The management of the UNICO department store has decided to enclose a 903 ft2 area outside the building for displaying potted plants and flowers. One side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing. If the pine board fencing costs $7/running foot and the steel fencing costs $4/running foot, determine the dimensions of the enclosure that can be erected at minimum cost.

Solving an Equation

We are given the equation:

The first step is to multiply the constants by the binomials in parentheses:

This step was correctly done by Jose.

The second step is to 'pass' the 4x from the right side of the equation to the left by adding 4x on both sides:

This step was also correct.

Now we must 'pass' 15 to the right by subtracting 15:

And here we find the first error. Jose subtracted 15-20 instead of 20-15 and erroneously got -5.

Answer: First error in step 3

The dimensions of the rectangle are L=10in, B=5in

A rectangle includes everything listed below:

Your polygon's four sides must be two congruent pairings in order to have two pairs of parallel sides. The length of the left and right sides, as well as the base and top, will be equal.

let width of rectangle be x, then length will be

B=5+x

given area of rectangle

A=50in²

area = length×width

A=L×B

50 = x×(5+x)

50=5x+x²

x²+5x-50=0

x²+10x-5x-50=0

x(x+10)-5(x+10)=0

x=-10 or x=5

since x=-10 is not possible

therefore, x=5

Length(L)=5+5=10in

Width(B) = 5in

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Step 1

There are 18,652 geese on a lake

Required: To round this off to the ten thousand place

Step 2

Hence, we will approximate the thousands and add its value to the ten thousand.

Step 3

The mechanic rounds the weight of the car to the nearest thousand and gets 4000 lb.

Using the rule below;

Therefore,

Therefore,

Slope-intercept format is represented by the following expression:

Then to rewrite it, we need to isolate the variable y, using inverse operations to solve equations:

Solution

Step 1

Two lines are perpendicular if the product of their slope = -1

Step 2

Step 2

Answer:

180

Step-by-step explanation:

So, in the first 4 games, they score 10 points. If this continues to happen in the remaining 18 games, it would be 180.

             10 x 18 = 180.

Part a: The people can arrive in 5040 ways

Part b: In 120 ways, Jim can arrive first and Kim last

Part c: The probability that Jim will arrive first and Kim last is 1/42

People invited to the party: Jim, Eduardo, Larry, Simone, Ian, Dawn, Tyrone, and Kim

Part a:

Since there are 7 people, the number of ways they can arrive is 7*6*5*4*3*2*1 =.5040 ways

Part b:

For Jim to arrive first and Kim last:

The remaining 5 people can arrive in any order so, the number of ways in which they can arrive is 5*4*3*2*1 = 120 ways

Part c:

The probability that Jim will arrive first and Kim last is given by:

Number of ways Jim can arrive first and Kim last/ Total number of ways in which all the people can arrive at the party

= 120/5040 = 1/42

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Answer:

f(x) = x^4

Step-by-step explanation:

h(x) = f(g(x)) = (x - 2)^4

g(x) = x - 2

h(x) = f(g(x)) = (g(x))^4

f(x) = x^4

In any equation in math, the most basic thing is the the fact that both expressions on either side of the equality sign are of the same value. This means -35 and 5b (in number 1) are of the same value. Therefore, whatever you do to the one on the left, you must likewise do to the one on the right. That is, if you have to add 10 to the one on the left, you must simultaneously add 10 to the one on the right. Hence, number 1 is solved as follows;

(1) -35 = 5b

To eliminate the 5 and isolate the b variable, divide both sides by 5

-35/5 = 5b/5

- 7 = b

(2) x - 6 = - 26

Add 6 to both sides of the equation;

x - 6 + 6 = - 26 + 6

x = - 20

(3) 130 = 13b

Divide both sides of the equation by 13

130/13 = 13b/13

10 = b

(4) 19 = 16 + m

Subtract 16 from both sides of the equation

19 - 16 = 16 - 16 + m

3 = m

(5) a + 15 = 11

Subtract 15 from both sides of the equation

a + 15 - 15 = 11 - 15

a = - 4

(6) p - 8 = - 8

Add 8 to both sides of the equation

p - 8 + 8 = - 8 + 8

p = 0

(7) - 17 + x = - 24

Add 17 to both sides of the equation

- 17 + 17 + x = - 24 + 17

x = - 7

(8) 4 + n = 13

Subtract 4 from both sides of the equation

4 - 4 + n = 13 - 4

n = 9

(9) - 3x = 0

Divide both sides of the equation by - 3

- 3x/-3 = 0/-3

x = 0

(10) 0.6 = m - 0.8

Add 0.8 to both sides of the equation

0.6 + 0.8 = m - 0.8 + 0.8

1.4 = m

(11) x - 5.3 = 1.27

Add 5.3 to both sides of the equation

x - 5.3 + 5.3 = 1.27 + 5.3

x = 6.57

Answer:

Step-by-step explanation:

18.5

Answer:

18.5

Step-by-step explanation:

PEMDAS (parenthesis, exponents, multiplication, division, addition, subtraction)

(8+7)+(3.5)

(15)+(3.5)

18.5

The correct answer is:

Mei statement that the inequality is -9 < -3 is True.

Mei is correct because -9 is to the left of -3 on the number line. ( first option in the picture).

Answer:

Step-by-step explanation:

The solution for the given system of equations, y = [tex]\frac{-1}{2}[/tex]x + 5 and y = 3x - 2 is (2,4) and the graph is attached below

The system of equations is a set of equations consist the same variables. If the given equation are all linear then, it is the system of linear equation.

To solve such system, it is required to figure out the variable values that can solve all the equations involved in the system.

For the given system of equation the variable value is x.

So,  [tex]\frac{-1}{2}[/tex]x + 5  = 3x - 2

2 + 5 = 3x + [tex]\frac{x}{2}[/tex]

7 = x ([tex]\frac{6+1}{2}[/tex]) = [tex]\frac{7x}{2}[/tex]

x = 2

Now apply the obtained value of x in either of the equations:

y = 3x - 2

y = 6 - 2

y = 4

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Answer: i believe its 0.46 im not for sure though

Step-by-step explanation:

The volume of the silo with given height and diameter is 4374π ft or 13734.36 ft. (approximately).

What is volume?

Volume is a measurement of 3-D space that is occupied. Numerous imperial units or SI-derived units, such as the cubic meter and liter, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship. The volume of a container is typically thought of as its capacity, not as the amount of space it takes up.

Given in the question,

The diameter of the cylindrical silo is 18 ft,

and its height is 54 ft.

Volume of a cylinder can be calculated using the formula:

[tex]V = \pi r^2 h[/tex]

Here, V = volume, r = radius, h = height,

We know that, radius is half of diameter. So, radius = 18/2 = 9 ft

Putting the given value in the formula:

[tex]V = \pi 9^2 \times 54[/tex]

[tex]V = \pi \times 81 \times 54[/tex]

V = 4374π ft.

Putting the value of π as 3.14 (approximately)

So, volume of the silo becomes 13734.36 ft.

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The order of the numbers from lowest to highest is 4.68 × 10⁻⁶,  8.34 × 10⁻², 1.2  × 10⁷, 3.24 × 10⁹ and  5.48  × 10⁹

The given numbers are expressed in standard form. Standard form is a way of writing numbers as a power 10 e.g 100 = 1 × 10² and 0.01 = 1 × 10⁻².

So converting the numbers back to ordinary numbers will be useful.

To do this, we will multiply or divide the powers of 10 with the decimal numbers.

We will multiply if the power is positive e.g 2.4 x 10² = 2.4 x 100 = 240 and divide if the power is negative  2.4 x 10⁻² = 2.4/100 = 0.024

3.24 × 10⁹  = 3.24 x 1000,000,000 =  3240000000

4.68 × 10⁻⁶ = 4.68 / 1000000 = 0.00000468

5.48  × 10⁹ = 5480000000

8.34 × 10⁻² = 8.34/100 = 0.0834

1.2  × 10⁷ = 12000000

Therefore, arranging from lowest to highest. We have:

4.68 × 10⁻⁶,   8.34 × 10⁻², 1.2  × 10⁷, 3.24 × 10⁹ and  5.48  × 10⁹

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1)  A number that is divided by 5, with the result as 50 less than if the number had been divided by 6 is; -1500

2) If both turtles survive until then, the number of years from today that the older turtle's age would be 3 times that of the younger turtle is; 146 years

1) Let the number be x. We are told that it is divided by 5, and the result is 50 less than if the number had been divided by 6. Thus, we have;

(x/6) - (x/5) = 50

Multiply through by 30 to get;

5x - 6x = 1500

-x = 1500

x = -1500

2) Let the older turtle be x and the younger one be y.

Today, the older turtle's age is 11 times that of the younger turtle. Thus;

Todays age;

Older turtle = 11y years

Younger turtle = y years

In 24 years, the older turtle's age will only be 7 times that of the younger turtle. Thus;

11y + 24 = 7(y + 24)

11y + 24 = 7y + 168

11y - 7y = 168 - 24

4y = 144

y = 144/4

y = 36

Thus;

Age of older turtle today = 11 * 36 = 396 years

Age of younger turtle today = 36 years

Thus, for older turtle to be thrice the age of younger turtle, then;

3(36 + t) = 396 + t

108 + 3t = 396 + t

2t = 292

t = 292/2

t = 146 years

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Given

To find the interval.

Explanation:

It is given that,

That implies,

a) The interval notation is, (-7,-5).

b) The interval notation is, [-6,6].

c) The interval notation is, (-7,-1).

d) The interval notation is, [5,7].

e) The interval notation is, [-2,-1).

Answer:

ez

Step-by-step explanation:

ezz

If the full-time year-round median salary for U.S. men in 2010 was $42,600. The​ full-time year-round median salary for U.S. men in 2010 was 121% of the​ full-time year-round median salary for U.S. women in 2010.

Using this formula

Median salary percentage = 2010 Median salary in US men / 2010 Median salary in US women

Let plug in the formula

Median salary percentage = $42,500 / $35,000

Median salary percentage = 1.2143 × 100

Median salary percentage = 121.43%

Median salary percentage = 121% (Approximately)

Therefore median salary for men in 2010 was 121% of  median salary for  women in 2010.

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To determine if a function is even or odd, we start from its definition.

While for an EVEN FUNCTION we have: F(x) = F(-X), for an ODD FUNCTION we have F(-X) = -F(X)

Now, from this, we can check that all the values the function achiever for any X value, the -X has same height. The function presents a symmetry over the Y-axis, and this implies in a function to be an EVEN FUNCTION.

And from the solution developed above, the only statement that is true is the

C) The function is an even function.

ANSWER

x = 38

EXPLANATION

To solve this equation, first, we have to apply the distributive property of multiplication over addition to eliminate the parenthesis,

Subtract 3x from both sides of the equation,

And add 8 to both sides,

Hence, the solution is x = 38.

Answer:

11.34 m³

Explanation:

The volume of a right rectangular prism can be calculated as:

So, replacing the height by 3.6 m, the length by 2.1 m, and the width by 1.5m, we get:

Therefore, the volume of the prism is 11.34 m³

8/9 - 1/3

To subtract these two fractions, first find a common denominator.

The common denominator will be the

least common multiple for the two denominators.

In this case, the least common multiple of 9 and 3 is 9.

So to subtract, a denominator of 9 is needed in each fraction.

8/9 already has 9 in the denominator so it stays the same.

To get a 9 in the denominator of 1/3, multiply top and bottom by 3.

This gives us 3/9.

So we have 8/9 - 3/9 which is 5/9.

#7777

(b) To determine the year the population will reach 1,200,000, substitute p(t) = 1,200,000 into p(t) above and calculate the value of t

The year when t= 8, given that t=0 in 2014 is the year 2022

(c) the rate of change of the population in the year 2019

Firstly, differentiate p(t) with respect to t

In the year 2019, t = 5

Substitute t=5 into the rate of change above

K (5 * 3)

K * 15

15K

The answer is 15K based on the information available. I asked the student twice if he has more details about this exercise but he become unresponsive.

Hope that this is the answer to the actual exercise.

Closing the session.

Answer:

2

Step-by-step explanation:

If you have 1 cookie and someone gives you another cookie you now have 2.

The teammates are 15 but 6 of them do not want the photo, so the number of the teammates who wants the photo is 15 - 6.

Now, each photo cost $2 adn the number of photo is equal to the number of teammates who wants the photo which is (15-6), so the expression for the total cost is:

We have to multiply the cost of each photo for the number of photo Greta will buy.

The zeros of the function are x = 3 and x = -3

The equation of the function is given as

f(x) = x(squared) - 9

Rewrite the equation properly

So, we have the following equation

f(x) = x^2 - 9

Express the equation as a difference of two squares

So, we have the following equation

f(x) = (x - 3)(x + 3)

Set the equation to 0

(x - 3)(x + 3) = 0

Split

x - 3 = 0 and x + 3 = 0

Solve for x

x = 3 and x = -3

Hence, the solutions are -3 and 3

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We want to find the diagonal length of the square given in the question.

Since this shape is a square, all four sides are of equal length. Therefore, each side of the square must be [tex]1[/tex] unit.

Next, we will use the Pythagorean Theorem to find the length of the hypotenuse of a right triangle. This value is also equal to the length of our diagonal. We can find the length of the diagonal using the formula below;

Therefore, the correct answer to our question is the following equality;

Second option should be the answer.