Points B and C are on parallel lines with s and T, respectively. The size of the angle BAC is 96 degrees. Find the acute angle between straight AC and straight t if it is known that it is three times the size of the acute angle between straight AB and straight S.

The combination that gives the most profit exists 12 VIP rings and 12 SST rings (900 / day).

This is a linear programming problem.

The objective function is profit R, which has to be maximized. [tex]$R=40 \mathrm{~V}+35 S$[/tex]

being V: number of VIP rings produced, and S : number of SST rings produced.

The restrictions are

Amount of rings (less or equal than 24 a day): [tex]$V+S \leq 24$[/tex]

Amount of man-hours (up to 60 man-hours per day):[tex]$3 V+2 S \leq 60$[/tex]

The number of rings of each type exists a positive integer: [tex]$V, S \geq 0$[/tex]

We get 3 points, in which 2 of the restrictions exists saturated. In one of these three points lies the combination of V and S that maximizes profit.

The points and the values for the profit function in that point are:

Point 1: V=0 and S=24

[tex]$R=40 \mathrm{~V}+35 S=40 \cdot 0+35 \cdot 24=0+840[/tex]

R = 840

Point 2: V=12 and S=12

R = 40 V+35 S [tex]=40 \cdot 12+35 \cdot 12=480+420[/tex]

R = 900

Point 3: V=20 and S=0

R = 40 V+35 S [tex]=40 \cdot 20+35 \cdot 0=800+0 \\[/tex]

R = 800

The combination that gives the most profit exists 12 VIP rings and 12 SST rings (900 / day).

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Answer:

7x+9=8

Step-by-step explanation:

4-x+7x-1-8-5x+6x+13

=7x+8

:]

We can represent this situation with a triangle, as shown below:

We need to calculate the angle that forms between the line of sight of the Life Guard and the swimmer. For that, we will have to use the tangent relation.

Rule of dilation:

Find the coordinates of the points in g(x) following the rule above:

Recall that in a geometric sequence, whenever we take one value of the sequence and divide it by the next number of the sequence, we would get a constant number unique to that sequence. If we take the first and second numbers and calculate the ratio, we get

if we do that with the second and third numbers, we get

this two numbers should be equal. So we get

if we multiply both sides by 3, we get

so option A is the correct option.

We can see two graphs and we need to determine the reason why graph A IS a function, and graph B is NOT a function.

To achieve that, we can proceed as follows:

1. A function is a relation in which for each element of the domain we have only (exactly) one element of the range.

2. The domain of a function is the values for x for which the function is defined, and the range is those values for y that result when the function takes values for x and after following the rule of the function (the values for which the function is defined).

3. To determine if a graph is a function, we can use the vertical line test. Given the above definitions, this test tells us that if a vertical line passes through a graph at more than a point, then the relation is NOT a function.

4. Now we can use the Vertical Line Test on each graph as follows:

As we can see from the graph, the vertical line passes through only one point (one value for y associated to x). We can see that the open circle indicates that the function is not defined for the value while the solid circle indicates that the function is defined for that value.

For instance, for x = -1 the value of the function is y = 0 (and not y = -1 - see the open circle). We have a similar case for x = 1 (y = 1) (not y = 0).

Therefore, graph A IS a function.

In this case, we can say that the vertical line passes through more than one point in most of the values. However, we can say that there are some values where the line passes through one point - from x = -3 to x = -2 (included) -, and for values greater than 2 (x>2).

However, since the vertical line test indicates that the line passes through more than a point (there are more than a value, y, for each x) then Graph B is NOT a function.

Therefore, in summary, we can say that using the method of the vertical line test, Graph A IS a function, while Graph B is NOT a function.

The piecewise function on the graph is,

f(x) = {  1 -3x ; if x ≤ 2

        { 4-x    ; if x > 2

The graph of a piecewise function is given. The left function is defined on the interval x ≤ 2 and the right function is defined on the interval x > 2.

To find the functions we need two points on each function since both functions are straight lines.

First we will find the left function defined on x ≤ 2.

So the two points are (x₁, y₁) = (0,1) and (x₂, y₂) = (2, -5).

Now slope of the left function, m₁ = (y₂ - y₁)/(x₂ - x₁)

                                                        = -5 - 1/2 - 0

                                                        = -6/2

                                                        = -3

So the equation of the left function is,

y - y₁ = m(x-x₁)

⇒ y - 1 = -3(x-0)

⇒ y = 1 -3x

Thus the left function is f(x) = 1 -3x

Consider the right function.

The two points on the graph of the right function are (x₁, y₁) = (4,0) and (x₂, y₂) = (6, -2).

So slope of the second function, m₂ = (y₂ - y₁)/(x₂ - x₁)

                                                            = -2 - 0/6-4

                                                            = -2/2

                                                            = -1

Now equation for the right function is,

y - y₁ = m(x-x₁)

⇒ y - 0 = -1(x-4)

⇒ y = 4 -x

So the right function is f(x) = 4-x

Hence the piecewise function is,

f(x) = {  1 -3x ; if x ≤ 2

        { 4-x    ; if x > 2

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Slavery and oppression of other people impact others as it brings about discrimination and fear.

In the olden days, slavery was so lucrative that the Mississippi River valley produced more millionaires per capita than any other region of the country. With cash crops like tobacco, cotton, and sugar cane, the southern states of America developed into the country's economic engine.

In Africa, the slave trade had a terrible impact. A culture of lawlessness and violence was encouraged by the financial incentives provided to warlords and tribes to participate in the slave trade. Economic and agricultural development in a large portion of western Africa was virtually impossible due to depopulation and a persistent fear of enslavement.

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1 rad x 180/pi =57.296 deg

so the answer is 744.845

Answer:

  -12 m/km

Step-by-step explanation:

You want to know the average elevation change per kilometer given the elevation changes from 876 meters to 672 meters over a distance of 17 kilometers.

The average elevation change per kilometer is found by dividing the elevation change by the number of kilometers. The elevation change is the difference between the ending elevation and the starting elevation.

  rate of change = ((end elevation) -(start elevation))/(distance)

  = (672 m -876 m)/(17 km) = (-204 m)/(17 km) = -12 m/km

The average elevation change is -12 meters per kilometer traveled from the lodge.

__

Additional comment

Expressing both dimensions in the same unit, we can find the average grade of the road to be ...

  (-12 m)/(1000 m) = -0.012 = -1.2% . . . . . average grade of the road

Let the equired amount of 80% alcohol mixture required be 'x' mL.

If C represents the concentration and V represents the correspon

The dimensions of the enclosure that can be erected at minimum cost are 21.25 feet by 42.50 feet

From the question, the given parameters are

Area = 903 square feet

Shape = rectangle

From the question, we understand that:

One side of the area would be enclosed by the external wall of the store

If the dimensions of the area are Length (L) and Width (W), then we have

Area = LW

Perimeter = 2L + W

Rewrite as

A = LW

P = 2L + W

Substitute 903 for A in A = LW

LW = 903

Make W the subject

W = 903/L

Substitute W = 903/L in P = 2L + W

P = 2L + 903/L

Differentiate the equation

So, we have

P' = 2 - 903/L²

Set to 0

2 - 903/L² = 0

So, we have

903/L² = 2

This gives

L² = 903/2

Divide

L² = 451.5

Take the square roots

L = 21.25

Substitute L = 21.25 in W = 903/L

W = 903/21.25

Evaluate

W = 42.50

Hence, the dimensions of the enclosure are 21.25 feet by 42.50 feet

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Answer:

70 points

Step-by-step explanation:

u = US points

c = Canadian points

n = Norwegian points

u = c + 2

n = c - 4

208 = u + c + n

208 = ( c + 2 ) + c + ( c - 4 ) = 3c - 2

Isolate c:

208 = 3c - 2

210 = 3c

c = 70

Answer:

d

Step-by-step explanation:

The number of years must be non-negative.

This eliminates all of the options except for d.

The given expression is

To add 2 fractions we have to give them the same denominators

In the up part (numerator) we have 2 different denominators a and b

Then the common denominator of the 2 fractions must be the product of them

Then the fraction will be

Now, we will multiply the denominator of up by the denominator of the first fraction (ab x b)

Multiply b by b to simplify, then

The numerator is 2b + 7a

The denominator is ab^2

The value of x in the equation given as 1/6(x - 3) = 1/3(x + 2) is 7

The equation is given as

1/6(x - 3) = 1/3(x + 2)

From the question, we can see that the equation is a linear equation with one variable

As a general rule: linear equations are equations that have constant average rates of change.

We start by multiplying both sides of the equation by 6

So, we have the following equation

6 * 1/6(x - 3) = 1/3(x + 2) * 6

Next, we evaluate the products

So, we have the following equation

x - 3 = 2x + 4

Next, we collect the like terms

So, we have the following equation

2x - x = 3 + 4

Evaluate the like terms in the above equation

x = 7

This means that the solution of the equation is 7

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Given data:

The given figure of the triangle.

The remote interior angles of ∠1 are,

Thus, the options (C) and (E) are correct.

The square roots would not be between 9 and 10 is [tex]\sqrt{80}[/tex].

[tex]\sqrt[]{80}=8.944\\ \sqrt[]{90}=9.486\\ \sqrt[]{95}=9.746\\ \sqrt[]{88}=9.380[/tex]

What are square roots?

The opposite of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number may be found by looking for a number that, when squared, yields the original value. It follows that a, a = b if "a" is the square root of "b." Every integer has two square roots, one of a positive value and one of a negative value because the square of any number is always a positive number. For instance, the square roots of 4 are both 2 and -2. However, the square root of a number is typically only expressed as the positive value.

The value of a number's power 1/2 is the number's square root. It is the number whose product by itself yields the original number, to put it another way. It is symbolized by the character "." The number behind the square root sign is referred to as the radicand, whereas the square root symbol itself is known as a radical.

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Answer:

$7.75 per hour

Step-by-step explanation:

10 days x 8 hours = 80 hours

$620/80 hours = $7.75 per hour

Answer:

$7.75 per hour

Step-by-step explanation:

8 x 10 =80

$620=80 hours

÷80 ÷80

$7.75=1 hour

The equation is PV = nRT.

The calculations for the ideal gas law are comparison of the Pressure and Volume of gas based upon amount and temperature.

The basic formula is PV = nRT where

P = Pressure in atmospheres (atm)

V = Volume in Liters (L)

n = number of moles (mol)

R = the Ideal Gas Law Constant

T = Temperature in Kelvin (K)

The value of n is the amount of the gas measured as moles.

One may need to convert a mass to moles by dividing the given mass of the gas by the molar mass of the gas to get moles.

Hence, The equation is PV = nRT.

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In order to add these numbers, first let's write all of them with the same number of decimal places:

17.34 = 17.340

8.03 = 8.030

0.009 = 0.009.

Then, let's add all algarisms that are in the same position in each number:

0 + 0 + 9 = 9

4 + 3 + 0 = 7

3 + 0 + 0 = 3

7 + 8 + 0 = 15 (5 plus 1 to next algarism)

1 + 0 + 0 (+ 1) = 2

So the final result is 25.379.

The tax on the chair is $7.50.

A tax is a mandatory financial charge or other sort of levy imposed by a governmental entity on a taxpayer in order to fund government spending and related public expenses.

The tax rate is the ratio at which a firm or individual is taxed in a tax system. A tax rate can be presented in numerous ways: statutory, average, marginal, and effective.

Let the cost of the chair be $150 and the assumed tax rate be 5%.

In this case, the tax on the chair will be:

= Tax rate × Cost of chair

= 5% × $150

= 0.05 × $150

= $7.50

Note that an overview was given as the information is incomplete.

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the original weight is 190 pounds

the new weight is 160 pounds

so the percentage of weight loss is

so she loss 15.78 per cent of the weight.

Step 1

State the formula for the area of a trapezoid

Step 2

Find the height

Hence, the height = 5m

Answer:

50 is next to 70 ,_(60) with the rest

Step-by-step explanation:

(50)_(60)+(70)

First item= $159.55

Chair= $49.75

Cubes= $29.87

Lamp= $19.78

Rounding the individual cost to the nearest $10, we get:

First item= $160

Chair= $50

Cubes= $30

Lamp= $20

The total cost will be:

$160+$50+$30+$20= $260.

The answer is: $ 260.

If the average number of babies born at a private hospital's maternity wing is 6 per hour. The probability that three babies are born during a particular 1-hour period in this maternity wing is 0.09.

Mean = 6 per hours

Number of babies = 3 babies

Hence,

Now let determine the probability

Let x represent the probability

Pr(X=3) = e^-6 × 6^3 ÷ 3!

Pr(X=3) =0 .535410 ÷ 6

Pr(X=3) = 0.089

Pr(X=3) =0.09 (Approximately)

Therefore we can conclude that 0.09 is the probability.

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EXPLANATION

Given the expression 12(3y+x).

Let's solve it:

Applying the distributive property:

12*3y + 12*x

Multiplying like terms:

36y + 12x

The answer is 36y + 12x

Question: what are the factors of the expression:

Solution:

Let the expression

If we apply the quadratic equation:

we get the zero of the polynomial

which is -1. Thus the polynomial can be factored in the following way

then, we can conclude that the factors of the given polynomial are:

(x+1) and (x+1)

Answer:

B

Step-by-step explanation:

4x + 2 = 22 ( subtract 2 from both sides )

4x = 20 ( divide both sides by 4 )

x = 5