hich is equivalent to RootIndex 5 StartRoot 1,215 EndRoot Superscript x?

243x
1,215 Superscript one-fifth x
1,215 Superscript StartFraction 1 Over 5 x EndFraction
243 Superscript StartFraction 1 Over x EndFraction

The value of x in the lines is 126 degree

We are given that;

Three parallel line and one intersecting line

Angles= (x-6) and 60

Now,

By supplementary angles property

Angle 1 + Angle 2 = 180 degree

Substituting the values of angles

x-6 + 60 = 180

x + 54 = 180

x = 180-54

x = 126

Therefore by supplementary angles answer will be 126 degree.

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A. In equation form: Revenue = 9x1 + 12x2 + 4x3 + 5x4 + 8x5

B. Non-negativity constraint: x1, x2, x3, x4, x5 ≥ 0

To solve this problem using E x c e l Solver, set up the revenue function and the constraints. Here's how you can do it:

a. Revenue Function:

Let's denote the number of cakes baked for each type as x1, x2, x3, x4, and x5 respectively.

The revenue function can be formulated as:

Revenue = (Selling Price of Cake 1 × Number of Cake 1) + (Selling Price of Cake 2 × Number of Cake 2) + (Selling Price of Cake 3 × Number of Cake 3) + (Selling Price of Cake 4 × Number of Cake 4) + (Selling Price of Cake 5 × Number of Cake 5)

In equation form:

Revenue = 9x1 + 12x2 + 4x3 + 5x4 + 8x5

b. Constraints:

The constraints for the availability of ingredients can be formulated as follows:

Milk constraint: 4x1 + 3x2 + x3 + 5x4 + 4x5 ≤ 280

Sugar constraint: 7x1 + 4x2 + 5x3 ≤ 300

Egg constraint: x1 + 2x2 + 3x3 + 4x4 + 5x5 ≤ 80

Flour constraint: 3x1 + 4x2 + 2x3 + 4x4 + 6x5 ≤ 250

Cream constraint: 4x1 + 5x3 + x4 + 3x5 ≤ 190

Non-negativity constraint: x1, x2, x3, x4, x5 ≥ 0

c. Solve the system of linear inequalities using E x c e l Solver:

To solve the system of linear inequalities using E x c e l Solver, follow these steps:

1. Open M i c r o s o f t E x c e l and enter the following data in a new sheet:

| | A | B |

|-----|-----------|-----------------|

| 1 | Cakes | Selling Price |

| 2 | Cake 1 | $9 |

| 3 | Cake 2 | $12 |

| 4 | Cake 3 | $4 |

| 5 | Cake 4 | $5 |

| 6 | Cake 5 | $8 |

| | | |

| | | Formula |

| 9 | Milk | 280 |

| 10 | Sugar | 300 |

| 11 | Eggs | 80 |

| 12 | Flour | 250 |

| 13 | Cream | 190 |

2. In cell B16, enter the formula for the revenue:

=B2×B7 + B3×B8 + B4×B9 + B5×B10 + B6×B11

3. In cell B18, enter the formula for the milk constraint:

=4×B2 + 3×B3 + B4 + 5×B5 + 4×B6

4. In cell B19, enter the formula for the sugar constraint:

=7×B2 + 4×B3 + 5×B4

5. In cell B20, enter the formula for the egg constraint:

=B2 + 2×B3 + 3×B4 + 4×B5 + 5×B6

6. In cell B21, enter the formula for the flour constraint:

=3×B2 + 4×B3 + 2×B4 + 4×B5 + 6×B6

7. In cell B22, enter the formula for the cream constraint:

=4×B2 + 5×B4 + B5 + 3×B6

8. In cell B24, enter the formula for the non-negativity constraint for Cake 1:

=B2

9. Repeat step 8 for the remaining cakes, entering the formulas in cells B25, B26, B27, and B28:

=B3

=B4

=B5

=B6

10. Now, select cells B16 to B28 and click on the "Solver" button in the "Data" tab.

11. In the Solver Parameters window, set the objective to maximize the cell B16 (Revenue).

12. Set the By Changing Variable Cells to B24:B28 (the number of cakes baked).

13. Click on the "Add" button in the "Subject to the Constraints" section.

14. In the Constraint window, select the range B18:B22 for the constraint cells.

15. In the Solver Parameters window, click on the "Add" button again and select the range B24:B28 for the non-negativity constraints.

16. Set the Solver options as desired, and click on the "Solve" button.

E x c e l Solver will calculate the optimal values for the number of cakes to be baked for each type that maximize the revenue, while satisfying the given constraints on ingredient availability. The solution will be displayed in cells B24:B28, indicating the number of cakes to be baked for each type.

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Answer:

900 kg

Step-by-step explanation:

Let's assume the cost price (C.P.) of sugar is Rs. x per kg.

The total quantity of sugar is 1500 kg.

Let the quantity of sugar sold at 8% profit be represented by y kg.

The quantity of sugar sold at 18% profit would then be (1500 - y) kg.

Using the rule of alligation, we can set up the following proportion:

(8% profit) y kg

-------------- = ------

(18% profit) (1500 - y) kg

Simplifying the proportions, we find that the difference in percentages is 4% (18% - 14% = 4%) and 6% (14% - 8% = 6%).

The ratio of these differences is 2:3.

This means that for every 2 kg of sugar sold at 8% profit, 3 kg of sugar is sold at 18% profit.

Since y represents the quantity sold at 8% profit (2 kg), we can calculate the quantity sold at 18% profit (3 kg) as follows:

(2 kg) * (3/2) = 3 kg

Therefore, the quantity sold at 18% profit is 900 kg.

Answer:

Can you please post the picture of the question, then I can help.

Answer:

Yes

Step-by-step explanation:

When you're dividing 2 numbers, the order of the negatives doesn't matter. As long as one of the numbers is negative, the result will be negative. Since the order of these numbers are the same (with 3 first and 4 second) they will have the same value.

Answer:

Did you ever get the answer

Step-by-step explanation:

Using proportions, it is found that he needs 39.5 grams of protein each day.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

First we have to convert his weight to kg. Each lb has 0.453592 kg, hence his weight in kg is given by:

132 x 0.453592 = 59.87 kg.

Each day, he needs to consume 0.66 g for each kilogram in his body, hence the amount of protein that he needs to consume each day is given by:

0.66 x 59.87 = 39.5.

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Answer:

476 feet

Step-by-step explanation:

The given problem when graphically depicted forms a right triangle which has been attached below.

We want to determine the distance between Runner A and Runner B in the diagram.

Using Trigonometric Ratios

In Right Triangle AHC

\(\tan 38^\circ =\dfrac{1700}{AC} \\$Cross multiply$\\AC *\tan 38^\circ =1700\\AC =\dfrac{1700}{\tan 38^\circ}\\\\=2175.9$ feet\)

In Right Triangle BHC

\(\tan 45^\circ =\dfrac{1700}{BC} \\$Cross multiply$\\BC *\tan 45^\circ =1700\\BC =\dfrac{1700}{\tan 45^\circ}\\\\=1700$ feet\)

The distance between the two runners,

AB=AC-BC

=2175.9-1700

=475.9

=476 feet ( to the nearest foot)

Answer:

It is a rate,

A rate is the ratio between two related quantities in different units.

Miles and hours are two different units and its 50 miles per 2 hours.

Answer:

\(W = 5h - 90 \\ 5h = W + 90 \\ h = \frac{W + 90}{5} \)

Answer:

h = w+90/ 5

Step-by-step explanation:

5h-90=w

5h/5= w+90/5

h= w+90/5

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

x=5

steps

they are vertical angles

they are equal

4x+90=110

4x=20

x=5

Answer:

Step-by-step explanation:

9900

Step-by-step explanation:

x -y = -3 can be solved easily then 4x+3y= -5

The two relationships that describe a function in the table are A: Name as a function of hair color, and D: Eye color as a function of hair color.

A function is a relationship between two sets of values in which each element of the first set corresponds to exactly one element of the second set. In this table, for each hair color there is only one associated name, so the relationship between name and hair color is a function. Similarly, for each hair color there is only one associated eye color, so the relationship between eye color and hair color is also a function.

Note that the other relationships listed in the question (B, C, E and F) are not functions because they do not have a one-to-one correspondence between the two sets of values. For example, in the relationship between eye color and name, multiple people (Juan and Keshia) have the same eye color (brown), so this relationship does not describe a function.

Therefore, options A and D are the correct answer.

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Answer:

The problem shown is correct so I would say true

a. The center of the circle is (-2, -1).

b. The radius of the circle is √136.

c. The equation of the circle is (x + 2)^2 + (y + 1)^2 = 136.

a. To find the center of the circle, we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

In this case, the endpoints of the diameter are P(-7, -4) and Q(3, 2).Applying the midpoint formula:

Midpoint = ((-7 + 3)/2, (-4 + 2)/2)

= (-4/2, -2/2)

= (-2, -1)

Therefore, the center of the circle is at the coordinates (-2, -1).

b. To find the radius of the circle, we can use the distance formula, which calculates the distance between two points (x1, y1) and (x2, y2). The radius of the circle is half the length of the diameter, which is the distance between points P and Q.

Distance = √\([(x2 - x1)^2 + (y2 - y1)^2]\)

Using the distance formula:

Distance = √[(3 - (-7))^2 + (2 - (-4))^2]

= √\([(3 + 7)^2 + (2 + 4)^2]\)

= √\([10^2 + 6^2\)]

= √[100 + 36]

= √136

Therefore, the radius of the circle is √136.

c. The equation for a circle with center (h, k) and radius r is given by:

\((x - h)^2 + (y - k)^2 = r^2\)

In this case, the center of the circle is (-2, -1), and the radius is √136. Substituting these values into the equation:

\((x - (-2))^2 + (y - (-1))^2\) = (√\(136)^2\)

\((x + 2)^2 + (y + 1)^2 = 136\)

Therefore, the equation of the circle is (x + 2)^2 + (y + 1)^2 = 136.

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Answer:

y= 11x

Step-by-step explanation:

find the slope: 22-11/2-1= 11/1 or 11

To find the y-intercept you can use the slope by subtracting 11 (inverse operation) from the y value of (1,11). So the y- intercept is (0,0). To write the equation plug in 11 for m and 0 for b. Since 0 has no value the equation would be y= 11x

Answer:

Step-by-step explanation:

The column has the shape of a cylinder hence the formula for the volume of a cylinder is

\(v=\pi r^2h\)

Given

diameter d= 390 mm

radius r= 390/2= 195 mm to meter = 0.195 m

length or height h= 3 m

applying the data to the formula we have

\(v=\pi *0.195^2*3\\\\ v=\pi*0.0038*3\\\\ v=\pi*0.0114\\\\ v=0.035 m^3\)

we can now use the volume in addition with the density given to solve for the mass using the expression for density

density= mass/volume

2.45= mass/0.035

mass= 2.45*0.035

mass= 0.085 mg

We know that weight

w= mass* acceleration

w= 0.085*9.81

w= 0.83 N

The benefit of obtaining a personal loan is getting large amounts of money to use immediately.

Option D is the correct answer.

A personal loan is a type of loan that individuals can take out from a bank, credit union, or online lender to cover personal expenses such as home improvements, medical bills, or other unexpected expenses.

We have,

The benefit of obtaining a personal loan can vary depending on the specific terms and conditions of the loan, but typically it allows individuals to borrow a larger amount of money upfront with a fixed interest rate and set repayment schedule, which can be beneficial for large expenses such as home renovations, debt consolidation, or major purchases.

However, the interest rates and repayment terms can vary depending on the borrower's credit score, income, and other factors, so it's important to compare options and choose a loan that meets one's specific needs and budget.

Thus,

The benefit of obtaining a personal loan is getting large amounts of money to use immediately.

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Answer:

8 dollars is the discount

Step-by-step explanation:

the shirt would be 12 dollars. you do 40% of $20

Answer:

the discount is $8 making the shirt $12

Answer: 1/8 :)

Step-by-step explanation: This pattern is dividing each previous number by two. 1 is half of 2, 1/2 is half of 1, 1/4 is half of 1/2, and 1/8 is half of 1/4.

The length of the semi-major axis of the ellipse is 7.

What is the semi-major axis of an ellipse?

The semi-major axis of an ellipse is the half of the longest diameter passing through its vertex and focus.

The general equation of an ellipse is :

⇒ x²/a²+y²/b²=1, where a is the semi-major axis and b, is the semi-minor axis

x²/49+y²/36=1

x²/(7²)+y²/(6²)=1

x²/a²+y²/b²=1

a=7

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Answer:

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.x-intercept(s) (13,0)y-intercept(s): (0,3)

Step-by-step explanation:

Answer: The Diagram of the refracted angle is attached below

answer :  ∅ = cos^-1 ( w/d )

Step-by-step explanation:

The trigonometric expression for the refracted angle  

with respect to ; Distance ( d )  and width ( w )

Cos ∅ = Adjacent / Hypotenuse ----- ( 1 )

where; adjacent = W . Hypotenuse = d

back to equation 1

Cos ∅ = w / d

∴ ∅ = cos^-1 ( w/d )

Answer:

The average speed here is 60 mph.

Step-by-step explanation:

We need to express the unit rate here.  That's the speed, which is defined as (distance) / (time):

                       1 mile

speed s(t) = ----------------

                       t (min)

We need to convert the unit of time (min) to the new unit of time (hrs):

                       1 mile           60 min

speed s(t) = --------------- * -------------- = 60 miles/hr = 60 mph

                       t (min)             1 hr

The average speed here is 60 mph.  This is not dependent on time, t, so we cannot calculate s(10) or s(12).  Because of this, s(t) = 60 mph.  The distance traveled in t hours is d(t) = s(t)*t.

To achieve a comparable rate of return, Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly on his ordinary annuity.

To find the interest rate, compounded monthly, that Hank would need to earn on an ordinary annuity for a comparable rate of return, we can use the present value formula for an ordinary annuity.

First, let's calculate the present value of Hank's payments. He made payments of $219 per month for 30 years, so the total payments amount to $219 * 12 * 30 = $78840.

Now, we need to find the interest rate that would make this present value equal to the selling price of the property, which is $195,258.

Using the formula for the present value of an ordinary annuity, we have:

PV = P * (1 - (1+r)\(^{(-n)})\)/r,
where PV is the present value, P is the payment per period, r is the interest rate per period, and n is the number of periods.

Plugging in the values we have, we get:
$78840 = $219 * (1 - (1+r)\({(-360)}\))/r.

Solving this equation for r, we find that Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly, in order to have a comparable rate of return.

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Answer: 8 1/3

Step-by-step explanation:

100/12 = 8.33333333

8 4/12

8 1/3

If  the shop’s tax rate is 25 percent and its discount rate is 12 percent. Net present value is $43,334.

Working capital for each years

Year                     0                1             2          3        4

Working capital  -17,000    -4000 -4000 -4000  29,000

Working capital invested from 0-3  will be recovered in year 4.    

Net present value    

Year                 0                  1                    2                   3                  4

Cost savings                  $164,000  $164,000     $164,000           $164,000

Depreciation                  -$87,000  -$139,200   -$83,520            -$50,112

Savings before tax           $77,000   $24,800 $80,480          $113,888

Taxes 25%                   -$19,250    -$6,200 -$20,120          -$28,472

Net income                       $57,750     $18,600 $60,360            $85,416

Add: Depreciation             $87,000   $139,200 $83,520            $50,112

Operating cash flow         $144,750  $157,800   $143,880          $135,538

Purchase of machine -435,000    

Investment in working capital-17,000   -4000 -4000 -4000         $29,000

Aftertax salvage value                                                                      $67,542

Net cash flow  -$452,000   $140,750  $153,800   $139,880      $232,080

Discount factor 12% 1         0.89286   0.79719      0.71178           0.63552

Present value -$452,000 $125,670 $122,608   $99,565          $147,491

Net present value $43,334  

Workings:

Calculation of depreciation based on MACRS    

Year      

1 435000×0.20=$87,000    

2 435000×0.32 =$139,200    

3 435000×0.1920=$83,520    

4 435000×0.1152=$50,112  

Total                            $359,832

Calculation of aftertax salvage value      

Sale proceeds                             $65,000    

Less: Book value of machine     $75,168

(435000-359,832)  

Loss on sale of machine             -$10,168    

Tax benefit 25%                            $2,542    

After tax salvage value              $67,542

($65,000+$2,542)

Therefore the project's NPV is $43,334.    

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