What is the standard form of the line in the equation y= 2/3x + 1/3

A. 2x + 3y = 1
B. 2x-3y = -1
C. 2x + 3y = -1
D. 2x-3y = 1

Answer:

y = x/4

Step-by-step explanation:

Use point (4, 1).

y = kx

1 = k * 4

k = 1/4

y = 1/4 x

y = x/4

In wider confidence intervals greater uncertainty introduced by the fatter tails of the t-distribution.

When finding the confidence interval for the population mean using a sample mean and known population variance.

The appropriate distribution to use is the Standard normal distribution if the sample size is sufficiently large.

However, if the sample size is small (typically less than 30) or if the population variance is unknown, then the Student t distribution should be used instead.

If the Student t-distribution is incorrectly used instead of the Standard normal distribution in this scenario, then the width of the confidence interval will increase.

This is because the Student t distribution has heavier tails than the Standard normal distribution, meaning that there is a greater chance of extreme values occurring.

As a result, the confidence interval based on the Student t distribution will need to be wider to accommodate this increased variability.

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Step-by-step explanation:

We have

\((sc^2x-1)^2\)

Which is the same as

\((sc^2x-1)(sc^2x-1)\)

To expand this polynomial, we can use the FOIL method. Meaning that we multiply the Fronts, Outsides, Insides, and Lasts together and then add each of these products.

The two fronts are \(sc^2x\) and \(sc^2x\),

\((sc^2x )(sc^2x )=s^2c^4x^2\)

The two Outsides are \(sc^2x\) and \(-1\),

\((sc^2x )(-1)=-sc^2x\)

The two Insides are \(-1\) and \(sc^2x\),

\((-1)(sc^2x )=-sc^2x\)

The two lasts are \(-1\) and \(-1\),

\((-1)(-1)=1\)

Now we just need to add these together to get

\(s^2c^4x^2-sc^2x-sc^2x+1\\\\s^2c^4x^2-2sc^2x+1\)

Answer:

\(cot^{4} x\)

Step-by-step explanation:

The required answer is the annual cost saved by shifting from the 500-bag lot size to the EOQ is $1,059.92.

Explanation:-

a. Economic order quantity (EOQ) is defined as the optimal quantity of inventory to be ordered each time to reduce the total annual inventory costs.

It is calculated as follows: EOQ = sqrt(2DS/H)

Where, D = Annual demand = 100 x 52 = 5200S = Order cost = $57 per order H = Annual holding cost = 0.30 x 10.75 = $3.23 per bag per year .Therefore, EOQ = sqrt(2 x 5200 x 57 / 3.23) = 234 bags. The average time between orders (TBO) can be calculated using the formula: TBO = EOQ / D = 234 / 100 = 2.34 weeks ≈ 2 weeks (rounded to nearest whole number).

Hence, the EOQ is 234 bags and the average time between orders is 2 weeks (approx).b. R is the reorder point, which is the inventory level at which an order should be placed to avoid a stockout.

It can be calculated using the formula:R = dL + zσL

Where,d = Demand per day = 100 / 5 = 20L = Lead time = 1 week (5 working days) = 5 day

z = z-value for 92% cycle-service level = 1.75 (from standard normal table)σL = Standard deviation of lead time demand = σ / sqrt(L) = 16 / sqrt(5) = 7.14 (approx)

Therefore,R = 20 x 5 + 1.75 x 7.14 = 119.2 ≈ 120 bags

Hence, the reorder point R should be 120 bags.c. An inventory withdraw of 10 bags was just made. Is it time to reorder?The current inventory level is 310 bags, which is greater than the reorder point of 120 bags. Since there are no open orders or backorders, it is not time to reorder.d. The store currently uses a lot size of 500 bags (i.e., Q = 500).What is the annual holding cost of this policy.

Annual ordering cost. Without calculating the EOQ, how can you conclude the lot size is too large?Annual ordering cost = (D / Q) x S = (5200 / 500) x 57 = $592.80 per year.

Annual holding cost = Q / 2 x H = 500 / 2 x 0.30 x 10.75 = $806.25 per year. Total annual inventory cost = Annual ordering cost + Annual holding cost= $592.80 + $806.25 = $1,399.05Without calculating the EOQ, we can conclude that the lot size is too large if the annual holding cost exceeds the annual ordering cost.

In this case, the annual holding cost of $806.25 is greater than the annual ordering cost of $592.80, indicating that the lot size of 500 bags is too large.e.

The annual cost saved by shifting from the 500-bag lot size to the EOQ can be calculated as follows:Total cost at Q = 500 bags = $1,399.05Total cost at Q = EOQ = Annual ordering cost + Annual holding cost= (D / EOQ) x S + EOQ / 2 x H= (5200 / 234) x 57 + 234 / 2 x 0.30 x 10.75= $245.45 + $93.68= $339.13

Annual cost saved = Total cost at Q = 500 bags - Total cost at Q = EOQ= $1,399.05 - $339.13= $1,059.92

Hence, the annual cost saved by shifting from the 500-bag lot size to the EOQ is $1,059.92.

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Dixon is 6 feet tall. Dixon's height can be determined using the concept of similar triangles.

To find Dixon's height, we can use the concept of similar triangles. Since Dixon's shadow is 9 feet long and Ariadne's shadow is 7.5 feet long, we can set up a proportion:

Dixon's height / Dixon's shadow = Ariadne's height / Ariadne's shadow

Let's denote Dixon's height as x. We have:

x / 9 = 5 / 7.5

Cross-multiplying, we get:

7.5x = 9 * 5

7.5x = 45

Dividing both sides by 7.5:

x = 45 / 7.5

x = 6

Therefore, Dixon is 6 feet tall.

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The complete question is:

Dixon and his little sister Ariadne stand next to each other on the playground on a sunny afternoon. Their mother measures their shadows.  Dixon's shadow is 9 feet long and  Ariadne's shadow is 7.5 feet long . If Ariadne is 5 feet tall, how tall is Dixon?

We must invest  396.90, at an interest rate of 8.

Hobby is the fee you pay to borrow cash or the cost you price to lend money. interest is most customarily contemplated as an annual percent of the amount of a mortgage. This percent is called the interest price on the loan. for example, a bank will pay you interest when you deposit your money in a savings account.

The forms of interest consist of simple hobby, accumulated hobby, and compounding hobby. while money is borrowed, generally via the way of a loan, the borrower is required to pay the interest agreed upon by the two events.

There has been a energetic hobby inside the elections inside the final  weeks. She'd appreciated him in the beginning, but soon lost interest. Synonyms: significance, issue, importance, moment extra Synonyms of interest. countable noun.

value = Amount*(1+i)n

                     = 500*(1+.08)3

                         = 500*0.7938

                  Present value = 396.90

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The sequence converges to 4/5.

To determine whether the sequence converges or diverges, we can use the ratio test.

Using the ratio test, we have:

lim n→[infinity] |(4(n+1)/(1+5(n+1))) / (4n/(1+5n))|

= lim n→[infinity] |(4n+4)/(5n+6)|

= 4/5

Since the limit is less than 1, the series converges.

To find the limit, we can rewrite the sequence as:

an = 4n / (5n + 1 - 1)

= 4n / 5n * (1 + 1/5n - 1/5n)

= (4/5) * (1 + 1/5n - 1/5n)

As n approaches infinity, the second term approaches zero, and we are left with:

lim n→[infinity] an = (4/5) * 1 = 4/5

The sequence converges to 4/5.

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You know that the gift has a shape of a Regular triangular prism. Then, you need to use the following formula for calculate the surface area of a triangular prism:

Where "B" is the area of the base, "P" is the perimeter of the base and "h" is the height of the prism.

Since the base of the triangular prism is a triangle at it is a regular prism:

Where "b" is the length of the base of the triangle, "H" is the height of the triangle and "s" is the length of any side of the triangle.

Then, you can rewrite the formula:

In this case:

Then, substituting values into the formula and evaluating, you get:

The answer is:

Answer:

car(c.p)=$8400

Step-by-step explanation:

L%=(c.p-s.p)100%

c.p

10%=(c.p-7560)100%

c.p

10c.p=100c.p-756,000

(10-100)c.p= -756,000

-90c.p= -756,000

-90 -90

c.p=8400

Looking at the figure, we can determine the following relations:

A.

The angles ∠BFC and ∠DFE are vertical angles.

B.

The angles ∠BFA and ∠DFE are neither vertical angles or a linear pair.

C.

The angles ∠BFC and ∠CFD are a linear pair.

D.

The angles ∠AFE and ∠AFC are a linear pair.

E.

The angles ∠BFE and ∠CFD are vertical angles.

F.

The angles ∠AFE and ∠BFC are neither vertical angles or a linear pair.

Since the angle ∠EFD is 50° and the angles ∠AFB and ∠EFD are congruent, the angle ∠AFE can be found with the relation:

The angles ∠DFC and ∠BFE are vertical angles, so we have:

The angles ∠BFC and ∠EFD are vertical angles, so they are congruent, therefore we have ∠BFC = 50°.

Therefore, a student has 756 different options for fulfilling the requirements by taking one course from each group.

To calculate the number of different options for fulfilling the requirements, we need to multiply the number of choices from each group.

Number of choices from the health group = 6

Number of choices from the civics group = 7

Number of choices from the critical thinking group = 9

Number of choices from the elective group = 2

To calculate the total number of options, we multiply these numbers together:

Total number of options = 6 * 7 * 9 * 2

= 756

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Answer:

That is correct

Step-by-step explanation:

If my answer is incorrect, pls correct me!

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Answer:

True

Step-by-step explanation:

18 = 3 x 6

Answer:

x < -55

Step-by-step explanation:

Step 1: Convert word to math

85 - 3x > 250

Step 2: Solve for x

Here we see that any value smaller than -55 will work.

Answer.if breadth is 1 then length is 38 cm

v= l×b×h

342=l×1×9

342=9l

l=342/9

l=38

____________________________

Breadth=1 cm

Height=9cm

Volume=342cm^3

Length=?

Now,

Volume=l*b*h

or,342=l*1*9

or,342=9l

or,l=342/9

length=38 cm

So the length is 38 cm

Hope it helps

Good luck on your assignment.

_______________________________

The equation representing a line parallel to the line through a(0, 2) and b(1, 0) is y = -2x + 2.

To find the equation of the line passing through points a(0,2) and b(1,0)

The first thing that needs to be determined is the slope of the line.

We can then use the point-slope form of the equation to find the equation of the line.

We can find the slope of the line by using the formula:m=(y₂ - y₁)/(x₂ - x₁)

where (x₁, y₁) = a(0, 2) and (x₂, y₂) = b(1, 0).

Substituting the values, we get:m=(0 - 2)/(1 - 0)=-2/1=-2

Therefore, the slope of the line passing through points a and b is -2.

A line parallel to this line will have the same slope.

Hence, we can use the slope-intercept form of the equation to find the equation of the parallel line.

The slope-intercept form of the equation is:y = mx + b ,where m is the slope and b is the y-intercept.

To find the equation of the parallel line, we need to find the value of b.

We know that the line passes through the point a(0, 2).

Hence, we can substitute the values of x and y into the slope-intercept form of the equation and solve for b.2 = -2(0) + b2 = bTherefore, the value of b is 2.

Now we can substitute the values of m and b into the slope-intercept form of the equation to get the equation of the parallel line:y = -2x + 2

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9514 1404 393

Answer:

  175.2 square feet

Step-by-step explanation:

The lateral area is the total area of the side faces. It excludes the area of the top and bottom "bases" of the prism.

It can be found by adding the areas of the four rectangles. The two you can't see have the same areas as the two you can see.

Since the height of each rectangle is 4 feet. the total area will be the product of that and the perimeter of the prism.

  LA = Ph . . . . perimeter times height

  LA = 2(L+W)h . . . . the perimeter is twice the sum of length and width

  LA = 2(12.3 ft + 9.6 ft)(4 ft) = 2(21.9 ft)(4 ft) = 175.2 ft²

The lateral area of the prism is 175.2 ft².

__

The attachment shows scribbling on two of the faces that contribute to the lateral area. As stated above, the other two faces are the same size as these.

The shortest distance between the first and third base is 127.28 feet.

The shortest distance can be determined using Pythagoras theorem.

The Pythagoras theorem: \(\sf a^2 + b^2 = c^2\)

where:

a = length

b = base

c = hypotenuse

\(\sf 90^2+ 90^2\)

\(\sf 8100 + 8100\)

\(\sf = \sqrt{16200} = 127.28 \ foot\)

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Answer:

B. 15.4 ft

Step-by-step explanation:

this answer, without any formulas used, can be answered correctly and logically.

answer c, d and e are eliminated as the opposite side cant be greater than the hypotenuse.

now we have to find which is correct between a and b

the answer will be 'B' as the value of sine of an angle keeps increasing as the angle itself increases. thus, giving a bigger value of the opposite side (required height). as 15.4 ft.

mathematically,

sin65° = x/17

17 × sin65° = x

where x is height of the side of the building.

Answer:

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The best description about the sampling distribution of means for the student's sample is mu x = 45, sigma x = 3.75, shape of distribution unknown.

Sampling distribution is defined as the probability distribution of a statistical measure which is got by the repeated sampling of a specific population.

Given that,

μ = 45 minutes and σ = 15 minutes

Sampling distribution of means for the student's sample is :

μₓ = μ = 45

σₓ = σ / √n, where n is the sample size.

σₓ = 15 / √(16) = 15 / 4 = 3.75

Now since the sample size 16 which is less than 30, shape of the distribution is unknown.

Hence the sampling distribution is, μₓ = 45, σₓ = 3.75, and the shape of distribution is unknown.

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Answer:Any number less than -13.

Step-by-step explanation:

If the number is real and rational and non-natural, this means that it can be any number in the negative number space.

Additionally, since the number has to be less than -13, then the number could be any number less than -13.

With all these things considered, the number is any number less than -13 that is real and rational.

Cheers.

Answer:

9

Step-by-step explanation:

given an ordered pair (x, y )

Then x is the input and y the output

Given

(1, 9 )

Then y = 9 represents the output

Answer:

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Step-by-step explanation:

Hope it Helps!!!!

The inequality that models the situation is:

\(15000 + 4s \geq 450000\)

Solving it, it is found that they need to sell at least 108,750 shirts.

During the day:

Hence, the earnings are:

\(T = 15000 + 4s\)

They want to earn at least 450,000, hence:

\(T \geq 450000\)

\(15000 + 4s \geq 450000\)

Solving it:

\(15000 + 4s \geq 450000\)

\(4s \geq 435000\)

\(s \geq \frac{435000}{4}\)

\(s \geq 108750\)

They need to sell at least 108,750 shirts.

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Answer:

D (12.8)

Step-by-step explanation:

There are ten spaces between 12 and 13, and the point is on the eighth space

Answer:the answer is d.

Step-by-step explanation:

Using combination, there are 840 ways to choose the 2 different goalies and 5 different forwards for the game.

Now we can multiply these two expressions to get the total number of ways the coach can choose the 2 different goalies and 5 different forwards for the game.

The Rosedale Thunders hockey team has 6 players who can play goalie and 8 different players who can play forward. The coach is able to dress 2 goalies and 5 forwards for the game. In how many ways can the coach choose the 2 different goalies and 5 different forwards for the game?

Let's denote the number of ways the coach can choose the goalies as C(6, 2), where "C" is the combination.C(6, 2) = 6! / (2! * (6 - 2)!) = 15 ways to choose 2 different goalies.And let's denote the number of ways the coach can choose the forwards as C(8, 5), where "C" is the combination.

C(8, 5) = 8! / (5! * (8 - 5)!) = 56 ways to choose 5 different forwards.Now we can multiply these two expressions to get the total number of ways the coach can choose the 2 different goalies and 5 different forwards for the game.

C(6, 2) × C(8, 5) = 15 × 56 = 840 ways to choose the 2 different goalies and 5 different forwards for the game.

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Answer:

37% = 37/100 as a fraction

Step by Step Solution

To convert 37 percent to a fraction follow these steps:

Step 1: Write down the percent divided by 100 like this:

37% = 37/100

Step 2: Multiply both top and bottom by 10 for every number after the decimal point:

As 37 is an integer, we don't have numbers after the decimal point. So, we just go to into decimal0.37. into fraction 37/100

Answer: Choice B) between 6:48 AM and 5:12 PM

=========================================================

Explanation:

I've seen this problem before, and the first part states that if the temperature is above 25 degrees C, then the air conditioner turns on to start cooling the castle.

We want to find values of t that satisfy f(t) > 25

This is the same as trying to solve f(t) - 25 > 0

So we have,

\(f(t) = 24 - 5\cos\left(\frac{\pi}{12}t\right)\\\\ f(t)-25 = 24 - 5\cos\left(\frac{\pi}{12}t\right)-25\\\\ f(t)-25 = -1 - 5\cos\left(\frac{\pi}{12}t\right)\\\\ f(t)-25 > 0\\\\ -1 - 5\cos\left(\frac{\pi}{12}t\right) > 0\\\\\)

To solve this inequality, we can graph using Desmos as I've done so below. See the attached image.

Note how I used x in place of t. This is because the graphing calculator graphs (x,y) coordinates.

Furthermore, note how I marked the two points (6.769, 0) and (17.231, 0)

Between these two points is when the curve is above the x axis, when f(t) > 25 is true. This is when the temperature is above 25 degrees C, and when the air conditioner is working.

When t = 6.769, this means that roughly 6.769 hours have passed since midnight which means we're somewhere between 6 am and 7 am. The only value that works from the answer choices is 6:48 AM.

Note how 0.769*60 = 46.14 is fairly close to 48. This error is likely due to how things are rounded.

Then focusing on the point  (17.231, 0) means that t = 17.231. So 17.231 hours have elapsed since midnight and we're now at roughly 1700 hours

1700 hours in military time = 17-12 = 5 pm

The time value t = 17.231 is between 5 pm and 6 pm. The only thing that works is 5:12 pm.

We can then note how 0.231*60 = 13.86 which is also probably due to rounding error (it's fairly close to 12 though).

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

In short, we found the function for f(t)-25 and graphed it as shown below. The two points (6.769, 0) and (17.231, 0) help us see when the AC is turned on, which is roughly between 6:48 AM and 5:12 PM. This seems like a reasonable time for the AC to be operational. Something like between 5:12 PM and 6:48 AM seems like a bad idea because the AC would be working mostly at night, instead of during the day.

Anything beyond t = 24 represents the next day, which is when the cycle starts all over again. So we only need to focus on the window from t = 0 to t = 24. Specifically, the portion of the f(t)-25 curve that is above the x axis.