Sydney read 50 pages in 40 minutes. She reads at a constant rate.
How many pages can Sydney read per minute?

Answer:

n = 4

Step-by-step explanation:

The expression must equal 6. Thus, we can make an equation:

3n - (2 + n) = 6

We distribute the negative and take away the parenthesis:

3n - 2 - n = 6

We combine like terms:

2n - 2 = 6

We add 2 to both sides to isolate n:

2n = 8

We divide each side by 2:

n = 4.

Answer:

1/6 sqrt(3) + 1/2

Step-by-step explanation:

(1 + sqrt(3))

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

sqrt(12)

Multiply the top and bottom by sqrt(12)

(1 + sqrt(3)) * sqrt(12)

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

sqrt(12)*sqrt(12)

sqrt(12) + sqrt(3) * sqrt(12)

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

12

Simplify

sqrt(4)sqrt(3) + 6

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

12

2 sqrt(3) +6

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

12

1/6 sqrt(3) + 1/2

The magnitude of the vector difference V′ is √5 units and the angle which V′ makes with the positive x-axis is 63.43°.

We are given vector difference V′=V2−V1 and we have to find the magnitude of the vector difference V′ and the angle which V′ makes with the positive x-axis.

(a) Graphical Analysis

From the above graph, we can say that V′=V2−V1and can find its magnitude using the following formula:|V′|=√(V′x)²+(V′y)²|V′|=√((2-1)²+(-5-(-3))²)=√2²+(-2)²=√8

Now, we have to find the angle which V′ makes with the positive x-axis.

From the above graph, we can see that

tan =V′yV′xtan =(-2)/(2-1)=-2

For the given problem, we have tan <0 and we have to find the between 180° and 270° as the resultant vector lies in the third quadrant.

Hence,=tan⁻¹2=63.43°

The magnitude of the vector difference V′ is √8 units and the angle which V′ makes with the positive x-axis is 63.43°.

(b) Analytical Method

Given vectors V1 = 1i - 5j and V2 = 2i - 3j.We know that V′=V2−V1=2i - 3j - (1i - 5j)=2i - 3j - 1i + 5j=1i + 2jHence, we have V′ = 1i + 2j = (1, 2) in Cartesian form.

Now, the magnitude of V′ can be determined using the formula:|V′|=√V′x²+V′y²|V′|=√(1)²+(2)²=√5 unitsAlso, we have to determine the angle made by V′ with the positive x-axis.tan =V′yV′xtan =2/1=2

For the given problem, we have tan >0 and we have to find the between 0° and 90° as the resultant vector lies in the first quadrant.

Hence,=tan⁻¹2=63.43°

∴ The magnitude of the vector difference V′ is √5 units and the angle which V′ makes with the positive x-axis is 63.43°.

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Answer:

What is 5% of 45.22?

That would be about 2.3

Now times that by 4 then there is your answer :)

Answer: 7,000

Step-by-step explanation: the hundred was greater than 5 so we round up any number after whatever you are doing if it’s 5 or greater you round up

The difference in the numbers of emails sent by each company is 4.19 × 10⁴.

The number of emails sent by company p = 6.1 × 10⁴

Converting scientific notation to real number

The number of emails sent by company p = 6.1 × 10000

Performing multiplication

The number of emails sent by company p = 61,000

The number of emails sent by company c = 191,00

Finding the difference using subtraction operation

Difference in number of mails = 61000 - 19100

Performing subtraction

Difference = 41,900

Converting the real number in scientific notation

Difference = 4.19 × 10⁴

Hence, the difference in the numbers of emails sent by each company is 4.19 × 10⁴.

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Answer:

The answer is d

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The increase in equilibrium GDP would be 125.

To calculate the increase in equilibrium GDP when planned investment increases from 20 to 45, we need to consider the multiplier effect. The multiplier is determined by the marginal propensity to consume (MPC), which is the fraction of each additional dollar of income that is spent on consumption.

In this case, the consumption function is given as C = 357 + 0.8Y, where Y represents GDP. The MPC can be calculated by taking the coefficient of Y, which is 0.8.

The multiplier (K) can be calculated using the formula: K = 1 / (1 - MPC).

MPC = 0.8

K = 1 / (1 - 0.8) = 1 / 0.2 = 5

The increase in equilibrium GDP (∆Y) is given by: ∆Y = ∆I * K, where ∆I represents the change in planned investment.

∆I = 45 - 20 = 25

∆Y = 25 * 5 = 125

Therefore, the increase in equilibrium GDP would be 125.

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The account must pay a 40 percent interest rate under Marcos.

A loan's or deposit's initial principal serves as the foundation for simple interest.

Contrarily, compound interest is calculated based on both the principal amount and the interest that is accrued on it each period.

Simple interest is simpler to compute than compound interest because it is just applied to the principal.

based on the information provided,

500+x=200

x=200/500

x=40

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Answer:

b => base  => 40 cm

h => altitude => 30 cm

A = h*b/2

h=b-10

600=(b-10)b/2

600 = (b^2-10b)/2

1200=b^2-10b

b^2-10b-1200=0

(b-40)(b+30)=0

b=40 cm

h=b-10 = 40-10=30

9514 1404 393

Answer:

Step-by-step explanation:

1. x +4y = 3.5 . . . . variables are defined in the problem statement

  2x +2y = 4

__

2. Subtract half the second equation from the first.

  (x +4y) -(1/2)(2x +2y) = (3.5) -(1/2)(4)

  3y = 1.5

  y = 0.5

  x = 2 -y = 1.5

The distance from home is 1.5 miles; the distance around the track is 0.5 miles.

__

3. 2x +6y = 2(1.5) +6(0.5) = 3+3 = 6

Avi walked 6 miles on Saturday.

__

4. 2p ≥ 2.5 . . . . variables are defined in the problem statement

  p +q < 3

__

5. No.

  2 + 1 < 3 is NOT TRUE

Answer:

18063600

Step-by-step explanation:

 3600 + 12.72 x 5000 = 18063600

It is advised to distribute bonuses to employees using either the weighted hours and job experience method or the weighted hours and annual salary method.

A frequency table lists a group of values along with how frequently each one occurs. The frequency of a given data value in your dataset is the number of times it appears. These tables assist you in determining which data values are typical and which are uncommon.

The given data is shown in the table,

Each employee receives the proper compensation based on outside factors when the number of hours worked is used to balance the job experience or the annual salary.

Thus, it is advised to distribute bonuses to employees using either the weighted hours and job experience method or the weighted hours and annual salary method.

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1. Variable manufacturing overhead rate variance

The formula Actual Hours × (Actual Rate - Standard Rate) is used to calculate the variable manufacturing overhead rate variance. This variance measures the difference between the actual variable manufacturing overhead cost incurred and the standard variable manufacturing overhead cost that should have been incurred, based on the standard rate per hour.

Variable manufacturing overhead rate variance = Actual Hours × (Actual Rate - Standard Rate)

The variable manufacturing overhead rate variance provides insight into how efficiently a company is utilizing its variable manufacturing overhead resources in terms of the rate per hour. A positive variance indicates that the actual rate paid per hour for variable manufacturing overhead was higher than the standard rate, resulting in higher costs. On the other hand, a negative variance suggests that the actual rate paid per hour was lower than the standard rate, leading to cost savings.

By analyzing this variance, management can identify areas where the company may be overspending or underspending on variable manufacturing overhead and take corrective actions accordingly, such as renegotiating supplier contracts or optimizing resource allocation.

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Answer:

x = -\(\frac{34}{27}\) and y = \(\frac{73}{27}\)

Step-by-step explanation:

2x + 5y = 11

7x + 4y = 2

Let's try elimination here since we have a system of equations:

-7(2x + 5y = 11) = -14x - 35y = -77

and

2(7x + 4y = 2) = 14x + 8y = 4

The x's cancel out now so let's combine the two equations:

-35 + 8 = -27

-77 + 4 = -73

-27y = -73

y = \(\frac{73}{27}\)

Now that we have y's value, let's plug that value in for y in the other equation. You may choose whichever equation you want to solve for x but it is recommended to use the easiest one. (Since this value is complicated, it won't really matter.)

2x + 5(\(\frac{73}{27}\)) = 11

2x + \(\frac{365}{27}\) = 11

2x = -\(\frac{68}{27}\)

x = -\(\frac{34}{27}\)

To check and make sure you have the correct values, plug both values into the orginal equation and make sure the equation is true.

\({\tt{2x + 5y = 11}}\)

\({\tt{7x + 4y = 2}}\)

\( \: \: \)

\({\tt{2x = 11 - 5y}}\)

\({\tt{7x = 2 - 4y}}\)

\( \: \: \)

\({\tt{x = ( 11 - 5y ) ÷ 2}}\)

\({\tt{x = \frac{11}{2} - \frac{5}{2} y}}\)

\( \: \: \)

\({\tt{x = ( 2 - 4y ) ÷ 7}}\)

\({\tt{x = \frac{2}{7} - \frac{4}{7} y}}\)

\( \: \: \)

_____________________

\( \: \: \)

\( \: \: \: \: \: \: {\tt{ \frac{11}{2} - \frac{5}{2} y = \frac{2}{7} - \frac{4}{7} y\: \: ( \times14)}}\)

\( \: \: \: \: {\tt{77 - 35y = 4 - 8y}}\)

\({\tt{ - 35y + 8y = 4 - 77}}\)

\( \: \: \: \: \: \: \: \: \: \: \: {\tt{ - 27y = - 73}}\)

\( \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\tt{y = \frac{73}{27} }}\)

\( \: \: \)

\( \: \: \)

\({\tt{x = \frac{2}{7} - \frac{4}{7} \times \frac{73}{27} }}\)

\({\tt{x = - \frac{34}{27} }}\)

\( \: \: \)

Answer:

5

Step-by-step explanation:

hope its right good luck

Number of members came to help = 5.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given,

15 members complete decoration in 12 hours,

After 4 hours left time = 8 hours

15 members will do the remaining work in 8 hours

Let x be the number of extra members join

15 + x members will do the remaining work in 6 hours

Work done = no. of members × time

Work is same

thus,

15 × 8 = 15+x × 6

120 = 90 + 6x

30 = 6x

x = 5

No. of extra members = 5

Hence, 5 members came to help.

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Answer: The answer is A.addition property of equality

Hope I helped

Pkease mark me as brainliest!

It is reasonable for Stacy to use a normal model for the sampling distribution of the sample proportion. This is because, according to the Central Limit Theorem,

when the sample size is large enough (typically considered to be at least 30), the sampling distribution of the sample proportion will be approximately normal, regardless of the shape of the population distribution.

In Stacy's case, she plans on surveying a random sample of students, which implies that she will have a sufficiently large sample size. Therefore, the conditions for using a normal model are satisfied.

In conclusion, Stacy can use a normal model for the sampling distribution of the sample proportion in her survey for the final project.

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The text discusses a production function and addresses various aspects of a firm's decision-making. It covers profit maximization, factor demand functions, supply function, profit function, Hotelling's lemma, cost minimization, conditional factor demand functions, and the cost function. These concepts are derived using mathematical calculations and formulas. Hotelling's lemma is verified, and the cost function is determined.

(a) The firm's profit maximization problem can be stated as follows: Maximize profits (π) by choosing the optimal levels of inputs (z and zo) that maximize the output (y) given the prices of output (p) and inputs (w, w₂).

(b) To derive the firm's factor demand functions, we need to find the conditions that maximize profits.

The first-order condition for input z is given by:

∂π/∂z = p * (∂f/∂z) - w = 0

Substituting the production function f(z) = z^(1/4) / z^(1/2) into the above equation, we have:

p * (1/4 * z^(-3/4) / z^(1/2)) - w = 0

Simplifying, we get:

p * (1/4 * z^(-7/4)) - w = 0

Solving for z, we find:

z = (4w/p)^(4/7)

Similarly, for input zo, the first-order condition is:

∂π/∂zo = p * (∂f/∂zo) - w₂ = 0

Substituting the production function f(zo) = z^(1/4) / z^(1/2) into the above equation, we have:

p * (1/2 * z^(1/4) * zo^(-3/2)) - w₂ = 0

Simplifying, we get:

p * (1/2 * z^(1/4) * zo^(-3/2)) - w₂ = 0

Solving for zo, we find:

zo = (2w₂ / (pz^(1/4)))^(2/3)

(c) To derive the firm's supply function, we need to find the level of output (y) that maximizes profits.

Using the production function f(z), we can express y as a function of z:

y = z^(1/4) / z^(1/2)

Given the factor demand functions for z and zo, we can substitute them into the production function to obtain the supply function for y:

y = (4w/p)^(4/7)^(1/4) / (4w/p)^(4/7)^(1/2)

Simplifying, we get:

y = (4w/p)^(1/7)

(d) The firm's profit function is given by:

π = p * y - w * z - w₂ * zo

Substituting the expressions for y, z, and zo derived earlier, we have:

π = p * ((4w/p)^(1/7)) - w * ((4w/p)^(4/7)) - w₂ * ((2w₂ / (pz^(1/4)))^(2/3))

(e) To verify Hotelling's lemma, we need to calculate the partial derivatives of the profit function with respect to the prices of output (p), input z (z₁), and input zo (z₂).

Hotelling's lemma states that the partial derivatives of the profit function with respect to the prices are equal to the respective factor demands:

∂π/∂p = y - z * (∂y/∂z) - zo * (∂y/∂zo) = 0

∂π/∂z₁ = -w + p * (∂y/∂z₁) = 0

∂π/∂z₂ = -w₂ + p * (∂y/∂z₂) = 0

By calculating these partial derivatives and equating them to zero, we can verify Hotelling's lemma.

(f) The firm's cost minimization problem can be stated as follows: Minimize the cost of production (C) given the level of output (y), prices of inputs (w, w₂), and factor demand functions for inputs (z, zo).

(g) To derive the firm's conditional factor demand functions, we need to find the conditions that minimize costs. We can express the cost function as follows:

C = w * z + w₂ * zo

Taking the derivative of the cost function with respect to z and setting it to zero, we get:

∂C/∂z = w - p * (∂y/∂z) = 0

Simplifying, we have:

w = p * (1/4 * z^(-3/4) / z^(1/2))

Solving for z, we find the conditional factor demand for z.

Similarly, taking the derivative of the cost function with respect to zo and setting it to zero, we get:

∂C/∂zo = w₂ - p * (∂y/∂zo) = 0

Simplifying, we have:

w₂ = p * (1/2 * z^(1/4) * zo^(-3/2))

Solving for zo, we find the conditional factor demand for zo.

(h) The firm's cost function is given by:

C = w * z + w₂ * zo

Substituting the expressions for z and zo derived earlier, we have:

C = w * ((4w/p)^(4/7)) + w₂ * ((2w₂ / (pz^(1/4)))^(2/3))

This represents the firm's cost function.

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Answer:

V=150

l Length  

10

w Width  

5

h Height  

3

Step-by-step explanation:

hope im right!

Answer:

It is 150!

Step-by-step explanation:

Took the test!

Please mark as brainliest!

-KanaKittyKat

B

It is quite obvious. America is capatalist, we are relatively free here. No laws regulate competing against other people nor regulating the ability to make a large profit from real estate.

if you were confused with C, the word bartering basically means trading goods. In order to acquire good most people use money, we do not have to trade things like bread for steak n stuff.

Hope it helps

The scale of the map can be written as:

1cm to 20km

We want to find the distance that 1 cm in the map representes in the real world.

We know the relation:

3cm = 60km

We want to get a 1 in the left side, then we can divide both sides by 3 to get:

1cm = 60km/3

1cm = 20km

Then the scale of the map is 1cm to 20km

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Answer:

P (3, - 2 )

Step-by-step explanation:

Solve the equations simultaneously for point of intersection P

5x + 3y = 9 → (1)

7x - 2y = 25 → (2)

Multiplying (1) by 2 and (2) by 3 and adding will eliminate the y- term

10x + 6y = 18 → (3)

21x - 6y = 75 → (4)

add (3) and (4) term by term to eliminate y

31x + 0 = 93

31x = 93 ( divide both sides by 31 )

x = 3

Substitute x = 3 into either of the 2 equations and solve for x

Substituting into (1)

5(3) + 3y = 9

15 + 3y = 9 ( subtract 15 from both sides )

3y = - 6 ( divide both sides by 3 )

y = - 2

Then P = (3, - 2 )

The two positive numbers whose product is 16 and whose sum is a minimum are 4 and 4.

To find two positive numbers whose product is 16 and whose sum is a minimum, we need to use the AM-GM inequality.

This inequality states that for any two positive numbers a and b, their arithmetic mean (AM) is greater than or equal to their geometric mean (GM), i.e.,(a + b)/2 ≥ √(ab)

Now, we need to use this inequality in reverse.

We want to minimize the sum (a + b), so we'll use the inequality as follows:(a + b)/2 ≥ √(ab)

Multiplying both sides by 2 gives us:(a + b) ≥ 2√(ab)

Now, we substitute 16 for ab, which gives us:(a + b) ≥ 2√16 = 8

To minimize the sum, we want equality to hold, so we need to choose a and b such that their geometric mean is 4.

The two positive numbers that satisfy this condition are 4 and 4, so the numbers are 4 and 4 and their sum is 8, which is the minimum possible sum.

Therefore, the two positive numbers whose product is 16 and whose sum is a minimum are 4 and 4.

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The correct choice is: C. Errors ≤ 0.05 for M ≤ 1

To estimate the absolute error in approximating cos(0.48) using the 3rd order Taylor polynomial centered at 0, we'll use the remainder term. The remainder term for a Taylor series is given by:

R_n(x) = (f^{(n+1)}(c) * (x - a)^{(n+1)}) / (n+1)!

Here, f(x) is cos(x), x = 0.48, a = 0 (center), n = 3 (order), and c is a value between a and x.

Since f(x) = cos(x), the derivatives will cycle through the trigonometric functions. Specifically:

f(x) = cos(x)
f'(x) = -sin(x)
f''(x) = -cos(x)
f'''(x) = sin(x)
f''''(x) = cos(x)

Since n = 3, we need the 4th derivative, which is f''''(x) = cos(x). Since |cos(c)| is at most 1 for all c, we have:

|M| ≤ 1

Now, we can plug everything into the remainder term formula:

R_3(0.48) ≤ (1 * (0.48)^4) / (4!)

R_3(0.48) ≤ (0.48^4) / 24

R_3(0.48) ≤ 0.053130496

The absolute error in approximating cos(0.48) using the 3rd order Taylor polynomial centered at 0 is less than or equal to 0.053130496. Rounded to two decimal places, the error is ≤ 0.05. So, the correct choice is:

C. Errors ≤ 0.05 for M ≤ 1

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Answer:

none my guy

Step-by-step explanation:

Answer:

D.  (4+7i)(4-7i)

and for 2nd

D. c = –3, d = –2

Step-by-step explanation:

edu 2021

Answer:

3/4 is greater

Step-by-step explanation:

If you change them both into decimals.  You can see that 3/4 is larger

3/4 = .75

11/16 = .6875

Put in your calculator 3÷4 and 11÷16

Answer:

3/4 is larger because

\(\frac{3}{4}\)*\(\frac{4}{4}\)=\(\frac{12}{16}\)                              \(\frac{12}{16}\) > \(\frac{11}{16}\)

Step-by-step explanation:

When making the denominators equal it is clear to see that 3/4 which is equal to 12/16 is greater than 11/16.

The figure is decomposed by separating it into three simpler shapes

The area of the complex shape is solved by splitting the shape into simpler shapes.

The splitting is also called decomposition, doing this will result to three shapes which are

Triangle

rectangle and

semicircle

Then are area is solved individually and added up

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