Universal Electric manufactures sell two models of lamps X and Whose profit being $ 15 and $ 10 respectively. The Process involves two workers A and B who are available for this kind of work with 100 and 80 hours per month respectively. A assembles X in 20 minutes and Y in 30 minutes. B paints X in 20 minutes and Y in 10 minutes. Assuming that all lamps made can be sold without difficulty, determine production figures that maximize profit.
y

The paper must be folded 43 times to get the thickness same as the distance from the earth to the moon.

Note that the function g is defined as [tex]g(n)=0.052^n.[/tex]

Let g(n) be the thickness that is g(n)=t.

Thus,

[tex]t & =0.05\left(2^n\right) \\\frac{t}{0.05} & =2^n \\\frac{100 t}{5} & =2^n \\20 t & =2^n\end{aligned}[/tex]

Take logarithms on both sides, thus

[tex]$$\begin{aligned}\log (20 t) & =\log \left(2^n\right) \\\log (20 t) & =n \log (2) \\n & =\frac{\log (20 t)}{\log (2)} \\n & =\log _2 20 t\end{aligned}$$[/tex]

Thus, [tex]g^{-1}=\log _2 20t[/tex]  is the required inverse function.

c) Given that the thickness of the paper is same as the distance from the earth to the moon that is t=384,472,300,000 mm.

To determine the corresponding value of n.

Note that the inverse function is defined as [tex]g^{-1}(t)=\log _2 20t[/tex]...

Substitute 384,472,300,000 in equation (1), thus

[tex]$$\begin{aligned}& g^{-1}(384,472,300,000)=\log _2(20 \times 384,472,300,000) \\& g^{-1}(384,472,300,000)=\log _2(20 \times 384,472,300,000) \\& g^{-1}(384,472,300,000)=42.806\end{aligned}$$[/tex]

Since, [tex]g^{-1}[/tex] determines the number of folds of the paper, the value must be the whole number.

Thus, [tex]g^{-1}(384,472,300,000)[/tex] is approximately equal to 43 .

Thus, the paper must be folded 43 times to get the thickness same as the distance from the earth to the moon.

The complete questions should be:

b. The function g has an inverse. The function g^{-1} determines the number of folds needed to give the folded paper a thickness of t mm. Write a function formula for g^{-1}.

c. Use your function in part (b) to determine how many times you must fold a piece of paper to make the folded paper have a thickness that is the same as the distance from the earth to the moon. (Assume the distance from the earth to the moon is 384,472,300,000 mm. folds

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Answer:

x=3+ay/4a

Step-by-step explanation:

4(x-3)/a=y

a*4(x-3)/a=a*y

4a(x-3)=ay

4a(x-3)/4a=ay/4a

x-3=ay/4a

x-3+3=3+ay/4a

x=3+ay/4a

Answer:

12 x 9 x 15 is 1620. then start multiplication on the subject

Answer: [tex]\cos P=r/q[/tex]

Step-by-step explanation:

Cosine is defined as adjacent/hypotenuse.

In relation to [tex]\angle P[/tex], the adjacent side is [tex]r[/tex] and the hypotenuse is [tex]q[/tex].

So, [tex]\cos P=r/q[/tex].

Answer:

representa 48

Step-by-step explanation:

The break-even point for Patty's Pies is C. 4,211 pies.

The break-even point is the sales units that equate the sales revenue with the total costs (fixed and variable).

At the break-even point, there is no profit, there is no loss.  Above this point, profits are generated.  Below it, losses are recorded.

Fixed cost = $20,000

Selling price per pie = $8.75

Variable cost per pie = $4.00

Contribution margin per pie = $4.75 ($8.75 - $4.00)

Contribution margin ratio = 54.29% ($4.75/$8.75 x 100)

Break-even point in sales units = Fixed costs ÷ Contribution margin per unit

= $20,000 ÷ $4.75

= 4,211 units

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Answer:

y=4x+11

Step-by-step explanation:

The monthly payment is $966.76.

What is monthly payment?

The amount paid each month to repay the loan over the course of the loan is known as the monthly payment. When a loan is taken out, not only the principal, or the original lent amount, but also the interest that accrues, must be repaid.

Given the amount of the loan is $1,450.

The number of installment is 18.

The APR of the loan is 8%.

The monthly rate of interest is 8%/12 = 2/3%

The formula of monthly installment is

[tex]M=P[\frac{r}{1-(1+r)^{-n}} ][/tex]

P =  principal = 1,450

r = rate of interest = 2/3%

n = number of instalment = 18

[tex]M=1450[\frac{0.67}{1-(1+0.67)^{-n}} ][/tex]

M = 966.76

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The expected value of X + 1 (Y - 1) can be calculated using the formula E(X + 1)(Y - 1) = E(X)E(Y) + E(X) - E(Y) + 1. Thus, the expected value of X + 1 (Y - 1) = 9/2 * 9/2 + 9/2 - 9/2 + 1 = 17. Therefore, the correct answer is d) 17.

The expected value of X + 1 (Y - 1) is a measure of the average value of the product of two independent random variables, X and Y. To calculate this expected value, we can use the formula E(X + 1)(Y - 1) = E(X)E(Y) + E(X) - E(Y) + 1. Since X and Y are independent random variables, we know that E(X) = E(Y) = 9/2. Plugging this value into the formula, we get E(X + 1)(Y - 1) = 9/2 * 9/2 + 9/2 - 9/2 + 1 = 17. This is the expected value of X + 1 (Y - 1). Therefore, the correct answer is d) 17.

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For measurements of the same quantity, there won't be a significant difference in the standard deviation.

The standard deviation for Tests A and B is almost the same.

Total quantity in test a = n1 = 100

Total quantity in test b = n2=400

We know that the standard error is defined as: [tex]S E=\frac{\sigma}{\sqrt{n}}[/tex]

where we have, for test A [tex]$$S E_A=\frac{\sigma}{\sqrt{100}}$$[/tex]

and for Test B [tex]$$S E_B=\frac{\sigma}{\sqrt{400}}=\frac{1}{2} * \frac{\sigma}{\sqrt{100}}$$[/tex]

So, from here, we can conclude that,

The standard error in Test A is twice as big as in Test B.

The complete question will be:

Which of the following statements is the most likely description of the comparison of the standard errors found in Test A and Test B?

The standard errors found in Test A and Test B will be about the same.

The standard error found in Test A will about be twice as big as the standard error found in Test B.

The standard error found in Test A will about be four times as big as the standard error found in Test B.

The standard error found in Test B will about be twice as big as the standard error found in Test A.

The standard error found in Test B will about be four times as big as the standard error found in Test A.

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Answer:

z = 20

Step-by-step explanation:

We can use the elimination method in a systems of 3 equations, just as we did when we were solving systems of 2 equations. While the method we apply it is the same, we have to apply it multiple times as elimination gets rid of one variable (usually) and since we're dealing with 3 variables, that still leaves us with 2 variables and we need to cancel once more.

We want to develop two linear equations, by applying elimination twice to each equation at least once, and then from there we can apply elimination once more.

Since we're solving for "z", we don't want to immediately cancel it out. So let's use the following two equations:
[tex]x+y-z=-5\\\\x-4y+3z[/tex]

Let's cancel out the "x", by manipulating one equation to be -x. We can do this by multiplying one equation by -1, but remember we have to apply this to both sides of the equation. Let's do it to the top one (you could also do it to the bottom one)

[tex]-1(x+y-z)=-(-5)\implies -x-y+z=5[/tex]

So now let's add the two equations:

[tex]\ \ \ (-x-\ y+\ z)=5\\+(\ \ x-4y + 3z) = 5\\ ------------\\ -5y+4z=10[/tex]

Now let's apply the same thing, but to the middle and bottom equation. Since they don't have the same absolute value coefficients (ignoring the sign) we need to multiple one by a value other than just negative one. So let's multiply the bottom equation by -2 so that the bottom will have a -2x which will cancel when adding it to 2x

[tex]-2(x - 4y + 3z) = -2(5)\\-2x + 8y - 6z = -10[/tex]

Now let's add the equations:

[tex]\ \ \ (\ \ 2x-y+z)=8\\+(-2x + 8y - 6z)=-10\\\\-----------\\7y - 5z = -2[/tex]

So now we have the two equations:

[tex]7y-5z=-2\\-5y+4z=10[/tex]

From here we can apply any method we want, from here I'll use substitution. Since we want to get rid of the "y", let's solve for "y" in terms of z, so once we substitute we have no "y" terms left.

[tex]7y-5z=-2\\7y=5z-2\\y=\frac{5z-2}{7}[/tex]

Now let's plug this into the second two-variable equation we made.

[tex]-5(\frac{5x-2}{7})+4z=10\\\\\frac{-25x+10}{7}+4z=10\\\\\frac{-25}{7}z+\frac{10}{7} + \frac{28}{7}z = \frac{70}{7}\\\\\frac{-25+28}{7}z = \frac{70-10}{7}\\\\\frac{3}{7}z = \frac{60}{7}\\\\z = \frac{60}{7} * \frac{7}{3}\\\\z = 20[/tex]

Answer:

I don't know the answer so how will I tell you

Answer: B. $13,720

Step-by-step explanation: To calculate Ford's proceeds, we need to first find the discount, which is equal to the interest on the loan multiplied by the principal amount of the loan. The interest is 8% of $14,000, or $1,120. The discount is then $1,120 * 90/360, or $310. The proceeds are equal to the principal amount minus the discount, or $14,000 - $310 = $13,720.

The probability of being dealt a blackjack on the next hand is 4.8%. This is because there are only 4 cards that could make up a blackjack (an Ace and a 10-valued card), and there are only 82 cards left in the deck after two hands. Therefore, the probability of being dealt a blackjack is 4/82, or 4.8%.

The probability of being dealt a blackjack on the next hand is 4.8%. This is because a blackjack is made up of an Ace and a 10-valued card, so the probability of being dealt one is 4/82, or 4.8%. This is because after two hands, there are only 82 cards left in the deck. Of those 82 cards, there are only 4 that can make up a blackjack. Therefore, the probability of being dealt a blackjack is 4/82, or 4.8%. The fact that the deck is not being shuffled after each hand does not affect the probability, as the used cards are being put to the side and not used again until the deck is reshuffled.

Probability of blackjack = (number of cards that can make a blackjack / total number of cards remaining in the deck)

Probability of blackjack

= (4 / 82)

Probability of blackjack

= 4.8%

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The equation of the line in point slope form and slope intercept form are  y - 8 = -(x + 6) and  y = -x + 2. respectively.

The equation of a line in slope intercept form is as follows:

y = mx + b

where

Therefore, equation of a line passing through (-6,8) and is perpendicular to the line y = x + 9.

Perpendicular lines have slopes that are the opposite of the reciprocal of each other.

Therefore, the slope is - 1.

Hence,

y = -x + b

Using (-6, 8)

8 = -(-6) + b

b = 8 - 6

b = 2

Therefore, the slope intercept form is y = -x + 2.

The equation of the line in point slope form is represented as follows:

y - y₁ = m(x - x₁)

where

m = slope

Using (-6, 8)

Therefore, the equation in point slope form is y - 8 = -(x + 6)

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By Side - Angle - Side Congruence Rule the given triangles are Congruent

What is SAS Rule of Congruence?

That is stated in the SAS regulation. If two sides and the included angle of one triangle equal two sides and the included angle of another, the triangles are congruent. An included angle is one created by the intersection of two specified sides.

Solution:

By Side - Angle - Side Congruence Rule the given triangles are Congruent

Since, two sides are equal andd the angle included between the sides is equal to

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Answer: One sweater: $13 and One shirt: $8

Step-by-step explanation: You have to use elimination. The first formula would be 1x + 3y = 37 and the other is 3x + 2y = 55. Once you use elimination, you just solve a one step equation. When you get x = 13, you plug the 13 into one of the formulas to get 8.

According to the statement given, Distance = Velocity X time = V1 X (t2 - t1), but this is the overestimate value

Velocity is the rate at which a moving object's location changes as observed from a specific frame of reference and measured at a specific time standard.

1. Distance = velocity X time

= V X (t2 - t2)

2. According to the statement given,

Distance = Velocity X time

= V1 X (t2 - t1)

but this is the overestimate value, because

Distance = Area under velocity - time curve

therefore, statement 2 is correct

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The surface area of the figure given which is a rectangular prism is 1362cm²

The total region or area covered by all the faces of a rectangular prism is defined as the surface area of a rectangular prism. A rectangular prism is a three-dimensional shape. It has six faces, and all the faces are rectangular-shaped. Therefore, both the bases of a rectangular prism must also be rectangles.

The surface area of the prism is calculated by the formula

A = 2[(lw) + (lh) + (wh)]

To solve this problem, we have to divide the prism into two different parts and solve for the area.

For the first rectangular prism;

A = 2[(lw) + (lh) + (wh)]

A = 2[(8 * 14) + (8 * 14) + (14 * 14)]

A = 840cm²

The area of the second figure will be;

A = 2[(8 * 17) + (17 * 5) + (8 * 5)]

A = 552cm²

The total surface area of the figure is 840cm² + 552cm² = 1362cm²

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Answer:

+2 or –10

Step-by-step explanation:

x² + 8x –5 = 15

x² + 8x = 15 + 5

x² + 8x = 20

using completing the square method

(½(8))² to be applied in both sides

x² + 8x + 16 = 20 + 16

factorise the LHS

(x+4)² = 36

x + 4 = √36

x + 4 = ±6

x = –4±6

x = –4 + 6 or –4–6

x = +2 or –10

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The sell order with the fifth lowest price (lowest bid) will be ranked fifth and will be executed last. In this case, the sell order with a price of $14 and a quantity of 10 will be executed last.

1. $10 - 20

2. $11 - 30

3. $12 - 50

4. $13 - 40

5. $14 - 10

1. The sell order with the lowest price (highest bid) is ranked first and will be executed first. In this case, the sell order with a price of $10 and a quantity of 20 will be executed first.

2. The sell order with the second lowest price (second highest bid) will be ranked second and will be executed second. In this case, the sell order with a price of $11 and a quantity of 30 will be executed second.

3. The sell order with the third lowest price (third highest bid) will be ranked third and will be executed third. In this case, the sell order with a price of $12 and a quantity of 50 will be executed third.

4. The sell order with the fourth lowest price (fourth highest bid) will be ranked fourth and will be executed fourth. In this case, the sell order with a price of $13 and a quantity of 40 will be executed fourth.

5. The sell order with the fifth lowest price (lowest bid) will be ranked fifth and will be executed last. In this case, the sell order with a price of $14 and a quantity of 10 will be executed last.

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The estimate probability that there is at least one such accident during a given year, P(X≥1) is equals to the 0.0952..

We have, the probability that there is a significant accident in a nuclear power plant during one year, p = 0.01

Total nuclear plants in country , n = 100

we have to calculate probability that there is at least one such accident during a given year.

Using Binomial Probability distribution,

X ~ Bin( 100, 0.01)

P(X= x ) = ⁿCₓ(p)ˣ (1-p)⁽ⁿ⁻ˣ⁾

Thus, the probability that there is at least one such accident during a given year, P(X≥1)

= 1 - P(there is no such event, P(X= 0)

= 1 - P(X= r ) = 1 - ⁿCᵣpʳ(1-p )⁽ⁿ⁻ʳ⁾

where p is probability of success

r = 0 , n = 100, p = 0.001

plugging all known values in above formula,

P(X≥ 1) = 1 - ¹⁰⁰C₀ (0.001)⁰(1- 0.001)⁽¹⁰⁰⁻⁰⁾

= 1 - ¹⁰⁰C₀ (0.001)⁰(0.999)¹⁰⁰

= 1 - 1 ×1 ×0.904792

=1 - 0.904792

=0.0952

Hence, required probability is 0.0952.

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The length of unknown side of the triangle will be 18 inch.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The two triangles are shown in figure.

Now,

Since, Both the triangle are similar.

Hence, There corresponding sides of the triangle are similar.

So, We get by definition of proportion visit:

⇒ 4 / 12 = 6 / x

⇒ 1/3 = 6/x

⇒ x = 6 × 3

⇒ x = 18 in

Thus, The length of unknown side of the triangle = 18 inch.

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A closed form for the corresponding generating function is all the donuts are chocolate and there are at least 3, therefore, x³/1 − x.

In math the word function refers the a set X to a set Y in mathematics assigns each element of X exactly one element of Y.

Here the domain and codomain of the function are denoted by the sets X and Y, respectively.

Here we have to find  a closed form for the corresponding generating function.

While we looking into the given question, we have identified the the  concept of function was first discussed by two Persian mathematicians named Al-Bruni and Sharaf al-Din al-Tutsi.

And the functions were originally used to represent the idealized relationship between varying quantities and other variables.

As for example, time has an impact on a planet's position.

Here the the number of different ways to compose a bag of n donuts subject to various restrictions.  As per these condition, we now that the option (a) is correct.

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It will take a ball 1.8 seconds to travel  27 m at a rate of 18m/s

The time it will take a ball to travel is solved from the formula of speed given as

speed = distance covered / time taken

from the problem

distance covered = 27 m

time taken = ?

speed = 15 m/s

substituting into the formula

15 = 27 / time

time = 27 / 15

time = 1.8 seconds

the time is 1.8 s

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Answer:

28.

Step-by-step explanation:

Si on a une perfusion d'héparine 20 000 unités dans 500 ml de dextrose 5 % à un débit de 1 000 ml/heure, le débit en unités/heure d'héparine est calculé en divisant le nombre d'unités d'héparine (20 000) par le volume de la solution de dextrose (500 ml) pour obtenir la concentration en unités/ml d'héparine dans la solution (40 unités/ml). Ensuite, on multiplie la concentration par le débit de la solution (1 000 ml/heure) pour obtenir le nombre d'unités/heure d'héparine qui sont perfusées. 40 unités/ml x 1 000 ml/heure = 40 000 unités/heure, et puisque 1 heure = 60 minutes, le débit en unités/minute est de 40 000 unités/heure / 60 minutes/heure = 666,67 unités/minute. Enfin, on divise le débit en unités/minute par la concentration en unités/ml pour obtenir le débit en ml/minute, soit 666,67 unités/minute / 40 unités/ml = 16,67 ml/minute. Comme 1 litre = 1 000 ml, le débit en litres/heure est de 16,67 ml/minute x 60 minutes/heure = 1 000 ml/heure, et puisque la concentration d'héparine dans la solution est de 20 000 unités/500 ml = 40 unités/ml, le débit en unités/heure est de 1 000 ml/heure x 40 unités/ml = 40 000 unités/heure. Par conséquent, la réponse finale est de 40 000 unités/heure / 60 minutes/heure = 666,67 unités/minute / 40 unités/ml = 16,67 ml/minute x 60 minutes/heure = 1 000 ml/heure x 40 unités/ml = 40 000 unités/heure = 28 unités/heure.

a. t distribution

b.  98% confidence the population mean number of texts per day is between and texts is  31. 455 and 36.945

c. Two percent  will not contain the true population mean number of texts per day.

Confidence interval

Given that,

xbar = 34.2

s = 12.7

n = 119

degrees of freedom, df = n - 1 = 118

a. t distribution

b.  CI level is 98%, hence α = 1 - 0.98 = 0.02

α/2 = 0.02/2

    = 0.01,

tc = t (α/2, df) = 2.358

CI = [tex](34.2 - 2.358 * \frac{12.7}{\sqrt{119} } , 34.2 + 2.358 *\frac{12.7}{\sqrt{119} } )[/tex]

CI = (31.455 , 36.945)

With 98% confidence the population mean number of texts per day is between 31.455 and  36.945 texts.

(c) Approximately 98 percent of these confidence intervals will contain the true population mean number of texts per day, while approximately 2 percent will not.

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The addition of function f(x) = 3 · x² - 1 and function g(x) = x + 2 is equal to (f + g)(x) = 3 · x² + x + 1. (Correct choice: B)

New functions can be created by combining functions, the most common operations are listed below:

In this problem we must determine the expression that is the result of the addition of two functions, whose definition is shown below:

(f + g) (x) = f(x) + g(x)

First, use the definition of the addition of two functions:

(f + g)(x) = (3 · x² - 1) + (x + 2)

Second, simplify the algebraic expression:

(f + g)(x) = 3 · x² + x + 1

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