Leslie got 7 out of 20 questions correct on her test. What percent of the questions did she get correct?

Answers

Answer 1
35%.


7/20= 3.5/10

Multiplying by 10 gets 35/100= 35%
Answer 2
If Leslie got a 7 out of 20 questions correct on her test the percentage would be35%

Related Questions

A county fair uses a chart....break even

Answers

Answer:

huh???

Step-by-step explanation:

A country fair uses a chart....break even sad story

The rate in the portion formula is not always expressed with a percent symbol?

Answers

That's correct. The rate in the portion formula can be expressed as a decimal, fraction, or percentage, depending on the context and what is most convenient for the problem being solved.

What is the proportional and ratio formula?

How do you calculate ratio and proportion? Ans: The ratio formula is written as a: b a/b for any two numbers. Contrarily, the percentage formula is written as a:b::c:da:b::c:da:b=cd.

What does a ratio example look like?

An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) 1 out of 4 are boys, and 3/ 4 are girls.

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Best way to solve this type of equation Ax+by=c

Answers

The best way to solve an equation of the form Ax+by=c could be either substitution, completing the squares or graphical method depending on the type of equation given.

Quadratic equation

The equation in the form Ax+by=c is a quadratic problem which could be approached in different ways depending on the specific equation given and the information provided.

The methods of approach are substitution, completing the squares or graphical method which all have proven to be suitable ways to arrive at the solution.

Hence, either of the three methods are good ways to solve such equation.

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Which lines are parallel?
M: y + 1 = -3 (x-1)
K: y =3(x+2)
P: y + 4 = 3x

Answers

The most appropriate choice for equation of line in slope intercept form will be given by-

line K is parallel to line P

line M is not parallel to both line K and line P.

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx +c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If \(\theta\) is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = \(tan\theta\)

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line

For M

y + 1 = -3(x - 1)

y + 1 = -3x + 3

y = -3x + 3-1

y = -3x + 2

Slope of M = -3

For K

y = 3(x+2)

y = 3x + 6

Slope of K = 3

For P

y + 4 = 3x

y = 3x - 4

slope of P = 3

Since Slope of K = Slope of P,

line K is parallel to line P

Since slope of M is different from slope of both K and P,

line M is not parallel to both line K and line P.

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answer this question please

answer this question please

Answers

Step-by-step explanation:

this is just a warm-up. almost everything is already there. you only need to put the numbers in.

so, what is unclear ?

please, tell me, so that I can help better.

the radius is always half of the diameter. or the diameter is twice the radius.

in our case : 12/2 = 6 cm.

the height is plainly written in the graph : 9 cm

Vcylinder = base area × height = pi×r² × height =

= 3.14 × 6² × 9 = 3.14×36×9 = 1,017.36 cm³

Vcone = 1/3 × Vcylinder = 1/3 × 1,017.36 = 339.12 cm³

Which ordered pair makes both inequalities true?
y> -3x +3
y22x-2
O (1,0)
O (-1,1)
O (2,2)
O (0,3)

Answers

None of the ordered pairs (1, 0), (-1, 1), (2, 2), and (0, 3) make both inequalities true.

To determine which ordered pair makes both inequalities true, we can substitute the given values into the inequalities and check for validity:

1. (1, 0):

  For y > -3x + 3: 0 > -3(1) + 3 -> 0 > 0, which is not true.

  For y < 2x - 2: 0 < 2(1) - 2 -> 0 < 0, which is not true.

  Therefore, (1, 0) does not satisfy both inequalities.

2. (-1, 1):

  For y > -3x + 3: 1 > -3(-1) + 3 -> 1 > 6, which is not true.

  For y < 2x - 2: 1 < 2(-1) - 2 -> 1 < -4, which is not true.

  Therefore, (-1, 1) does not satisfy both inequalities.

3. (2, 2):

  For y > -3x + 3: 2 > -3(2) + 3 -> 2 > -3, which is true.

  For y < 2x - 2: 2 < 2(2) - 2 -> 2 < 2, which is not true.

  Therefore, (2, 2) does not satisfy both inequalities.

4. (0, 3):

  For y > -3x + 3: 3 > -3(0) + 3 -> 3 > 3, which is not true.

  For y < 2x - 2: 3 < 2(0) - 2 -> 3 < -2, which is not true.

  Therefore, (0, 3) does not satisfy both inequalities.

None of the given ordered pairs satisfy both inequalities simultaneously.

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Consider the line =−8x7y−8.
Find the equation of the line that is parallel to this line and passes through the point −6, 4.

Find the equation of the line that is perpendicular to this line and passes through the point −6, 4.

Answers

Consequently, the equation of the line passing through (-6, 4) and perpendicular to the provided line is y = (7/8)x + 25/4.

How to calculate the equation of the line?

We use the fact that parallel lines have the same slope to determine the equation of a line that is perpendicular to a given line and passes through a point. provided that it takes the form y = mx + b, where m is the slope, the provided line has a slope of -8/7. The parallel line will therefore similarly have a slope of -8/7.

The point-slope form of a line is used to determine the y-intercept of a parallel line: y - y1 = m(x - x1), where (x1, y1) is the point the line passes through. We obtain: y - 4 = (-8/7)(x + 6) by substituting (-6, 4) and -8/7 for m.

This equation can be simplified to y = (-8/7)x - 40/7.

We make use of the fact that perpendicular lines have opposing reciprocal slopes to determine the equation of a line that is perpendicular to the supplied line and passes through (-6, 4). provided that the provided line has a slope of -8/7, the perpendicular line will have a slope of 7/8.

Again using the point-slope representation of a line, we arrive at: y - 4 = (7/8)(x + 6)

This equation can be simplified to: y = (7/8)x + 25/4

Consequently, the equation of the line passing through (-6, 4) and perpendicular to the provided line is y = (7/8)x + 25/4.

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Consider f(x)=root(x-5)
Find the value of x for which f is undefined

Answers

Answer:

x < 5

Step-by-step explanation:

For real numbers, you can take the square root of a positive number and of zero. You cannot take the square root of a negative number.

The radicand, x - 5, cannot be negative.

If the radicand is negative, the function is undefined.

x - 5 < 0

x < 5

Which statements best describe an effective claim in an argumentative essay? Select two options. It is precise and clear. It is debatable but cannot be refuted. It is emotional and states an opinion. It states a bias using clear language. It states a fact using precise language

Answers

The statements which best describe an effective claim in an argumentative essay are:

A. It is precise and clear.

E. It states a fact using precise language.

An argumentative essay can be defined as a literary work which comprises an expression of a writer's stance (position) on a specific topic or subject matter.

A claim refers to a statement that is used by a writer to prove, substantiate or support an argument. Thus, it is an assertive statement expressed by a writer to prove that an argument is true, factual, and real.

In this context, the main function of an effective claim in an argument is simply to precisely and clearly state a fact based on a writer's opinion.

In conclusion, the following statements which best describe an effective claim in an argumentative essay are:

It is precise and clear.It states a fact using precise language.It is debatable but can't be refuted because it is based on factual and logical reasoning.

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Answer:

Its A and B

Step-by-step explanation

The Question is in the attachment below

The Question is in the attachment below

Answers

Answer:

Step-by-step explanation:

It is J I’m pretty sure

The graph of a function f is given. Use the graph to estimate the following.

The graph of a function f is given. Use the graph to estimate the following.

Answers

Local maximum: (-6, 8)

Local maximum: (6, 3)

Local minimum: (0, -2)

Local minimum: (9, 2)

Increasing from: n ∈ (-∞, -6) ∪ (0, 6) ∪ (9, ∞)

Decreasing from: n ∈ (-6, 0) ∪ (6, 9)

What is local maximum and minimum?

The maximum and minimum of a function, sometimes referred to as the extremum in mathematical analysis, are its biggest and lowest values, respectively, either on the whole domain or within a specified range. A maximum within a constrained domain, particularly a point on a function whose value exceeds the values of every other point in its vicinity. A point on a graph (or its related function) with a value that is lower than all other points close to it.

A real-world problem scenario can be solved by using the local maximum and minimum to get the best equational solution. It is possible to calculate the input values for which these expressions have a maximum or minimum output by using the local maximum and minimum.

Local maximum: (-6, 8)

Local maximum: (6, 3)

Local minimum: (0, -2)

Local minimum: (9, 2)

Increasing from: n ∈ (-∞, -6) ∪ (0, 6) ∪ (9, ∞)

Decreasing from: n ∈ (-6, 0) ∪ (6, 9)

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look at attachment!!!!

look at attachment!!!!

Answers

Answer:

x = 5

Step-by-step explanation:

We know that BD = 2x - 1 and BC + CD = BD.  Thus, we can set the sum of (x- 3) and 7 equal to 2x - 1 to find x:

BC + CD = BD

x - 3 + 7 = 2x - 1

x + 4 = 2x - 1

x + 5 = 2x

5 = x

Thus, x = 5

Checking the validity of our answer:

We can check that our answer is correct by plugging in 5 for x in x - 3 and 2x - 1 and checking that we get the same answer on both sides of the equation:

5 - 3 + 7 = 2(5) - 1

2 + 7 = 10 - 1

9 = 9

Thus, our answer is correct.

Use the substitution method to determine the solution type of the following system.

3y – 6x = 3

y = 2x + 1

Question 7 options:

Infinitely many solutions


(3, –1)


(2, 0)


No solutions

Answers

Answer:

Step-by-step explanation:

3y – 6x = 3     -----------------------------------(I)

y = 2x + 1      ----------------------------------(II)

Substitute y = 2x + 1 in equation (I)

3*(2x+ 1) - 6x = 3

3*2x + 3*1 -6x = 3

  6x + 3 - 6x = 3              

               3 = 3

So, no solutions

Answer:

Use the substitution method to determine the solution type of the following system.

3y – 6x = 3

y = 2x + 1

Correct Answer

Infinitely many solutions

No solutions

(3, –1)

(2, 0)

Step-by-step explanation:

Evaluate the left hand side to find the value of a in the equation in simplest form.

Evaluate the left hand side to find the value of a in the equation in simplest form.

Answers

The value of a in the equation in the simplest form will be 17 / 6.

We are given an equation:

x³ / x^(1/6) = x^(a)

We need to evaluate the left hand side to find the value of a in the equation in simplest form.

We know that:

x^ (a) / x^ (b) = x^ ( a - b)

Using this, we get that:

x^ (3 - 1/6) = x^ (a)

x^ (17/6) = x^ (a)

By comparing the bases, we get the value of a as:

a = 17 / 6.

Therefore, the value of a in the equation in the simplest form will be 17 / 6.

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In analyzing hits by certain bombs in a war, an area was partitioned into 570 regions, each with an area of 0.75 km^ 2 . A total of 535 bombs hit the combined area of 570 regions Assume that we want to find the probability that randomly selected region had exactly two hits the Poisson distribution formula

In analyzing hits by certain bombs in a war, an area was partitioned into 570 regions, each with an area

Answers

Answer:

0.1723 = 17.23% probability that randomly selected region had exactly two hits.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\(\mu\) is the mean in the given interval.

535 bombs hit the combined area of 570 regions

This means that the mean number of hits per region is given by:

\(\mu = \frac{535}{570} = 0.9386\)

Find the probability that randomly selected region had exactly two hits

This is P(X = 2).

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

\(P(X = x) = \frac{e^{-\0.9386}*(0.9386)^{2}}{(2)!} = 0.1723\)

0.1723 = 17.23% probability that randomly selected region had exactly two hits.

which graph represents a function?

which graph represents a function?

Answers

I can determine a function by drawing a vertical line. If this line pass trought the graph only one time, it's a function.

The only function there is the last one. (Right bottom)

which graph represents a function?

Question
From a point P on a level ground and directly west of a pole, the angle of elevation of the top of the pole is 45° and from point Q east of the pole, the angle of elevation of the top of the pole is 58°. If |PQ|= 10m, calculate, correct to 2 significant figures, the:
a) distance from P to the pole;
b) height of the pole.

QuestionFrom a point P on a level ground and directly west of a pole, the angle of elevation of the top

Answers

a) The distance from point P to the pole  is: 6.2 m

b) The height of the Pole is: 6.2 m

How to find the distance and height from angle of elevation?

The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.

Now, we are given that:

The angle of elevation of the top of the pole =  45°

Angle of elevation of the top of the pole = 58°.

|PQ|= 10m

a) PR is distance from point P to the pole and using trigonometric ratios, gives us:

PR/sin 58 = 10/sin(180 - 58 - 45)

PR/sin 58 = 10/sin 77

PR = (10 * sin 58)/sin 77

PR = 8.7 m

b) P O can be calculated with trigonometric ratios as:

P O = PR * cos 45

P O = 8.7 * 0.7071

P O = 6.2 m

Now, the two sides of the isosceles triangle formed are equal and as such:

R O = P O

Thus, height of pole R O = 6.2 m

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QuestionFrom a point P on a level ground and directly west of a pole, the angle of elevation of the top

Solve the equation 42 = v + 35 for v.


A. −77

B. 77

C. −7

D. 7

Answers

Answer:

v = 7

Step-by-step explanation:

42 = v + 35

-35        -35

7 = v

The answer is D. 7

I took the quiz and got it right

Is the the right answer???

Is the the right answer???

Answers

i believe the answer is 35, 50 is supplementary and then you get 130 which you add to 15 to get 145. Triangles are 180 degrees so then 180-145 is 35.

Pls help I’ll brainlest ASAP

Pls help Ill brainlest ASAP

Answers

Answer:

x=24

Step-by-step explanation:

the answer is x=24…!!

Given that f(x) = x - 3, g(x) = 4x and h(x) = 2f(x - 3) + g(x+1),
then what is the value of h(6)?

Answers

Answer: The value of h(6) is 28.

Step-by-step explanation: First, we need to calculate the value of f(x-3):f(x-3) = (x-3) - 3 = x - 6

Next, we need to substitute this into h(x) and simplify:h(x) = 2f(x-3) + g(x+1) = 2(x-6) + 4(x+1) = 6x - 8

Finally, we can substitute x = 6 to find h(6):h(6) = 6(6) - 8 = 28

Answer:

h(x)= 2f(x-3) + g(x+1)

h(x)= 2(x-3-3)+4x+1

h(x)= 2(x-6)+4x+1

h(x)=2x-12+4x+1

h(x)=6x-11

h(6)=36-11

h= 25

WILL GIVE BRAINLIST
MATH




CONVERT EACH MEASUREMENT

SHOW STEPS ALL


9 1/8 lbs to ounces

Answers

Answer:

146 Ounces.

Step-by-step explanation:

9.125 \((\frac{1}{8})\) lbs to ounces.

Multiply the mass value by 16.

To Check Work:

Divide 146 by 16 which equals \(\frac{73}{8}\)/ 9.125.

Divide 146 by 9.125 \((\frac{1}{8})\) which equals 16.

if y is directly porportional to x^2 and the difference in the values of y when x=1 and x=3 is 32, find the value of y when x=-2

Answers

Answer:

Step-by-step explanation:

y=kx²

y₁=k(1)²=k

y₃=k(3)²=9k

y₁-y₃=k-9k=32

-8k=32

k=-4

y=-4x²

y₋₂=-4(-2)²=-16

a marketing agency selected a random sample of television viewers to test the claim that the proportion of viewers who watch a particular show is less than 0.20 at a level of significance of 0.05. the test yielded a p -value of 0.47. assuming all conditions for inference were met, which of the following is the correct conclusion?

Answers

Correct conclusion , Proportion of viewers is not less than 0.20.

What is proportion ?

A proportion is a way to express the relationship between two or more quantities or values. It is a statement that asserts that two ratios or fractions are equal, such as "2/5 is equal to 4/10". Proportions can be written in different ways, such as "2 to 5 is equal to 4 to 10", or "2:5 = 4:10".

the proportion of viewers who watch the particular show is less than 0.20. The p-value of 0.47 is greater than the level of significance of 0.05, meaning that the results of the test are not statistically significant and do not provide enough evidence to reject the null hypothesis that the proportion of viewers who watch the particular show is greater than or equal to 0.20. Therefore, the marketing agency cannot conclude that the proportion of viewers who watch the particular show is less than 0.20.

Correct conclusion , Proportion of viewers is not less than 0.20.

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Write the equation of the line parallel to y=1/2x−6 that passes through (−10,4).

Answers

Answer:

y = 1/2 x + 9

Step-by-step explanation:

y = 1/2 x + b

4 = (1/2)(-10) + b

4 = -5 + b

b = 9

7)
Which is the correct solution for the system?
3y = 6 - 2x
8x = 3y - 1
A)
5
and y =
B)
5
x = 2 and y =
win
C)
2
x = 3 and y =
12 /
UIN
x = 3 and y =
OM

Answers

Answer:

3y = 6 - 2 ( 0 ) take

x zero and find value of y

3y = 6 - 2 ( 0 )

3y = 6 - 0

3y = 6

both sides divide by 3

ans : y = 2

now we can find so the value of x

3y = 6 - 2x

3( 0 ) = 6 - 2x

when we find the value x we take y ( 0 ) zero

3 ( 0 ) = 6 - 2x

0 = 6 - 2x

0 + 6 = - 2x

6 = -2x

both sides divide by -2

ans or value of x is 3

Step-by-step explanation:

first

- find one of the values of x and y

two :

- when you solving this

take y ( 0 ) if you search / find the value of X

Simplify the following expression.

29.718 - 29.63

Answers

Answer:

0.088 is the answer...

Miguel plots points A, B, and C in the coordinate plane.

A. What is the distance between points A and B? Explain your reasoning.
B. Is (gif triangle) ABC an equilateral triangle? Explain your reasoning.

Miguel plots points A, B, and C in the coordinate plane.A. What is the distance between points A and
Miguel plots points A, B, and C in the coordinate plane.A. What is the distance between points A and

Answers

is △ABC equilateral?  well, we dunno, however let's check for all sides' length.

\(~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{-6}~,~\stackrel{y_2}{-2}) ~\hfill AB=\sqrt{(~~ -6- (-3)~~)^2 + (~~ -2- 2~~)^2} \\\\\\ ~\hfill AB=\sqrt{( -3)^2 + ( -4)^2} \implies AB=\sqrt{ 25 }\implies \boxed{AB=5}\)

\(B(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad C(\stackrel{x_2}{0}~,~\stackrel{y_2}{-2}) ~\hfill BC=\sqrt{(~~ 0- (-6)~~)^2 + (~~ -2- (-2)~~)^2} \\\\\\ ~\hfill BC=\sqrt{( 6)^2 + ( 0)^2} \implies BC=\sqrt{ 36 }\implies \boxed{BC=6} \\\\\\ C(\stackrel{x_1}{0}~,~\stackrel{y_1}{-2})\qquad A(\stackrel{x_2}{-3}~,~\stackrel{y_2}{2}) ~\hfill CA=\sqrt{(~~ -3- 0~~)^2 + (~~ 2- (-2)~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -3)^2 + (4)^2} \implies CA=\sqrt{ 25 }\implies \boxed{CA=5}\)

well, not quite.

PLES HELP ASAP Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

Show that the ratios
10
20
and
30
60
form a proportion by finding a common multiplier.
Show that the ratios in part (a) are equal by writing them in simplest form.

Answers

Can you explain more

Consider the following advertisement for BrightLending, a short-term personal loan operator.

Loan amount: $800

Deposit date: Tuesday, May 17, 2022

Repayments: 22 payments of $203.40 bi-weekly

1st Payment due: Friday, May 27, 2022

a) If someone took out the $800 loan shown in the ad, how much would they pay in total for the loan?

b) How long is it taking this person to pay off the loan, in years?

Answers

Answer:

a) $4,475.20

b) it would take approximately 0.846 years or approximately 10 months to pay off the loan.

Step-by-step explanation:

if we nevermind the deposit and repayment dates, since they are not relevant for this case, so we have only a loan for $800 to be repaid in 22 weeks, at 203.40 every other week, biweekly namely.

Now, we can also nevermind the biweekly part, 22 payments are 22 regardless if it's done daily or yearly or bimonthly or bidecade, 22 is just 22.

a)

22 payments at 203.4 is just (22)(203.4) = 4474.8.

b)

how long does that take?

well, hell the loaner doesn't give much choices, you pay it every other week 22 times, how many weeks is that? 22*2 = 44 weeks.

Since we know a year has 52 weeks, then 44 weeks is just 44/52 of a year, namely

\(\cfrac{44}{52}\implies \cfrac{11}{13} ~~ \approx ~~ \text{\LARGE 0.85}~years\)

Other Questions
Your business is up and running and you arent losing money. Its time to grow your business and bring in more revenue. You decide to hire a Sales Manager whose sole job is bringing customers into your door. How will you compensate them? Of the target compensation, how much is delivered through base salary versus target incentives? How many different components or performance measures are used in the sales compensation plan? What are they? For your responses, put your Sales Applicant hat on. Is this job appealing to you? Would you try to renegotiate this compensation plan or performance measures? This should be another section since it is the second part of the discussion. TheConsideration clause in a life insurance policy indicates that a policyowner's consideration consists of a completed application and-the initial premium -agreeing to a physical examination -delivery of policy -disclosure of any medical conditions causes and concequences of global warming Determine whether each of the following is linearly dependent / independent. (i) {e2, 1, ex} (i) {tan(x), sec(x), 1} 1 0 2 (iii) 2 0 2 {[-1] [: 1]:[:] [-0 ?)[-1 }]} _1 9 which demands were common to most early labor workers Two identical positively charged particles are located on the x-axis. The first particle is located at z--65.5 cm and has a net charge of q!--28.9 nC. The second particle is loc and also has a net charge of q2 +289 nC. Calculate the electric potential at the origin (x-0) due to these two charged particles. 9 nC. The second particle is located at + x=0 N-m Enter answer here (a) You are given that two solutions of the homogeneous Euler-Cauchy equation, 22 2 (le yle)) 2y(a) = 0, 2>0. ( are y1 =T and y2 22 Confirm the linear independence of your two solutions (for 2 > 0 Eastside middle school has 75% student participation in the fall carnival. determine which of the simulations below could not of the probability of a student participating. 3 reasons why a introductory rate or balance transfer APR of 0% might not be a good offer after all a(n) __________ is used for determining an appropriate listing price for a sellers home. ing leaves, stems, roots, and fruits, may be reduced in size.2 Read this sentence from the passage and the directions that follow.High salinity (saltiness) can reduce growth and even cause death.What is the most important reason the author includes this explanation at the beginningof the passage?A. to define the word salinity in a way that a nonscientist can understandto identify where plants are most affected by saltC. to justify why the text focuses on salt damage and its solutionsD. to explain what causes salinity and where it comes fromB. When weighting everyone in the class, Dr. Smith gathers the following raw data in pounds: 100, 120, 125, 125, 130, 160, 180, 180, 190, 190, 190, 200, 220. What is the median What is the solution of startfraction 1 over c minus 3 endfraction minus startfraction 1 over c endfraction = startfraction 3 over c (c minus 3) endfraction? Which of these was true under the Articles of Confederation?A. Congress passed laws allowing for free passage between states.B. Members of Congress were required to attend votes on all laws.C. Laws were passed if the two largest states voted for them.D. Congress was able to pay debts run up in the war.SUBMIT Which month in Spanish is not a cognate with it's Englishcounterpart? Consider a household in the static two-good model with preferences over two goods, c 1and c 2, represented by utility function (A) from problem 1: u(c 1,c 2)=c 1c 21, with each good priced at P 1and P 2. The household receives an exogenous amount of income, Y. The government levies a proportional sales tax at a rate of con c 1, resulting in a tax-inclusive price of (1+ c)P 1: (a) Write down the budget constraint for this household. (b) Using indifference curve analysis, graphically locate the optimal choice (c 1,c 2), given the budget constraint from part (a). Label slopes and intercepts on your graph. (c) Set up and solve the consumer's optimization problem (be sure to show all work). Solve for (c 1,c 2) as a function of exogenous parameters. (d) Use economic logic with your answer from part (c), and your graph from part (b), to give an example of how the presence of the sales tax rate c>0 can affect the optimal consumption choice relative to the case where c=0. How did the early colonists survive in there new land during intinal years What is the average pH of the Pacific Ocean between Pago Pago and Apia? 1). 10 = 4x +x2). -6 = -2x -5 -13). -15 = 2v +v4). -6 = 2v +4v5). -2x +x = 56). -a -a = -87). -5p -6p = 08).-3k -6k = -99). 38 +7x = 5(1+8x)10). -30 -8x = -6(x+5)11).4(-4n+12)= 3(n-3)12). 2(5+5x) = 8(x+1)explain step by step plzzz Debbie is 22. She wants to invest part of her monthly salary in order to have $760,000 when she retires at 66. Suppose that she invests the money in a fund paying interest at an annual rate of 5.4%, compounded continuously. Assume a continuous money flow, then Debbie needs to invest $____per month.