tank a starts with 340 liters of water. it has a leak and is losing water at a rate of 5 liters of water per minute. at the same time, tank b starts with 500 liters of water and also has a leak. it is losing water at a rate of 9 liters per minute. the variable t represents the time in minutes. after how many minutes will the two tanks have the same amount of water? how much water will be in the tanks at that time?

The correct answer is $56,000.the total profit for Pinewood Furniture Company, considering only the production of 200 chairs and 400 tables

To determine the total profit for Pinewood Furniture Company, we need to calculate the profit generated from producing 200 chairs and 400 tables.

Each chair generates a profit of $80, and if 200 chairs are produced, the total profit from chairs would be:

200 chairs * $80/profit per chair = $16,000.

Similarly, each table generates a profit of $100, and if 400 tables are produced, the total profit from tables would be:

400 tables * $100/profit per table = $40,000.

Therefore, the total profit for Pinewood Furniture Company, considering only the production of 200 chairs and 400 tables, would be:

$16,000 (profit from chairs) + $40,000 (profit from tables) = $56,000.

Hence, the correct answer is $56,000.

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Answer:

8.8%

Step-by-step explanation:

We first divide the new amount by the original and close it with brackets.

Our one year will be shown as 1/1 as an indices

(761.60/700)^1/1

= 1.088

We then convert it to 0.088 and times it by 100.

0.088×100= 8.8% Compound interest rate.

This is correct as:

700×1.088= 761.6

Have a nice day! :)

\(m = \frac{ - 1}{a} = \frac{ - 1}{2} \\ y = \frac{ - 1}{2} x + b\)

Since we are looking for the greatest integer solution, we take the largest integer value that satisfies this inequality, which is x = 0. Therefore, the greatest integer solution of the inequality |2x + 3| - 4 ≤ 0 is x = 0.

First, we isolate the absolute value expression by adding 4 to both sides of the inequality:

|2x + 3| ≤ 4.

Next, we split the inequality into two separate cases based on the sign of the expression inside the absolute value:

1. When 2x + 3 is nonnegative (i.e., 2x + 3 ≥ 0):

  In this case, the inequality simplifies to 2x + 3 - 4 ≤ 0, which gives 2x - 1 ≤ 0. Solving this inequality, we find x ≤ 1/2.

2. When 2x + 3 is negative (i.e., 2x + 3 < 0):

  In this case, the inequality simplifies to -(2x + 3) - 4 ≤ 0, which gives -2x - 7 ≤ 0. Solving this inequality, we find x ≥ -7/2.

Combining both cases, we have the solution: -7/2 ≤ x ≤ 1/2.

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soln

=5×17

=85 is answer

If the company wants to keep its production costs under $175,000, then  5.6 ≤ x ≤ 24.13 constraint is reasonable for the model given that the function C(x) = −0.74x² + 22x + 75 ,the production cost C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands. This can be obtained by using the given graph of the function.

A constraint is a condition of an optimization problem that should be satisfied the condition.

From the we have the function,

⇒ C(x) = −0.74x² + 22x + 75

the production cost C, in thousands of dollars for a tech company to manufacture a calculator, x is the number of calculators produced, in thousands.

In the graph the dotted line is the line where C(x) is $175,000. Above this line every the value is greater than $175,000.

The points where this line, that is C(x) = y = 175, intersect the graph of the given function C(x) = −0.74x² + 22x + 75 is (5.6, 175) and (24.13, 175).

Therefore, x ≥ 5.6 and x ≤ 24.13  

⇒ 5.6 ≤ x ≤ 24.13

Hence if the company wants to keep its production costs under $175,000, then  5.6 ≤ x ≤ 24.13 constraint is reasonable for the model given that the function C(x) = −0.74x² + 22x + 75 ,the production cost C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands.

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Answer:

0 ≤ x < 5.6 and 24.13 < x ≤ 32.82

Step-by-step explanation:

Answer:

\(Area_{kite}=736m^2\)

Step-by-step explanation:

There are a few methods to find the area of this figure:

1. kite area formula

2. 2 triangles (one top, one bottom)

3. 2 triangles (one left, one right)

4. 4 separate right triangles.

Recall the formula for area of a kite:  \(Area_{kite}=\frac{1}{2} d_{1}d_{2}\) where d1 and d2 are the lengths of the diagonals of the kite ("diagonals" are segments that connect non-adjacent vertices -- in a quadrilateral, vertices that are across from each other).

If you've forgotten why that is the formula for the area of a kite, observe the attached diagram: note that the kite (shaded in) is half of the area of the rectangle that surrounds the kite (visualize the 4 smaller rectangles, and observe that the shaded portion is half of each, and thus the area of the kite is half the area of the large rectangle).

The area of a rectangle is \(Area_{rectangle}=bh\), sometimes written as \(Area_{rectangle}=bh\), where w is the width, and h is the height of the rectangle.

In the diagram, notice that the width and height are each just the diagonals of the kite.  So, the Area of the kite is half of the area of that surrounding rectangle ... the rectangle with sides the lengths of the kite's diagonals.Hence, \(Area_{kite}=\frac{1}{2} d_{1}d_{2}\)

For our situation, each of the diagonals is already broken up into two parts from the intersection of the diagonals.  To find the full length of the diagonal, add each part together:

For the horizontal diagonal (which I'll call d1): \(d_{1}=40m+6m=46m\)

For the vertical diagonal (which I'll call d2): \(d_{2}=16m+16m=32m\)

Substituting back into the formula for the area of a kite:

\(Area_{kite}=\frac{1}{2} d_{1}d_{2}\\Area_{kite}=\frac{1}{2} (46m)(32m)\\Area_{kite}=736m^2\)

If one doesn't remember the formula for the area of a kite, and can't remember how to build it, the given shape could be visualized as 2 separate triangles, the given shape could be visualized as 2 separate triangles (one on top; one on bottom).

Visualizing it in this way produces two congruent triangles.  Since the upper and lower triangles are congruent, they have the same area, and thus the area of the kite is double the area of the upper triangle.

Recall the formula for area of a triangle:  \(Area_{triangle}=\frac{1}{2} bh\) where b is the base of a triangle, and h is the height of the triangle (length of a perpendicular line segment between a point on the line containing the base, and the non-colinear vertex).  Since all kites have diagonals that are perpendicular to each other (as already indicated in the diagram), the height is already given (16m).

The base of the upper triangle, is the sum of the two segments that compose it:  \(b=40m+6m=46m\)

Finding the Area of the upper triangle\(Area_{\text{upper }triangle}=\frac{1}{2} (46m)(16m) = 368m^2\)

Finding the Area of the kite

\(Area_{kite}=2*(368m^2)\)

\(Area_{kite}=736m^2\)

The given shape could be visualized as 2 separate triangles (one on the left; one on the right).  Each triangle has its own area, and the sum of both triangle areas is the area of the kite.

Note:  In this visualization, the two triangles are not congruent, so it is not possible to  double one of their areas to find the area of the kite.

The base of the left triangle is the vertical line segment the is the vertical diagonal of the kite.  We'll need to add together the two segments that compose it:  \(b=16m+16m=32m\).  This is also the base of the triangle on the right.

Finding the Area of left and right triangles

\(Area_{\text{left }triangle}=\frac{1}{2} (32m)(40m) = 640m^2\)

The base of the right triangle is the same length as the left triangle: \(Area_{\text{right }triangle}=\frac{1}{2} (32m)(6m) = 96m^2\)

Finding the Area of the kite

\(Area_{kite}=(640m^2)+(96m^2)\)

\(Area_{kite}=736m^2\)

If you don't happen to see those composite triangles from option 2 or 3 when you're working this out on a particular problem, the given shape could be visualized as 4 separate right triangles, and we're still given enough information in this problem to solve it this way.

Calculating the area of the 4 right triangles

\(Area_{\text{upper left }triangle}=\frac{1}{2} (40m)(16m) = 320m^2\)

\(Area_{\text{upper right }triangle}=\frac{1}{2} (6m)(16m) = 48m^2\)

\(Area_{\text{lower left }triangle}=\frac{1}{2} (40m)(16m) = 320m^2\)

\(Area_{\text{lower right }triangle}=\frac{1}{2} (6m)(16m) = 48m^2\)

Calculating the area of the kite

\(Area_{kite}=(320m^2)+(48m^2)+(320m^2)+(48m^2)\)

\(Area_{kite}=736m^2\)

Answer:

As x decreases in value.f(x) decreases in value.......

Answer:

C. The cost of mailing 10 pounds of books is twice the cost for 5 pounds of books

Step-by-step explanation:

The equation below shows the formula for calculating the shipping cost, C for book orders,

where p is the weight of the books in pounds. There is a $3 handling fee on every order.

C = $0.75p + $3

Which statement is not true about the cost?

A. The cost for shipping books varies according to the weight of the order.

Yes

C = $0.75p + $3

A change in the weight of books changes the cost for shipping the books

B. The cost of mailing books increases by 0.75 for each additional pound of books.

Yes

C. The cost of mailing 10 pounds of books is twice the cost for 5 pounds of books

C = $0.75p + $3

For 10 pounds

C = $0.75p + $3

= 0.75(10) + 3

= 7.5 + 3

C = $10.5

For 5 pounds

C = $0.75p + $3

= 0.75(5) + 3

= 3.75 + 3

C = $6.75

D. The cost of the handling fee is unrelated to the weight of the books.

C. The cost of mailing 10 pounds of books is twice the cost for 5 pounds of books.

This statement is not true

The circumcenter of a triangle is the point in the plane equidistant from the three vertices of the triangle.

In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius.

Not every polygon has a circumscribed circle. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic.

A related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it, if the circle's center is within the polygon. Every polygon has a unique minimum bounding circle, which may be constructed by a linear time algorithm.

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Answer:

49

Step-by-step explanation:

Complementary angles always add up to 90 degrees, so make and equation. First, say that angle ABC and angle QRS add up to ninety degrees. Substitute the values to get 41 degrees plus angle QRS equals 90 degrees, and once you subtract 41 from both sides, you get angle QRS equals 49 degrees.

Hope this helps. :)

The QRS is 49

We know that

The complementary angles are those whose sum is 90 degrees

So,

x + 41 = 90

x = 49

So, QRS = 49

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Answer:

The correct option is;

f(x) = 64(three-fourths)Superscript x minus 1

Step-by-step explanation:

The first peak height that the bouncing toy reaches = 64 inches

The second peak height that the bouncing toy reaches = 48 inches

The third peak height that the bouncing toy reaches = 36 inches

Therefore, given that the sequence has a common ratio, r = 48/64 = 36/48 = 3/4

The first term of the sequence, a = The first peak height reached = 64

The xth term of the geometric sequence with general form, xth term = ar⁽ˣ⁻¹⁾

The xth term of the geometric sequence, f(x), is therefore, given as follows;

\(f(x) = 64 \times \left(\dfrac{3}{4} \right) ^{(x - 1)}\)

The correct option is;

f(x) = 64(three-fourths)Superscript x minus 1

Step-by-step explanation:

The first peak height that the bouncing toy reaches = 64 inches

The second peak height that the bouncing toy reaches = 48 inches

The third peak height that the bouncing toy reaches = 36 inches

Therefore, given that the sequence has a common ratio, r = 48/64 = 36/48 = 3/4

The first term of the sequence, a = The first peak height reached = 64

The xth term of the geometric sequence with general form, xth term = ar⁽ˣ⁻¹⁾

The xth term of the geometric sequence, f(x), is therefore the correct answer is C

Answer: 2(x-2)=6

Step-by-step explanation: when they say twice, so you make is times 2, then it said the difference of a number which would be a variable, or x, and 2, is 6, so one part is =6, next is the variable -2, so you can use x-2, then in order to multiply everything, you need to make parenthesis. So, it would be x-2=6, but you forgot the parathesis, so 2(x-2)=6

Answer:

x ∈ ( - ∞ , - 8 ) ∪ ( - 8 , 0 ) ∪ ( 0 , 8 ) ∪ ( 8 , ∞ )

Step-by-step explanation:

x³ - 64x = x( x² - 64 ) ≠ 0 ⇒ x ≠ 0 and x ≠ ± 8

x ∈ ( - ∞ , - 8 ) ∪ ( - 8 , 0 ) ∪ ( 0 , 8 ) ∪ ( 8 , ∞ )

Answer:

105%

Step-by-step explanation:

Step 1- divide 21 by 20: 21 ÷ 20 = 1.05

Step 2- multiply the result by 100 and add the percentage sign: 1.05 × 100% = 105%

Answer: 21/20 = 105%

Have a great day! :D

105%

Step-by-step explanation:

Divide 21 by 20

21 ÷ 20 = 1.05

Multiply the result by 100 and add the percentage sign

1.05 x 100% = 105%

Answer: 21/20 = 105%

Hope this helps lovely! <3

Answer:

d). 4(9a - 3b)

Step-by-step explanation:

a). 4(6a-9b)

= 24a - 36b

b). 4(8a-3b)

= 32a - 12b

c). 4(9a+3b)

= 36a + 12b

d). 4(9a - 3b)

= 36a - 12b

Answer:

Step-by-step explanation:

Number of reveloutions made in 1 second = 2

Number of revolutions made in 60 seconds ( 1 minute) = 2*60 = 120

Number of revolutions made in (60 minutes)  1 hour  = 120 *60 = 7200

Circumference of circle =   πd    

                                       \(= \dfrac{22}{7}*70\\\\\\= 22*10\\\\= 220 cm\)

The distance traveled in 1 revoultion = the circumference of the cirlcle

                                                             = 220 cm

The distance travelled in 7200 revoultion = 7200 * 220

                                                                      =1584000 cm

                                                                       = 1584000 ÷ 100000

                                                                       = 15.84 km

                                                                        = 15.8 km

Speed = 15.8 km/h

The correct graph of the system of equations is D) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.

What is the system of equations?

A system of equations is a set of two or more equations with the same variables. The goal of a system of equations is to find the values of the variables that simultaneously satisfy all the equations in the system.

The given equations are

3x + y = 12

x + 4y = 4

To graph the system of equations, we can start by finding the x-intercepts and y-intercepts of each line.

The x-intercept is the point where the line crosses the x-axis, which means that the y-value is 0. To find the x-intercept, we can set y = 0 and solve for x:

3x + y = 12

3x + 0 = 12

3x = 12

x = 4

So, the x-intercept of the first line is (4, 0).

Next, we can find the y-intercept, which is the point where the line crosses the y-axis, meaning that the x-value is 0. To find the y-intercept, we can set x = 0 and solve for y:

3x + y = 12

0 + y = 12

y = 12

So, the y-intercept of the first line is (0, 12).

We can repeat this process for the second line to find its x-intercept and y-intercept:

x + 4y = 4

x + 4 * 0 = 4

x = 4

So, the x-intercept of the second line is (4, 0).

Next, we can find the y-intercept by setting x = 0:

x + 4y = 4

0 + 4y = 4

4y = 4

y = 1

So, the y-intercept of the second line is (0, 1).

Now that we have found the x-intercepts and y-intercepts of each line, we can plot these points on a coordinate plane and draw lines through them to obtain the graph of the system of equations.

The graph shows a line with an x-intercept at (4, 0) and a y-intercept at (0, 12). There is a second line with an x-intercept at (4, 0) and a y-intercept at (0, 1).

Therefore, the correct graph of the system of equations is D) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.

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As a leader, Jui-En tbelieve that he should change his behaviors to match the circumstances because no style works all the time. Jui-En is applying the socialized approach to leadership.

Employee motivation can be boosted by socialization, affirming reward, lead their vision, offer impressive benefits and encourage the temwork.

Employees who socialize who can sosialized in the workplace can increase their work efficiency because its reduce the work pressure by sharing information and teamwork which is important to thriving a company.

So, the correct answer is sosialized.

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The ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is (2, -1).

option C.

The ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is determined as follows;

The four points include;

A = (1, 2)

B = (2, - 3)

C = (-2, - 2)

D = (-3,  1)

The  ordered pair that can be plotted together with these four points, must fall withing these coordinates. Going by this condition we can see that the only option that meet this criteria is;

(2, - 1)

Thus, the ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is (2, -1).

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Answer: 3 weeks

Step-by-step explanation:

We have to note firstly that 12 inches = 1 foot.

The equation given to represent the height in the question, h = 3w + 3.

The number of weeks that it will take the plant to reach one foot will then be:

h = 3w + 3

12 = 3w + 3

3w = 12 - 3

3w = 9

w = 9/3

w = 3

It'll take 3 weeks

Answer:

4 pi

Step-by-step explanation:

diameter = 2r

4 =2r

r =2

area = pi × (r)^2

= pi × 2^2

= 4 pi

Answer:

None of the given options represents an infinite loop.

Step-by-step explanation:

The first option, for (k = 1; k <= 4; k = k - 1), will not execute because the condition k <= 4 will be false initially, and the loop will terminate immediately.

The second option, for (k = 1; k <= 4; k = k 1), will iterate four times, incrementing k by 1 in each iteration, and then terminate.

The third option, for (k = 0; k <= 10; k = k 1), will iterate eleven times, incrementing k by 1 in each iteration, and then terminate.

The fourth option, for (k = 1; k < 3; k = k 1), will iterate twice, incrementing k by 1 in each iteration, and then terminate.

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Answer:

y=1x+13

Step-by-step explanation:

we can plug in the two points into the slope-intercept formula

-7=-20(1)+b

solve for the right side

-7=-20+b

add 20 to both sides

13=b

plug the y intercept into the equation

y=1x+13

A positive integer n and then flip a fair coin n times. you win a prize if you get exactly 2 heads The chance of winning with an optimal choice of n is 0.375 (or 37.5%).

To maximize the chances of winning the game, you need to choose a value for n that maximizes the probability of getting exactly 2 heads in n coin flips.

Let's consider the probability of getting exactly 2 heads in n coin flips. This can be calculated using the binomial probability formula:

P(X = k) = C(n, k) * (0.5)^k * (0.5)^(n-k)

Where:

- P(X = k) is the probability of getting exactly k heads,

- C(n, k) is the number of combinations of n items taken k at a time (n choose k),

- (0.5)^k is the probability of getting k heads,

- (0.5)^(n-k) is the probability of getting (n-k) tails.

To find the values of n that maximize the probability of winning, we can calculate the probability of getting exactly 2 heads for different values of n and compare them.

Let's calculate the probabilities for n = 1, 2, 3, and so on, until we observe a pattern:

For n = 1:

P(X = 2) = C(1, 2) * (0.5)^2 * (0.5)^(1-2) = 0

For n = 2:

P(X = 2) = C(2, 2) * (0.5)^2 * (0.5)^(2-2) = 0.25

For n = 3:

P(X = 2) = C(3, 2) * (0.5)^2 * (0.5)^(3-2) = 0.375

For n = 4:

P(X = 2) = C(4, 2) * (0.5)^2 * (0.5)^(4-2) = 0.375

For n = 5:

P(X = 2) = C(5, 2) * (0.5)^2 * (0.5)^(5-2) = 0.3125

From the above calculations, we can observe that the probabilities of winning increase until n = 3 or n = 4, and then start to decrease.

So, the two equally good choices for the best n are n = 3 and n = 4.

The chance of winning with an optimal choice of n is 0.375 (or 37.5%).

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Answer:

Area of a circle is denoted by: πr^2 where r is the radius of the circle. = 16/2 = 8 feet.

Step-by-step explanation: