximately what percent was spent on elective defense or other elective federal programs in the 2016 federal budget? If the air temperature is -14F how many degrees must it rise to reach 0F