combining like terms: -1 - 7x + x​

Answer:

-16

Step-by-step explanation:

m^2 + n^2

-5^2 + 3^2 = -16

The fraction which should go into the boxes marked A and B in their simplest form is 3/4 and 1/4 respectively.

Total number of fruits Amy has = 10

Number of Apples = 7

Number of Oranges = 3

First random pieces of fruits chosen:

Probability of choosing Apples = 6/9

Probability of choosing Oranges = 3/9

Second random pieces of fruits chosen:

Probability of choosing Apples = 6/8

= 3/4

Probability of choosing Oranges = 2/8

= 1/4

Therefore, the probability of choosing Apples or oranges as the second piece is 3/4 or 1/4 respectively.

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Step-by-step explanation: 15 x 2/3 = 10.

-zomba

Answer:

148$ per night.

Step-by-step explanation:

888 divided by 6 = 148.

The Answer is 148

888/6=148

1. To find the potential GDP (Y*), we substitute the given values into the production function:

Y = AL^(2/3)K^(1/3)

Y* = A(1000)^(2/3)(125)^(1/3)

Y* = 10(1000)^(2/3)(125)^(1/3)

Y* = 10(10^2)(5)

Y* = 50,000

2. The equation for the Aggregate Demand Curve (AD) in the form of Y = a + bp can be derived from the given information. Since we know that the main components of Aggregate Expenditure Function (AEF) are:

C = 300 + 0.8Y

I = 300

G = 200

And we assume a closed economy with NX = 0, the equation for AD becomes:

Y = C + I + G

Y = (300 + 0.8Y) + 300 + 200

Y = 800 + 0.8Y

0.2Y = 800

Y = 4000 + 5p

3. To find the current Short-Run Equilibrium value for Real GDP (Y) and the price level (p), we set AD equal to AS:

4000 + 5p = 5p

4000 = 0

Since the equation does not hold true, there is no short-run equilibrium value for Y and p based on the given information.

4. In the graph, the Aggregate Demand (AD), Short-Run Aggregate Supply (AS), and Long-Run Aggregate Supply (LRAS) curves will be represented. The x-intercept of AD indicates potential GDP, and the intersection of AD and AS determines the short-run equilibrium. If the short-run equilibrium is to the right of potential GDP, it indicates an inflationary gap. If it's to the left, it indicates a recessionary gap. If the short-run equilibrium coincides with potential GDP, it represents long-run equilibrium.

(Note: As a text-based AI, I'm unable to draw the graph here, but you can plot it on a graph paper or use a graphing tool to visualize it based on the given equations.)

5. Drawing the MS (Money Supply) and MD (Money Demand) curves, we have:

MS: $8,000

MD: 20,000 - 1,000i

The equilibrium in the money market occurs where the MS and MD curves intersect. The prevailing market interest rate (i*) is determined by the point of intersection.

6. With an increase in autonomous consumption of 180, the new short-run equilibrium Real GDP will be determined by adjusting the consumption component in the AD equation:

Y = (300 + 0.8(180 + Y)) + 300 + 200

Solving for Y, we find the new short-run equilibrium Real GDP.

7. To close the output gap by changing the Money Supply (MS), we need to determine the change in MS required to achieve the desired level of Real GDP. This can be calculated by adjusting the MS until the short-run equilibrium reaches the desired Real GDP. The new interest rate can also be calculated based on the changes in MS.

8. If the Central Bank wants to reduce the money supply by raising reserve requirements instead, the amount by which the reserve requirements need to be raised can be calculated to achieve the desired level of Real GDP. This can be done by adjusting the reserve ratio until the short-run equilibrium reaches the desired Real GDP.

9. With the Second MD Curve (MD = 20,000 - 400i), the Central Bank would need to change the Money Supply by a different amount compared to the First MD Curve (MD = 20,000 - 1,000i) to close the inflationary gap. This is because the slopes of the two MD curves are different, resulting in different changes in the equilibrium interest rate and Money Supply.

10. Keynesians are more likely to believe that the First MD Curve (MD = 20,000 - 1,000i) is more likely to be the case. This is because Keynesian economics emphasizes the role of fiscal policy and government intervention in managing the economy. On the other hand, the First MD Curve is more in line with the monetarist point of view, which focuses on the control of money supply and the importance of monetary policy in economic management.

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Answer:

5/365 years, or 0.014 years

Step-by-step explanation:

Just like any conversion of units, we just set up the starting amount and multiply it by the correct ratio:

    5 days (1 year/ 365 days) = 5/365 years = 0.014 years

You just need to make sure you choose the right ratio. In this case, I know that 1 year is 365 days, and I'm trying to cancel the days unit, therefore I put the year in the numerator and the days in the denominator.

I hope this helps :D

Answer:

0.01

Step-by-step explanation: 5 ÷ 365 ( days of year)  and it gives you 0.013 then round to nearest  hundredth and since 3 is less than 5 it becomes a 0

Answer:

E) 36 ft²

Step-by-step explanation:

Formulae

The shape is made up of 2 congruent triangles and 3 different rectangles.

Area of triangle = 1/2 x 3 x 4 = 6 ft²

Area of rectangle 1 = 2 x 4 = 8 ft²

Area of rectangle 2 = 2 x 3 = 6 ft²

To calculate the area of the 3rd triangle, we need to use Pythagoras' Theorem to determine the length of the hypotenuse of the right triangle.

   a² + b² = c²

⇒ 3² + 4² = c²

⇒ 25 = c²

⇒ c = √(25)

⇒ c = 5 ft

Therefore, area of rectangle 3 = 2 x 5 = 10 ft²

Total Surface Area

Total SA = 2 triangles + rectangle 1 + rectangle 2 + rectangle 3

               = (2 x 6) + 8 + 6 + 10

               = 36 ft²

About $6,000 more compound interest than simple interest is earned after 35 years, and about $12,500 more compound interest than simple interest is earned after 45 years.

What is a graph ?

A graph is a visual representation of data that shows the relationship between two or more variables. It is a way of presenting information in a clear and concise manner that makes it easy to interpret and understand.

Graphs can be used to show trends over time, compare different groups or categories, or illustrate the relationship between two or more variables.

Since the graph shows the balance for two accounts with the same principal and annual interest rate, we can assume that one account is earning simple interest while the other is earning compound interest.

To estimate the amount of compound interest earned after 35 years, we can look at the difference in balance between the two accounts at that time. From the graph, we can see that the balance for the simple interest account after 35 years is approximately $4,000, while the balance for the compound interest account is approximately $10,000. Therefore, the amount of compound interest earned after 35 years is approximately:

$10,000 - $4,000 = $6,000

To estimate the amount of compound interest earned after 45 years, we can again look at the difference in balance between the two accounts at that time. From the graph, we can see that the balance for the simple interest account after 45 years is approximately $5,500, while the balance for the compound interest account is approximately $18,000. Therefore, the amount of compound interest earned after 45 years is approximately:

$18,000 - $5,500 = $12,500

Therefore,  about $6,000 more compound interest than simple interest is earned after 35 years, and about $12,500 more compound interest than simple interest is earned after 45 years.

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a. The probability that the teller is busy, P(0), is 0.1667

b. The Probability (teller is idle) is 0.8333

c. The Probability of 3 customers in the system 0.1019

d. The average number of customers waiting for service 4.1667

e. The average number of customers in the system is 5

f. The average time a customer spends in the system is 0.25 hour or 15 minutes.

g. The Average time a customer spends in the waiting line is 0.2083 hour or 12.5 minutes

The given M|M|1 system at BBA Bank, the probability that the teller is busy is 0.1667, the probability that the teller is idle is 0.8333, the probability of having 3 customers in the system is 0.1019, the average number of customers waiting for service is 4.1667, the average number of customers in the system is 5, the average time a customer spends in the system is 15 minutes, and the average time a customer spends in the waiting line is 12.5 minutes. These measures provide insights into the performance and efficiency of the bank's drive-through teller window.

To determine the performance measures of the M|M|1 system for BBA Bank, we can use the properties of the exponential distribution and the formulas for queuing theory. Given that the arrival rate is 20 customers per hour and the average service time is 2.5 minutes, we can calculate the following:

(a) Probability (teller is busy):

The utilization factor, ρ, can be calculated as the ratio of the arrival rate to the service rate:

ρ = λ/μ

where λ is the arrival rate and μ is the service rate. In this case, λ = 20 customers/hour and μ = 60 minutes/hour divided by the average service time of 2.5 minutes:

ρ = 20/((60/2.5)) = 20/24 = 0.8333

The probability that the teller is busy, P(0), is given by:

P(0) = 1 - ρ

P(0) = 1 - 0.8333 = 0.1667

(b) Probability (teller is idle):

The probability that the teller is idle, P(∞), can be calculated as the complement of the probability that the teller is busy:

P(∞) = ρ

P(∞) = 0.8333

(c) Probability of 3 customers in the system:

The probability of having n customers in the system, P(n), can be calculated using the formula:

P(n) = (1 - ρ) * ρ^n

P(3) = (1 - 0.8333) * (0.8333)^3 = 0.1019

(d) Average number of customers waiting for service:

The average number of customers waiting in the system, Lq, can be calculated using the formula:

Lq = ρ^2 / (1 - ρ)

Lq = (0.8333)^2 / (1 - 0.8333) = 4.1667

(e) Average number of customers in the system:

The average number of customers in the system, L, can be calculated as the sum of the average number of customers waiting and the customer being served:

L = Lq + ρ = 4.1667 + 0.8333 = 5

(f) Average time a customer spends in the system:

The average time a customer spends in the system, W, can be calculated using the formula:

W = L / λ

W = 5 / 20 = 0.25 hour or 15 minutes

(g) Average time a customer spends in the waiting line:

The average time a customer spends in the waiting line, Wq, can be calculated using the formula:

Wq = Lq / λ

Wq = 4.1667 / 20 = 0.2083 hour or 12.5 minutes

In summary, for the given M|M|1 system at BBA Bank, the probability that the teller is busy is 0.1667, the probability that the teller is idle is 0.8333, the probability of having 3 customers in the system is 0.1019, the average number of customers waiting for service is 4.1667, the average number of customers in the system is 5, the average time a customer spends in the system is 15 minutes, and the average time a customer spends in the waiting line is 12.5 minutes. These measures provide insights into the performance and efficiency of the bank's drive-through teller window.

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a. The probability that Miami will be hit by a hurricane in any given year can be calculated as the inverse of the historical frequency of hurricane hits, which is 1/25. Therefore:

Probability of Miami being hit by a hurricane in any given year = 1/25

b. The probability that Miami will be hit by hurricanes in both of the next two consecutive years can be calculated as the product of the individual probabilities, assuming that the occurrence of hurricanes in different years is independent. Therefore:

Probability of Miami being hit by hurricanes in both of the next two consecutive years = (1/25) * (1/25) = 1/625

c. The probability that Miami will be hit by hurricanes in either the next year or the year after can be calculated as the sum of the probabilities of each event occurring, minus the probability of both events occurring (since they are not mutually exclusive). Therefore:

Probability of Miami being hit by hurricanes in either the next year or the year after = (1/25) + (1/25) - [(1/25) * (1/25)] = 48/625

d. The probability that Miami will be hit by at least one hurricane in the next seven years can be calculated using the complement rule: the probability of no hurricanes in seven years is (24/25)^7, so the probability of at least one hurricane is 1 minus that value. Therefore:

Probability of Miami being hit by at least one hurricane in the next seven years = 1 - (24/25)^7 ≈ 23.071% (rounded to three decimal places)

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Hayley will travel from Telford Central to Shrewsbury in 0 hours and 21 minutes if she takes the quickest route.

Based on the timetable provided, the fastest option for Hayley to get from Telford Central to Shrewsbury is by taking the 0915 train from Wellington to Shrewsbury, which arrives at 0920. Therefore, the total time it will take her is 21 minutes (from 0805 departure of Wellington to 0920 arrival in Shrewsbury).

To convert 21 minutes to hours and minutes, divide 21 by 60 to get the decimal value of 0.35 hours. Then convert the decimal value to minutes by multiplying it by 60, which gives:

0.35 hours × 60 = 21 minutes

So, it will take Hayley 0 hours and 21 minutes to get from Telford Central to Shrewsbury taking the fastest option.

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a) The number of ways to form a committee of 6 people from the department is 177,100.

b) The number of ways to form a committee of 6 people with an equal number of men and women is 54,600.

c) The number of ways to form a committee of 6 people with more women than men is 91,455.

a) To form a committee of 6 people from the department, we can choose 6 individuals from a total of 25 people (10 men + 15 women). The order in which the committee members are chosen does not matter, and we are not concerned with any specific positions within the committee. Therefore, we can use the concept of combinations.

The number of ways to choose 6 people from a group of 25 is given by the combination formula:

C(25, 6) = 25! / (6! * (25 - 6)!) = 25! / (6! * 19!) = 177,100

Therefore, there are 177,100 ways to form a committee of 6 people from the department.

b) In this case, we need to choose an equal number of men and women for the committee. We can select 3 men from the available 10 men and 3 women from the available 15 women. Again, the order of selection does not matter.

The number of ways to choose 3 men from 10 is given by the combination formula:

C(10, 3) = 10! / (3! * (10 - 3)!) = 10! / (3! * 7!) = 120

Similarly, the number of ways to choose 3 women from 15 is:

C(15, 3) = 15! / (3! * (15 - 3)!) = 15! / (3! * 12!) = 455

To find the total number of ways to form a committee with an equal number of men and women, we multiply these two combinations:

Total = C(10, 3) * C(15, 3) = 120 * 455 = 54,600

Therefore, there are 54,600 ways to form a committee of 6 people with an equal number of men and women.

c) In this case, we need to form a committee with more women than men. We can choose 1 or 2 men from the 10 available men and select the remaining 6 - (1 or 2) = 5 or 4 women from the 15 available women.

For 1 man and 5 women:

Number of ways to choose 1 man from 10: C(10, 1) = 10

Number of ways to choose 5 women from 15: C(15, 5) = 3,003

For 2 men and 4 women:

Number of ways to choose 2 men from 10: C(10, 2) = 45

Number of ways to choose 4 women from 15: C(15, 4) = 1,365

The total number of ways to form a committee with more women than men is the sum of these two cases:

Total = (Number of ways for 1 man and 5 women) + (Number of ways for 2 men and 4 women)

     = 10 * 3,003 + 45 * 1,365

     = 30,030 + 61,425

     = 91,455

Therefore, there are 91,455 ways to form a committee of 6 people with more women than men.

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Answer:

Priya, Hailey, Shetal

Step-by-step explanation:

Let's pretend the clock is currently at 4. Hailey auditioned 10 mins before, so she auditioned at 3:50.

Priya auditioned 30 mins before Hailey, meaning she auditioned at 3:20.

Then, Shetal auditioned 5 mins before 4, meaning she auditioned at 3:55.

So, going in time, the order will be  3:20, 3:50, 3:55

So, Priya, Hailey, Shetal

Answer:

In summary, the translation and scale factor are:

Translation: (x,y)↦(x+5,y+4)

Scale factor: 2

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

-7 + 12

it's the same as

12 - 7

=5

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{5}}}}}\)

Step-by-step explanation:

\( \star{ \text{ - 7 + 12}}\)

\( \sf{ \: The \: negative \: and \: positive \: integers \: are \: always \: subtracted \: but \: posses \: the \: sign \: of \: the \: bigger \: integer}\)

\( \hookrightarrow{5 }\)

\( \text{Hope \: I \: helped !}\)

\( \text{Best \: regards !!} \)

~\( \text{TheAnimeGirl}\)

Answer:

it is not factorable

Step-by-step explanation:

Answer:

35 students

Step-by-step explanation:

If there are 4 girls, then there are 3 boys

You will multiply both by 5 to get 20

So 3×5 is 15

20+15 = 35

Answer: 35 students

Explanation: Divide 4 into 20 to see how many sets of 4 girls there are. So there are 5 sets of four girls.

Five times three is 15.

In total (15 + 20), there are 35 students.

Plz mark brainliest:)

Answer:

X = 3/2.

Step-by-step explanation:

Please refer to the attachment given above.

The value of x in the equation 2\(^{(2x)}\) = 2³ is 1.5.

To find the value of x in the equation 2\(^{(2x)}\) = 2³, we can use the property of exponents that states: If two exponential expressions have the same base and are equal, then their exponents must be equal.

In this case, we have 2\(^{(2x)}\) = 2³. Since the bases are the same (both are 2), we can equate the exponents:

2x = 3

Now, to solve for x, divide both sides by 2:

x = 3/2

So, the value of x is 3/2 or 1.5.

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"From a table of integrals, we know that for \(\(a \neq 0\)\) and \(\(b \neq 0\):\)

\(\[\int \cos(at) \, dt = \frac{1}{a} \cdot \cos(at) + \frac{1}{b} \cdot \sin(bt) + C\]\)

and

\(\[\int e^a t \cos(bt) \, dt = \frac{e^{at}}{a} \cdot \cos(bt) + \frac{b}{a^2 + b^2} \cdot \sin(bt) + C\]\)

Use this antiderivative to compute the following improper integral:

\(\[\int_{-\infty}^{0} \cos(3t) \, dt = \lim_{{T \to \infty}} \int_{0}^{T} e^t \cos(3t) \, e^{-st} \, dt = \lim_{{T \to \infty}} \text{ if } s \neq 1, \, \text{ or } \lim_{{T \to \infty}} \text{ if } s = 1.\]\)

For which values of \(\(s\)\) do the limits above exist? In other words, what is the domain of the Laplace transform of \(\(\frac{1}{\cos(3)} \cdot e^t \cos(3t)\)\)?

Evaluate the existing limit to compute the Laplace transform of  on the domain you determined in the previous part:

\(\[L\{e^t \cos(3t)\\).

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The most appropriate choice for distance will be given by

Veronica has not calculate the number of animals seen per kilometer, she has arranged only on the basis of animals seen.

What is distance?

Distance is how much ground travelled by an object during its motion.

Here,

For River Edge

Number of animals seen = 8

Length of hike =  3 km

Number of Animals seen per km = 8/3

                                                      =2.66

For Wooden Marsh

Number of animals seen = 24

Length of hike =  8 km

Number of Animals seen per km = 24/8

                                                       =3

For Canyon Creek

Number of animals seen = 35

Length of hike =  15 km

Number of Animals seen per km = 35/15

                                                      =2.33

So from least to greatest it will be

Canyon Creek, River Edge, Marshy Land

Veronica has not calculate the number of animals seen per kilometer, she has arranged only on the basis of animals seen. That was her mistake.

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Answer:

B

Step-by-step explanation:

The volume of the prism is

The volume of the prism is solved by the formula

= area of triangle * depth

Area of the triangle

= 1/2 base * height

base = p = cos 51.34 * √41 = 4

height = q = sin 51.34 * √41 = 5

= 1/2 * 4 * 5

= 10

volume of the prism

= area of triangle * depth

= 10 * 7

= 70 cm³

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The probability of selecting two yellow balls from a box containing 12 white, 5 yellow, and 3 red balls without replacement is 0.08 or 8%. If the balls are selected with replacement, the probability of getting two balls of the same color is 0.225 or 22.5%.

(a) When two balls are selected without replacement, the total number of balls decreases after each selection. Initially, there are 20 balls in the box, with 5 of them being yellow. The probability of selecting the first yellow ball is 5/20. After the first yellow ball is removed, there are 19 balls remaining, with 4 of them being yellow. Therefore, the probability of selecting the second yellow ball is 4/19. To find the probability of both events occurring, we multiply the probabilities together: (5/20) * (4/19) = 0.0526 or approximately 0.053. Hence, the probability of getting two yellow balls without replacement is 0.053, which is equivalent to 5.3%.

(b) When two balls are selected with replacement, the total number of balls remains the same after each selection. In this case, the probability of selecting a yellow ball is 5/20, and the probability of selecting another yellow ball on the second draw is also 5/20. To find the probability of both events occurring, we multiply the probabilities together: (5/20) * (5/20) = 0.0625 or 6.25%. However, since we want the probability of selecting two balls of the same color (regardless of the color), we need to consider all three colors: white, yellow, and red. Therefore, we multiply the probability of getting two yellow balls (0.0625) by 3, resulting in 0.1875 or 18.75%. Rounded to one decimal place, the probability of getting two balls of the same color when selected with replacement is 0.2 or 20%.

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Using division, we know that Leo replaces 6 new strings from 3 guitars which are a total of 18 strings.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.

The other operations are multiplication, addition, and subtraction.

On a fundamental level, counting the instances in which one number is included within another is one interpretation of the division of two natural numbers.

When no more full chunks of the size of the second number can be allocated during the computation of the quotient, the division with a remainder or Euclidean division of two natural numbers yields an integer quotient, which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that remains.

So, we know that:

6 new strings are put on each guitar.

He uses 18 strings.

Then, the number of guitars:

⇒ 18/6 = 3

Therefore, using division, we know that Leo replaces 6 new strings from 3 guitars which are a total of 18 strings.

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Answer:

x = 116°

Step-by-step explanation:

number of degrees in a pentagon is (5-2)180° = 540°

x + 121 + 90 + 115 + 98 = 540

x + 424 = 540

x = 116°

Answer:

Step-by-step explanation:

f(4)=-3(4)+5 = -12+5=-7

Answer:

(1) Hundred

(2) Numerator

(3) Percent

Step-by-step explanation:

Answer:

3x-4y+3 is linear equation.

3×1-4×1+3

3-4+3

3+3-4

6-4

2

Answer:

Well there's no way to really simplify it cuz we aren't given what x and y are equal too.  Plus, none of the terms are the same, so you can't combine anything.