Graph the feasible region and find the values of x and y that give the maximum possible value of g=8x+12y subject to the following constraints.

Carlos can expect the value of the computer to be $580 three years after purchase.

To model the value of the computer, we can use the formula:

y = abˣ

We know that the initial value of the computer is $1,350, so a = 1350.

We also know that one year after purchase, the value of the computer is $810, so we can use this to find the value of b:

810 = 1350b

b= 0.6

b = 0.6

So our exponential equation is:

y = 1350(0.6)ˣ

To find the value of the computer 3 years after purchase, we can substitute x = 3:

y = 1350(0.6)³

y = 583

Hence, Carlos can expect the value of the computer to be $580 three years after purchase.

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Answer:

14 mins

Step-by-step explanation:

2/6 = x/42

6x=84

x=14

For the given right-angled triangle the measure of the angle is 11.30°.

Given adjacent base of the triangle =  10

given opposite side of the triangle = 2

To find out the angle we can use a little bit of trigonometry. By trigonometry, we know that tan ∠ = opposite side / adjacent side.

So, we can use the above tan ∠ relation to find the angle.

Tan ∠ = opposite side / adjacent side

Tan ∠ = 2/10

Tan ∠ = 1/5

∠ = Tan⁻¹(1/5)

∠ = 11.30°.

From the above explanation, we can conclude that the measure of the angle for the given right triangle is 11.30°.

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Without knowing the exact number of turtles in 2005, we cannot determine the exact number of turtles in 2010. However, we can use the information given to set up an equation.

Let x be the number of sea turtles in 2005.

According to the problem, the number of sea turtles in 2010 was twice the amount in 2005, or 2x.

We can set up an equation:

2x = number of sea turtles in 2010

We don't know the exact value of x, so we cannot solve for the number of turtles in 2010.

Answer:

The yellow region is 13.73 cm squared

Step-by-step explanation:

---

Area of square:

[tex]8 * 8 = 64 cm^2[/tex]

Area of the 4 quarter-circles:

[tex]4(\pi r^2)/4[/tex]

The fours cancel each other, we are left with:

[tex]\pi r^2[/tex]

r = 4, so substitute that, we get:

[tex]\pi 4^2 = 16 \pi cm^2[/tex]

Which can be approximated to 50.27 cm squared

Subtract the area of the circle from the square:

[tex]64 - 50.27 = 13.73 cm^2[/tex]

So the area of the yellow region is 13.73 cm squared

The surface area of the shape will be 46 yards².

Surface area refers to the total area that the surface of a three-dimensional object covers. It is measured in square units, such as square meters (m²), square centimeters (cm²), square feet (ft²), etc.

The formula for the surface area of the 2 bases is just b*h

12*8=96 yd²

Finding the lateral area:

(10*10)+(10*10)+(12*10)=

100+100+120=

320 yd²

Add the lateral surface area and the surface area of the 2 bases for the total surface area:

320+96=416 yd²

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Answer:

The graph will be a circle with center (0, 2) and radius 6.

Answer:

see below

Step-by-step explanation:

The Reason for #1 is literally GIVEN to you.

Statement #2: Since the Base Angles of an isosceles triangle are congruent, this statement should be ∠CAB≅∠CBA.

Reason #3: Notice that the statement repeats itself (AB=AB). This demonstrates the REFLEXIVE property.

Reason #4: (Clue) Note which items have been Given or Proven congruent and use it as the triangle congruence property. It helps to actually mark them. Your choices are SSS, SAS, ASA, and AAS.

Reason #5: (Clue) Since the triangles of which AM and BN are of part are now proven congruent, these Corresponding Parts are Congruent as well.

The piecewise function is

f(x) = { x -3 , x≤3

             8, -3 < x ≤ 5

           x+10, x>6

For values less than or equal to -3, we have a line with a positive slope. We have two lines, y = x - 2, and y = x - 3.

1. For y = x - 2

-5 = -3 - 2= -5

2. For y = x - 3

-5 = -3-3 = -6

The fact that the domain is specified for x less than -3  further demonstrates that the first choice is not an option.

Additionally, we know that the function's value is equal to 8 for the range from x greater than -3 to less than or equal to 5.

Additionally, the equation is given as y = -x + 10 and the line has a negative slope for values greater than 6.

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There are possible 4,782,969 different telephone numbers.

We will multiply the number of options for each digit to calculate the total number of possible telephone numbers,.

Using the multiplication principle to estimate the number of possible telephone numbers for each digit:  

n1 x n2 x n3 x ... x nk

Here:

the first three digits are fixed: 011

The 4th digit (the first digit of the local phone number) can be any digit from 1 - 9 (i.e. 9 options).

The remaining 6 digits (the second to seventh digit of the local phone number) can be any digit from 0 to 9, except 0 (9 options for each digit).

Therefore, the total number of possible telephone numbers:

9 x 9 x 9 x 9 x 9 x 9 x 9 = 4,782,969,

Therefore, 4,782,969 different telephone numbers are possible.

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Answer: The least common multiple is (x−5) (x−5)

Step-by-step explanation:

The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.

Answer: ≅ $0.02

Step-by-step explanation:

First, lets find the area of the large triangle

0.5 x 14 x 11 = 77 mm^2

Next lets find the area of the middle rectangle:

4 x 14 = 56 mm^2

Last lets find the area of the small triange:

0.5 x 14 x 3 = 21 mm^2

So the total area is: 77 + 56 + 21 = 154 mm^2

the total cost is given to be: 1.52 + 0.42 + 0.92 = $2.86

dividing the cost by the area to find the cost/mm:

2.86/154 ≅ $0.02

Answer:  C, yes

Step-by-step explanation:

Again you have do the same thing to both sides

They added 1 to both sides

Answer is C , yes they are same

Answer:

The expression $11.75x + $20 represents the total price for the order, including delivery to the school.

In this expression, 'x' represents the number of boxes of paints being purchased, and $11.75 represents the cost of each box. The term $11.75x represents the total cost of the boxes of paints based on the number of boxes being purchased.

The term $20 represents the delivery cost to the school, which is added to the total cost of the boxes of paints.

By multiplying the cost per box ($11.75) by the number of boxes (x) and adding the delivery cost ($20), you can calculate the total price for the order, including delivery.

The wrestler's weight at the first match will be 152.1 pounds. The solution has been obtained by using the substitution method.

What is the substitution method?

The substitution method is a strategy used in algebra to solve simultaneous linear equations. In this process, as the name suggests, the value of one variable from one equation is swapped in the second equation.

We are given that the given situation can be modeled by the equation

y = −1.1x + 162.

Now, we need to find weight at the first match which is 9 weeks away.

So, we get that x = 9.

By substituting this value in the equation, we get

⇒ y = -1.1 (9) + 162

⇒ y = -9.9 + 162

⇒ y = 152.1

Hence, the wrestler's weight at the first match will be 152.1 pounds.

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Answer:

12.8

Step-by-step explanation:

Quotient means the answer of two things divided.

62.72/4.9=12.8

Answer:

25$ if the tickets were involved it would be 70$

Santiago would have to pay $87 in total if he bought 6 snacks for everyone to share. The cost increases to $60 + 4.5*x when a variable number of snacks, represented by x, are bought.

The topic of this question is

Mathematics

, specifically about using multiplication and addition in problem-solving.

Firstly, Santiago is going to see a movie with his 3 kids. Therefore, he needs to buy 4 tickets. If each ticket costs $15, then the total cost for movie tickets will be 4 * 15 = $60.

Secondly, if Santiago buys 6 snacks for everybody to share with each snack costing $4.50, the total cost for snacks will be 6 * 4.5 = $27. The total money Santiago would have to pay for his family would then be the sum of the costs of the tickets and snacks, which is 60 + 27 = $87.

Regarding the case when Santiago bought x snacks for everybody to share, the total cost would become 60 + 4.5*x. This formula gives the total cost based on the given number of snacks.

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Answer:

2 (n - 3) (n - 6)

Step-by-step explanation:

[tex]-7n+5n^2+6-3n^2-11n+30[/tex]

Group like terms and combine...

[tex]2n^2-18n+36[/tex]

Observe that all terms contain a factor of 2.  Factor out a 2...

[tex]2(n^2-9n+18)[/tex]

The leading coefficient is 1.  The shortcut applies.  Find the factors of "c" (18)

Of these factor pairs, -3 & -6 will multiply to make 18, and add to make -9 (the "b").

Finish factoring the trinomial into two binomials:

[tex]2(n-3)(n-6)[/tex]

To verify that this is a valid factoring, distribute, and recombine terms:

[tex]2(n-3)(n-6)[/tex]

[tex]2(n^2-3n-6n+18)[/tex]

[tex]2(n^2-9n+18)[/tex]

Based on an exponential decay factor, Michael's stereo equipment will be worth $2,116 after 8 years, given the decreasing rate of 9% per year.

The decay factor is represented by (1 - r), where r is the constant periodic decreasing rate.

The decay factor is used in exponential decay functions to determine the depreciated value of an asset.

Current price of stereo equipment = $2,500

Annual decreasing rate = 9%

Decrease factor = 0.91 (100% - 9%)

The number of years = 8 years

Value of the equipment after 8 years = ($2,500 x 0.91^8)

= $2,116.125 ($2,500 x 0.47025)

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The price of the bed after mark up is $475.00

Discount results in the reduction of the selling price of the product, which makes it more attractive for the customer.

The first discount given is 25% , therefore the price of the bed before mark up is

25/100 × 800

= 25×8

= 200

the price before mark up = 800-200 = $600

Another 25% is given after the first sale, there the price of the bed after mark up is

25/100 × 600

=$ 125

price after markup = 600-125

= $475.00

therefore the price of the bed after markup is $475.00

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Looking at the information provided, we can guess the triangle is similar to the one attached.

Therefore the area of the joint triangle is 40.825 unit²

a = b = 3 is the side lengths of the equilateral triangle c = 5 is the side length shared by both triangles = 12 which is the base of the right triangled = 13 which is the hypotenuse of the right triangle

The height of the equilateral triangle is 4.33 units.

Looking at this information, we solve for the area of the  equilateral triangle;

Area = (base × height) / 2 (5 × 4.33) / 2= 10.825

Area = (base × height) / 2

Area of the right angle triangle = (12 × 5) / 2 = 30

The total area 10.825 + 30 = 40.825

The above answer is partly based on the figure provided in the image. The numbers used were the ones provided by you, except for the height of the equilateral triangle.

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Looking at the information provided, we can guess the triangle is similar to the one attached. Therefore the area of the joint triangle is 40.825 unit²

a = b = 3 is the side lengths of the equilateral triangle

c = 5 shared by both triangles

12 = the base of the right triangle

13 = the hypotenuse of the right triangle

4.33 = height of the equilateral triangle

To solve the total area, we say

Triangle 1

Area = (base × height) / 2

(5 × 4.33) / 2= 10.825

Triangle 2

Area = (base × height) / 2

Area of the right angle triangle = (12 × 5) / 2 = 30

The total area ∴ 10.825 + 30 = 40.825

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(a) The two dots on the graph at 53 represent two different samples of size 40 that both had a range of 53.

(b) No, the simulation does not provide evidence that the sample range is a biased estimator of the population.

Range is a statistical measure that refers to the difference between the highest and lowest values in a set of data. In other words, it is the distance between the largest and smallest values in a dataset.

(a) The two dots on the graph at 53 represent two different samples of size 40 that both had a range of 53.

(b) No, the simulation does not provide evidence that the sample range is a biased estimator of the population. A biased estimator systematically overestimates or underestimates the population parameter of interest. The fact that the distribution of sample ranges is approximately symmetric and centered around the true population range suggests that the sample range is an unbiased estimator of the population range. However, the variability of the sample range is quite large, which means that a single sample range may not be a very precise estimate of the population range.

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Answer: No, 2^7 is not equal to 2x7.

2^7 means 2 raised to the power of 7, which is 2 multiplied by itself 7 times:

2^7 = 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128

On the other hand, 2x7 means 2 multiplied by 7:

2x7 = 2 x 7 = 14

So 2^7 is not equal to 2x7.

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

See, 2 ^ 7 is 2 TO THE POWER OF 7, which is repeated multiplication.

2 x 7 is 2 MULTIPLIED BY 7

2 ^ 7 written out completely is:

2 * 2 * 2 * 2 * 2 * 2 * 2 = 128

See the repeated multiplication above?

2 x 7 is just 14.

See the difference!

14 is NOT equal to 128

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The car will be worth half its original value after 4 years

A graph for straight-line depreciation for a car is given.

a

The number of years the car totally depreciates is 8 years as seen in the graph which is x -intercept.

Step 3/7

The model makes straight-line depreciation. In a straight line depreciation equation, the intercepts are

(0, maximum car value) and (maximum lifespan,0)

Let y represent the value of the car at any time during its lifetime. The minimum y -value is zero dollars and the maximum y -value is the purchase price of $25,600

The intercepts are (0, 25, 600) and (8,0)

Determine the slope of the equation.

Two points determine a line, so only two points are needed to determine the slope of a line.

Let the coordinates of the -intercept be the first point. That is, (xi,yi) = (0, 25, 600)

Let the coordinates of the -intercept be the second point. That is (x2, y2)= (8,0)

Use the slope ratio as shown below;

The slope of the depreciation equation is.

-3200

The general form for the equation of a straight line is:

y = mx + b

Where m represents the slope of the line and b represents the y-intercept.

The slope is -3,200 and the -intercept is 25,600 as obtained.

Therefore, the straight line depreciation equation is:

y = -3,200x + 25,600

Therefore, the value of the car after 4 years is $12,800

b.

Use the depreciation equation and substitute x=5 years to find the car worth after 5 years.

Therefore, the value of the car after 5 years is $9,600

c.

The half value of the car is half of $25,600 which is $12,800

The car will be worth half its original value after 4 years

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The ratio of 8 : 1/3 is equivalent to the simplified ratio of 24 : 1.

To analyze and describe the ratio 8 : 1/3, we need to convert the fraction to a ratio with a whole number. One way to do this is to express the fraction as a ratio with a denominator of 3:

1/3 = 1:3

Now we can rewrite the ratio 8 : 1/3 as:

8 : 1:3

We can simplify this ratio by multiplying both terms by 3 to get rid of the fractional term:

8 × 3 : 1:3 × 3

24 : 1

Therefore, the ratio 8 : 1/3 is equivalent to the simplified ratio 24 : 1. This means that for every unit in the second part of the ratio, there are 24 units in the first part of the ratio. In other words, the first part of the ratio is 24 times larger than the second part.

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Answer:

Words of the Devil, by Parau na te Varua ino, is a painting that was created in 1892 in French Polynesia. The painting depicts a scene from Tahitian mythology, in which the goddess Hina is visited by the devil, who is represented as a horned figure with a large, forked tongue. The painting is rich in detail and vivid color, with the figures depicted in bright, bold colors that stand out against the darker background.

The style of the painting is characteristic of the Tahitian art of the time, which was heavily influenced by the traditional Polynesian art forms of carving, tattooing, and tapa cloth decoration. The figures in the painting are depicted in a stylized, almost abstract way, with exaggerated features and bold, sweeping lines. The use of bright colors and bold brushstrokes gives the painting a dynamic, almost chaotic energy that reflects the intense emotions of the scene.

Overall, Words of the Devil is a powerful and striking work of art that captures the mythology and cultural traditions of French Polynesia in the late 19th century.

The interquartile range of the data will be 0.215.

The lower half is:

7.86, 7.87, 7.99, 8.03

The median of the lower half is:

(Q1) = (7.87 + 7.99) / 2 = 7.93

The upper half is:

8.06, 8.08, 8.09, 8.20, 8.43

The median of the upper half is:

(Q3) = (8.09 + 8.20) / 2 = 8.145

The IQR is the difference between the third and first quartiles:

IQR = Q3 - Q1 = 8.145 - 7.93 = 0.215

Lower outlier threshold: Q1 - 1.5 x IQR = 7.93 - 1.5 x 0.215 = 7.5955

Upper outlier threshold: Q3 + 1.5 x IQR = 8.145 + 1.5 x 0.215 = 8.4795

None of the data points fall outside these thresholds, so there are no outliers in this data set.

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Using multiplication operation, the amount of pension that Edith will receive after 4 years of service and using the vesting percentage and the pension multiplier is $49,725.

The pension amount is the product of the multiplication of the average salary, the vesting percentage and the pension multiplier factor.

Multiplication operation is one of the four basic mathematical operations, including addition, subtraction, and division.

Edith's average salary = $65,000

The number of years of service = 4 years

Pension Multiplier = 2%

Pension multiplier factor = 1.02 (100% + 2%)

Vesting percentage = 75%

Pension to be received = $49,725 ($65,000 x 75% x 1.02)

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