Benjamin​ & Associates, a real estate​ developer, recently built 195 condominiums in​ McCall, Idaho. The condos were either two​-bedroom units or three​-bedroom units. If the total number of bedrooms in the entire complex is 497​, how many two​-bedroom units are​ there? How many three​-bedroom units are​ there?

Answer:

y = 0

Step-by-step explanation:

When the degree of the denominator of a rational function is greater than the degree of the numerator, then the equation of the horizontal asymptote is

y = 0

here degree of numerator is 1 and degree of denominator is 2

Degree of denominator > degree of numerator, thus

y = 0 ← equation of horizontal asymptote

Answer:

(about) 61.1

Step-by-step explanation:

To find the height, or H, we can use

sin (45 degree angle) =H/85

rearrange as H=85* sin (45 degrees) =(about) 61.1

Answer: the price of 1 yard of chicken wire is $2

Step-by-step explanation:

Let x represent the cost of one yard of landscaping fabric.

Let y represent the cost of one yard of chicken wire.

Charlotte pays $24 for 3 yards of landscaping fabric and 6 yards of chicken wire. This means that

3x + 6y = 24 - - - - - - - - - - 1

Kami pays $30 for 6 yards of landscaping fabric and 3 yards of chicken wire. This means that

6x + 3y = 30 - - - - - - - - -2

Multiplying equation 1 by 6 and equation 2 by 3, it becomes

18x + 36y = 144

18x + 9y = 90

Subtracting

27y = 54

y = 54/27 = 2

Substituting y = 2 into equation 1, it becomes

3x + 6×2 = 24

3x = 24 - 12 = 12

x = 12/3 = 4

Answer:

$2 per yard.

Step-by-step explanation:

Let the price per yard of landscaping fabric be f and the price of chicken wire per yard be c.

3f + 6c = 24     Multiply this equation by  - 2:

-6f - 12c = -48 Also:

6f + 3c = 30

Adding the last 2 equations:

-9c = -18

c = 2.

Answer:  The correct option is

(E) 70.

Step-by-step explanation:  We are given to find the number of  triangles and quadrilaterals altogether that can be formed using the vertices of a 7-sided regular polygon.

To form a triangle, we need any 3 vertices of the 7-sided regular polygon. So, the number of triangles that can be formed is

[tex]n_t=^7C_3=\dfrac{7!}{3!(7-3)!}=\dfrac{7\times6\times5\times4!}{3\times2\times1\times4!}=35.[/tex]

Also, to form a quadrilateral, we need any 4 vertices of the 7-sided regular polygon. So, the number of quadrilateral that can be formed is

[tex]n_q=^7C_4=\dfrac{7!}{4!(7-4)!}=\dfrac{7\times6\times5\times4!}{4!\times3\times2\times1}=35.[/tex]

Therefore, the total number of triangles and quadrilaterals is

[tex]n=n_t+n_q=35+35=70.[/tex]

Thus, option (E) is CORRECT.

Answer:

Step-by-step explanation:

Perpendicular slopes are the opposite reciprocals of the slopes given.  Our slope in 8 is -2.  That means that the perpendicular slope is 1/2.  If the line goes through (2, -1), then

[tex]y-(-1)=\frac{1}{2}(x-2)[/tex] and

[tex]y+1=\frac{1}{2}x-1[/tex] and

[tex]y=\frac{1}{2}x-2[/tex]

9 is a tiny bit trickier because we don't have the slope, the x term, on the opposite side of the equals sign from the y.  Let's do that and then we can determine the slope of that given line.  Moving over the 3x and isolating the y:

y = -3x + 5

So the slope is -3.  That means that the perpendicular slope is 1/3.  If the line goes through (-9, 3), then

[tex]y-3=\frac{1}{3}(x-(-9))[/tex] and

[tex]y-3=\frac{1}{3}(x+9)[/tex] and

[tex]y-3=\frac{1}{3}x+3[/tex] so

[tex]y=\frac{1}{3}x+6[/tex]

Answer:

Step-by-step explanation:

8) y = -2x + 1 and the line passes through (2, - 1)

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

y= -2x + 1

Comparing with the slope intercept form, slope = - 2

If two line passing through the given point is perpendicular to the given line, it means its slope is the negative reciprocal of that of the given line. Therefore, the slope of the line passing through (2,-1) is 1/2

To determine the intercept, we would substitute m = 1/2, x = 2 and y = -1 into y = mx + c. It becomes

- 1 = 1/2 × 2 + c = 1 + c

c = - 1 - 1 = - 2

The equation becomes

y = x/2 - 2

9) 3x + y = 5 and the line passes through (-9, 3)

The equation of the given line is

3x + y = 5

y = -3x + 5

Comparing with the slope intercept form, slope = - 3

If two line passing through the given point is perpendicular to the given line, it means its slope is the negative reciprocal of that of the given line. Therefore, the slope of the line passing through (- 9, 3) is 1/3

To determine the intercept, we would substitute m = 1/3, x = -9 and y = 3 into y = mx + c. It becomes

3 = 1/3 × -9 + c = - 3 + c

c = 3 + 3 = 6

The equation becomes

y = x/3 + 6

The question is not complete without a picture depicting the pot stickers production. I found a similar question with a table for the production of pot stickers which is attached to this answer. If the actual table is different from the table in this answer, you can still answer your question accordingly using my working and reasoning.

Answer:

Day 6

Step-by-step explanation:

It was given that the usual production of the kitchen is between 20 to 22 pot stickers per hour. Day 1 to 3, the production is within the range given.

However on day 4 and 5, the production is dropped to 10 and 15 - probably due to the workers unfamiliar with the machine.

On day 6 and 7, the production increases to 50 and 55. Therefore the day the machine makes positive impact is on day 6 where the production starts to make a significant increase.

We cannot determine the exact day when the new machine makes a positive impact on production at Sayuri's Asian Café.

The question asks on which day the new machine makes a positive impact on production at Sayuri's Asian Café. To determine this, we need to compare the production before and after the machine was introduced. Unfortunately, the statement provided does not mention the production levels before the machine. Therefore, we cannot determine the exact day when the machine makes a positive impact.

When considering mortgage payments, homeowners insurance, property tax and maintenance costs over 30 years, the true cost of the $96,000 home is $287,068.80.

The true cost of a home not only includes the original purchase price but also takes into account annual homeowners insurance, property taxes, and maintenance costs. In this case, the purchase price is $96,000, homeowners insurance costs $1012 per year, property taxes are 1.1% of the home price each year, and annual home maintenance is 1% of the home price.

First, calculate the total mortgage payments made over 30 years. The monthly payment is $545.08, so the total mortgage payments are:

30 years * 12 months/year * $545.08/month = $196,228.80

Next, calculate the total cost of homeowners insurance over 30 years:

30 years * $1012/year = $30,360

Then, calculate the total property taxes over 30 years:

30 years * 1.1% of $96,000/year = $31,680

Lastly, calculate the total home maintenance over 30 years:

30 years * 1% of $96,000/year = $28,800

Adding all of these costs together gives the total cost of the home:

$196,228.80 + $30,360 + $31,680 + $28,800 = $287,068.80

So, the correct answer is option C: $287,068.80.

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For this case we have to:

x: Variable that represents Tyler's age

y: Variable that represents Tiffany's age

According to the data of the statement we can propose the following equations:

[tex]x = y + 4\\x + 10 = 2y[/tex]

To solve we substitute the first equation in the second equation:

[tex]y + 4 + 10 = 2y\\14 = 2y-y\\14 = y[/tex]

So, Tiffany is 14 years old.

Then Tyler has:

[tex]x = 14 + 4\\x = 18[/tex]

Tyler is 18 years old.

Answer:

Tyler: 18 years old

Tiffany: 14 years old

Answer:

[tex]x<-\frac{1}{6}[/tex]

Step-by-step explanation:

[tex]\frac{7-2x}{-4} +2<-x[/tex]

Subtract 2 from both sides

[tex]\frac{7-2x}{-4} <-x-2[/tex]

mutliply both sides by -4, flip the inequality

[tex]7-2x >4x+8[/tex]

Add 2x on both sideds

[tex]7>6x+8[/tex]

Subtract 8 from both sides

[tex]-1>6x[/tex]

Divide both sides by 6

[tex]x<-\frac{1}{6}[/tex]

To solve for x, the given inequality (7 - 2x) / (-4) + 2 < -x can be simplified by isolating the variable on one side of the inequality. The value of x is found to be x < -15/2, making option C) x greater than negative one over six the correct answer choice.

The given inequality is:

(7 - 2x) / (-4) + 2 < -x

To solve for x, we need to isolate it on one side of the inequality. Let's simplify the equation step by step:

(7 - 2x) / (-4) + 2 < -x

7 - 2x + 8 < -4x (Added 2 to both sides)

15 - 2x < -4x

15 < 2x - 4x (Moved -2x to the right side)

15 < -2x

-15/2 > x

So the value of x in the inequality is x < -15/2. Therefore, the correct answer is option C) x greater than negative start fraction one over six end fraction.

Answer:

[tex]\frac{x-3}{3x}[/tex]

Step-by-step explanation:

Lindsay can paint 1/x of a certain room in 20 minutes.

1 hour = 3 times 20 minutes

rate of work by Lindsay in 20 minutes is [tex]\frac{3}{x}[/tex]

Let 't' be the work done by Joseph

rate of work by Joseph in 20 minutes is [tex]\frac{3}{t}[/tex]

Both completed the work in 1 hour

[tex]\frac{3}{x} +\frac{3}{t} =1[/tex]

solve the equation for 't'

Subtract 3/x on both sides

[tex]\frac{3}{t} =1-\frac{3}{x}[/tex]

[tex]\frac{3}{t} =\frac{x-3}{x}[/tex]

cross multiply it

[tex]3x=t(x-3)[/tex]

Divide both sides by x-3

[tex]\frac{3x}{x-3} =t[/tex]

Work done together is

[tex]\frac{x-3}{3x}[/tex]

Answer:one piece is 42 centimeters and the other piece is 14 centimeters

Step-by-step explanation:

Let x represent the length, in centimeters, of one piece of the ribbon.

Let y represent the length, in centimeters, of the other piece of the ribbon.

The ribbon, 56 cm long is cut into two pieces. This means that

x + y = 56 - - - - -- - - - -1

One of the pieces is three times longer than the other. This means that

x = 3y

Substituting x = 3y into equation 1, it becomes

3y + y = 56

4y = 56

y = 56/4 = 14 centimeters

x = 3y = 2×14 = 42 centimeters

Answer:

  (a) 74√3 N

  (b) 37√3 N

  (c) 111 N

Step-by-step explanation:

(a) The moment about the hinge produced by the beam is the product of the weight of the beam and the distance of its center from the wall. The tension in the wire counteracts that moment.

The tension in the wire acts at a horizontal distance from the wall that is twice the distance to the beam's center, so the tension's vertical component is only half the weight of the beam.

Since the wire is at a 30° angle to the wall, the horizontal component of the tension is 1/√3 times the vertical component. Altogether, the tension in the wire is (2/√3) times half the beam's weight, or 74√3 N.

__

(b) The horizontal force at the hinge counteracts the horizontal component of the tension in the wire, so is 111/√3 N = 37√3 N.

__

(c) The vertical component of the force at the hinge is half the beam weight, so is 111 N.

a) The tension in the wire is 192.3 N. b) The horizontal component of the force of the hi-nge on the beam is 96.1 N. c) Vertical component of the force of the hi-nge on the beam is 55.5 N.

(a) To find the tension in the wire, we can use a torque balance around the hi-nge. The torques due to the weight of the beam and the tension in the wire are equal and opposite, so we have:

T * L * cos(30°) = W * L/2

where:

T is the tension in the wire

L is the length of the beam

W is the weight of the beam

Solving for T, we get:

T = W * cos(30°) / 2

Substituting the known values, we get:

T = 222 N * cos(30°) / 2

= 192.3 N

Therefore, the tension in the wire is 192.3 N.

(b) The horizontal component of the force of the hi-nge on the beam is equal to the tension in the wire multiplied by the sine of the angle between the wire and the beam. This angle is 30°, so we have:

[tex]F_h[/tex] = T * sin(30°)

Substituting the known values, we get:

[tex]F_h[/tex] = 192.3 N * sin(30°)

= 96.1 N

Therefore, the horizontal component of the force of the hi-nge on the beam is 96.1 N.

(c) The vertical component of the force of the hi-nge on the beam is equal to the weight of the beam minus the tension in the wire multiplied by the cosine of the angle between the wire and the beam. This angle is 30°, so we have:

[tex]F_v[/tex] = W - T * cos(30°)

Substituting the known values, we get:

[tex]F_v[/tex] = 222 N - 192.3 N * cos(30°)

= 55.5 N

Therefore, the vertical component of the force of the hi-nge on the beam is 55.5 N.

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Answer:

Step-by-step explanation:

Chrissie likes to tip a server in a restaurant a minimum of 25% of her lunch bill. She and her friend have a lunch bill that is $13.78. This means that the amount of tip that she would give to the server would be

25/100 × 13.78 = 0.25 × 13.78 = $3.445

If Chrissie says the tip will be $3.00, he is incorrect because the tip is $3.445 which is higher than $3

If her friend says that the amount is not a minimum of 25% he is correct because a minimum if 25% is $3.445 which is higher than $3

XY = 17

Step-by-step explanation:

It is given that x is the mid-point of WY, so it divides WY in two equal parts

WX and XY so the sum of both lengths will constitute the length of WY

[tex]WY = WX+XY\\XY = WY - WX[/tex]

putting values

[tex]XY = 10x-26 -(3x-1)\\= 10x-26-3x+1\\= 7x-25[/tex]

As X is the mid-point,

[tex]WX = XY\\3x-1 = 7x-25\\3x-1-3x = 7x-25-3x\\-1 = 4x-25\\-1+25 = 4x-25+25\\24 = 4x[/tex]

Dividing both sides by 4

[tex]\frac{4x}{4} = \frac{24}{4}\\x = 6[/tex]

XY = 7x-25

[tex]=7(6) -25\\= 42-25\\=17[/tex]

So,

XY = 17

Verification:

WX = XY

[tex]3x-1 = 7x-25\\3(6)-1 = 7(6)-25\\18-1 = 42-25\\17 = 17[/tex]

Keywords: Linear equations, polynomials

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We can use the points (-30, 42) and (-27, -30) to solve.

Slope formula: y2-y1/x2-x1

= -30-42/-27-(-30)

= -72/3

= -24 (Answer)

Best of Luck!

Amount saved by Nicole is $ 105

Solution:

Given that Patrician saves $ 1.20 everyday and Nicole saves $ 2.80 daily

The two girls saved $ 150.00 together

To find: Amount saved by Nicole

Let "x" be the number of days for which Patrician and Nicole saved money

Given that they both saved $ 150.00 together

So we can frame a equation as:

[tex]\text{(amount saved by patrician + amount saved by nicole) } \times x = 150.00[/tex]

[tex](1.20 + 2.80) \times x = 150\\\\4x = 150\\\\x = 37.5[/tex]

Therefore amount saved by nicole:

Nicole has saved $ 2.80 daily for "x" days

[tex]\text{ Amount saved by Nicole } = x \times 2.80\\\\\text{ Amount saved by Nicole } = 37.5 \times 2.80 = 105[/tex]

Thus amount saved by Nicole is $ 105

Answer:

Step-by-step explanation:

10) The opposite sides of a parallelogram are equal. It means that

a + 15 = 3a + 11

3a - a = 15 - 11

2a = 4

a = 4/2 = 2

Also,

3b + 5 = b + 11

3b - b = 11 - 5

2b = 4

b = 4/2 = 2

11) The opposite angles of a parallelogram are congruent and the adjacent angles are supplementary. This means that

2x + 11 + x - 5 = 180

3x + 6 = 180

3x = 180 - 6 = 174

x = 174/3 = 58

Therefore,

2x + 11 = 2×58 + 11 = 127 degrees

The opposite angles of a parallelogram are congruent, therefore,

2y = 127

y = 127/2 = 63.5

12) The diagonals of a parallelogram bisect each other. This means that each diagonal is divided equally at the midpoint. Therefore

3y - 5 = y + 5

3y - y = 5 + 5

2y = 10

y = 10/2 = 5

Also,

z + 9 = 2z + 7

2z - z = 9 - 7

z = 2

Answer:

  (-10, -6), (4, -6), (-3, -13), (-3, 1)

Step-by-step explanation:

The easiest points to find that have rational coordinates are the ones 7 units up or down, left or right from the given point. Those are listed above.

We used the distance formula to find four points that could serve as the other end of a line segment with one end at (-3, -6) and length of 7 units. The four points are (0, -6 + √40), (0, -6 - √40), (-3 + √13, 0), and (-3 - √13, 0).

Finding the Other End Point of a Line Segment

To find four points that can serve as the other end point of a line segment with one end point at (-3, -6) and a length of 7 units, we use the distance formula. The distance formula is:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

Given, (x₁, y₁) is (-3, -6) and the distance is 7, we need to find (x₂, y₂) such that:

√((x₂ + 3)² + (y₂ + 6)²) = 7

Squaring both sides: (x₂ + 3)² + (y₂ + 6)² = 49

(0 + 3)² + (y₂ + 6)² = 49

9 + (y₂ + 6)² = 49

(y₂ + 6)² = 40

y₂ + 6 = ±√40

y₂ = -6 ± √40

(x₂ + 3)² + (0 + 6)² = 49

(x₂ + 3)² + 36 = 49

(x₂ + 3)² = 13

x₂ + 3 = ±√13

x₂ = -3 ± √13

Thus, the four possible points for the other end point of the line segment are (0, -6 + √40), (0, -6 - √40), (-3 + √13, 0), and (-3 - √13, 0).

Lacy would earn a commission of $104.

Lacy would earn 0.06x dollars on phones sale and 0.02y dollars on computer sales.

Step-by-step explanation:

Given,

Commission earned on phones sales = 6% = [tex]\frac{6}{100}=0.06[/tex]

Commission earned on computer sales = 2% = [tex]\frac{2}{100}=0.02[/tex]

Worth of phones sold = $1100

Commission amount = 0.06*1100 = $66

Worth of computers sold = $1900

Commission amount = 0.02*1900 = $38

Total commission amount = 66+38 = $104

Lacy would earn a commission of $104.

For $x of phones, we will multiply the given amount with commission rate;

Commission amount of $x phones = 0.06*x = 0.06x

For $y computers;

Commission amount of $y computers = 0.02*y = 0.02y

Lacy would earn 0.06x dollars on phones sale and 0.02y dollars on computer sales.

Keywords: percentage, addition

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Answer:

The measure of an interior angle in a regular triangle is 60 degrees

Step-by-step explanation:

we know that

A regular triangle has three equal sides and three equal interior angles

Remember that the sum of the interior angles in a triangle must be equal to 180 degrees

so

Divide 180 by 3 to determine the measure of each interior angle

[tex]\frac{180^o}{3}=60^o[/tex]

A regular triangle is called equilateral triangle

therefore

The measure of an interior angle in a regular triangle is 60 degrees

Answer:

37/9 pounds

Step-by-step explanation:

+ them together

Answer:

Step-by-step explanation:

robbie is carrying his history textbook and his lunch in his backpack today.

The history textbook weighs 2 5/6 pounds. Converting 2 5/6 pounds to improper fraction, it becomes

17/6 pounds.

His lunch weighs 1 2/3 pounds. Converting 1 2/3 pounds to improper fraction, it becomes

5/3 pounds.

Total weight of the back backpack today would be the sum of the weight of his history textbook and his lunch. It becomes

17/6 + 5/3 = 27/6 = 4 1/2 pounds

Answer:

2

Step-by-step explanation:

Answer:

  24/7 = 3 3/7 inches

Step-by-step explanation:

The triangle can be represented by a line in the first quadrant with y-intercept 8 and x-intercept 6. Then its equation is ...

  x/6 +y/8 = 1 . . . . . intercept form of the equation of the line

  4x + 3y = 24 . . . . multiply by 24 to get standard form

Since the square will have the origin as one corner, and all sides are the same length, the opposite corner will lie on the line y=x. Then we're solving the system ...

  4x +3y = 24

  y = x

to find the side length.

__

By substitution for y, this becomes ...

  4x +3x = 24

  7x = 24

  x = 24/7 = 3 3/7

The length of the side of the square is 3 3/7 inches.

The question involved finding the side length of a square inscribed in a right triangle. The correct approach uses additional geometry to set up a system of equations resulting from segments on the legs of the triangle equal to the side length of the square. Solving these equations reveals that the side length of the square is 2 inches.

The student is seeking to find the length of the side of a square inscribed in a right triangle with legs measuring 6 inches and 8 inches. To determine this, one can use the Pythagorean theorem which relates the legs of a right triangle to its hypotenuse. However, in this scenario, the side of the square also acts as a 'leg' of two smaller right triangles within the original triangle. The length of the square, let's call it 's', plus the square's length (again 's') will equal the longer leg of the triangle (8 inches); similarly, 's' plus the length from the corner of the square to the right angle of the triangle (which is also 's') will equal the shorter leg (6 inches).

Therefore, we have two equations: 2s = 8 and 2s = 6. Since both cannot be true with the same value of 's', we realize that the premise of the question must be reconsidered. The actual process involves a bit more geometry, using the fact that the segments along the legs that are not part of the square must be equal respectively, leading to a system of equations to solve for the length of the side of the square. Let's denote these segments as 'x'; hence the equations are s + x = 6 and s + x = 8. Subtracting these equations from the original leg lengths gives us x = 6 - s and x = 8 - s. As these segments are equal, we can set them equal to each other, getting 6 - s = 8 - s, which simplifies to s = 2 inches.

Answer:her total sales is 25

Step-by-step explanation:

Let x represent her total sales.

Nicole's job pays her salary plus commission. She earns a daily salary of $60 plus 15% commission of her total sales. This means that the amount that she receives for x total sales would be

60 + 15/100× x

= 60 + 0.15x

On Monday, she earned a total of $63.75. This means that

63.75 = 60 + 0.15x

63.75 - 60 = 0.15x

0.15x = 3.75

x = 3.75/0.15 = 25

Answer:6

Step-by-step explanation:

Let digit be r=abc

if tens digit of [tex]\frac{r}{10}[/tex] is 3.2

i.e. [tex]\frac{r}{10}[/tex] is written as ab.c

so tens digit is a=3

If the hundreds digit of 10r is 6

i.e. 10r is written as abc0

its hundreds digit is b=6

thus tens digit of abc is b=6

To find the tens digit of the integer r, we use the information that the hundreds digit of 10r is 6, indicating that the tens digit of r is also 6.

The question is asking to determine the tens digit of a positive integer r. To solve this, we need to analyze the given facts separately:

From statement 2 alone, we can determine that the tens digit of the positive integer r is 6.

Answer:

It prints 65 copies in 1  minute.

It takes 80 minutes to print 5200 copies.

Step-by-step explanation:

In 5 minutes the machine prints 325 copies and it can print at that steady state.

We have to find the number of copies it prints in  1 minute.

So ,number of copies in 1 minute = [tex]\frac{number of copies in 5 minute}{5}[/tex]

                                          = [tex]\frac{325}{5}[/tex]

                                           = 65

Hence it prints 65 copies in 1  minute.

The time taken to print 5200 copies = [tex]time to make 1 copy \times 5200[/tex]

                                            = [tex]\frac{1}{65} \times 5200[/tex]

                                             = 80 minutes

Answer:

[tex]A_{new}=9A_{original}[/tex]

Step-by-step explanation:

The are of a trapezoid is:

[tex]A_{original}=\frac{(a+b)}{2}h[/tex]

where:

When a geometric figure dilates, every coordinate of the original figure must be multiplied by the scale factor of this dilatation. In our case this factor is 3, therefore we will have:

[tex]A_{new}=\frac{(3a+3b)}{2}3h[/tex]

[tex]A_{new}=9\frac{(a+b)}{2}h[/tex]

[tex]A_{new}=9A_{original}[/tex]

The new area is 9 times the original one.

I hope it helps you!

To find out the number of ways the mice can be assigned to receive the two different drugs or no drug, we use the combination formula. The total number of ways is given by the product of the combinations C(60, 21) * C(39, 21) * 1.

In this problem, we are given a group of 60 mice and we need to find the number of ways the mice can be assigned to receive drug A, drug B, or no drug. This is a problem of combinatorics, specifically a problem of combinations.

We have 60 mice and we want to choose 21 for the drug A. The number of ways to do this is given by the combination formula C(n, k) = n! / [k!(n-k)!], where 'n' is the total number of items, 'k' is the number of items to choose, and '!' represents the factorial function. So for drug A, it will be C(60, 21).

Then, from the remaining 39 mice, we need to choose 21 for drug B. The number of ways we can do this is C(39, 21).

Finally, the remaining 18 mice will serve as the control group. Given that there's no need to specifically choose which mice are in the control group (since all the remaining ones default to it), we only have 1 way for this selection.

 Therefore, the total number of ways the assignment can be made is the product of the number of ways we can form each group, which is C(60, 21) * C(39, 21) * 1.

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The number of ways the assignment of treatments to the mice can be made is 10278857927713471414080000.

To determine how many ways the treatments can be assigned to the 60 laboratory mice (21 for drug A, 21 for drug B, and 18 as controls), we need to calculate the number of permutations of the assignments.

The total number of mice is 60, consisting of:

- 21 mice for drug A

- 21 mice for drug B

- 18 mice as controls

The number of ways to assign treatments is the number of permutations of these groups within the total set of mice. This can be calculated using the multinomial coefficient:

[tex]\[ \frac{60!}{21! \times 21! \times 18!} \][/tex]

Where:

- 60!  is the factorial of 60 (total number of mice)

- 21! is the factorial of 21 (number of mice for drug A)

- 21! is again the factorial of 21 (number of mice for drug B)

- 18! is the factorial of 18 (number of control mice)

Let's compute this step-by-step:

1. Calculate 60!:

[tex]\[ 60! = 60 \times 59 \times 58 \times \ldots \times 2 \times 1 \][/tex]

2. Calculate 21!:

[tex]\[ 21! = 21 \times 20 \times \ldots \times 2 \times 1 \][/tex]

3. Calculate 18!:

[tex]\[ 18! = 18 \times 17 \times \ldots \times 2 \times 1 \][/tex]

Now, plug these into the formula:

[tex]\[ \frac{60!}{21! \times 21! \times 18!} = \frac{60 \times 59 \times \ldots \times 2 \times 1}{(21 \times 20 \times \ldots \times 2 \times 1) \times (21 \times 20 \times \ldots \times 2 \times 1) \times (18 \times 17 \times \ldots \times 2 \times 1)} \][/tex]

[tex]\[ \frac{60!}{21! \times 21! \times 18!} = \frac{83209871127413901442763411832233643807541726063612459524492776964096000000000000000}{51090942171709440000} \][/tex]

[tex]\[ \frac{60!}{21! \times 21! \times 18!} = 10278857927713471414080000 \][/tex]

Answer:

30 gallons

Step-by-step explanation:

let x represent the full container, then

[tex]\frac{1}{10}[/tex] x + 21 = [tex]\frac{4}{5}[/tex] x

Multiply through by 10 to clear the fractions

x + 210 = 8x ( subtract x from both sides )

210 = 7x ( divide both sides by 7 )

30 = x

The volume of the container is 30 gallons

Answer: the volume of the container is 30 gallons

Step-by-step explanation:

Let V represent the volume of the container, in gallons.

The initial volume of grains in the container is 1/0 × V = V/10

If 21 additional gallons of grain are added, the container is 4/5 full. This means that 21 gallons of grain + V/10 will occupy 4/5 of the volume of the container. Therefore

4/5 × V = 21 + V/10

4V/5 = 21 + V/10

4V/5 - V/10 = 21

7V/10 = 21

Multiplying the left hand side and right hand side of the equation by 10, it becomes

7V/10 × 5 = 21 × 10 = 210

7V = 210

V = 210/7 = 30

Answer:

Building is 56.58 feet long.

Step-by-step explanation:

Consider the provided information.

An aerial photograph from a U-2 spy plane is taken of a building suspected of housing nuclear warheads.

When the photograph is taken, the angle of elevation of the sun is 30°.

By comparing the shadow cast by the building in question to the shadows of other objects of known size in the photograph, scientists determine that the shadow of the building in question is 98 feet long.

As we know: [tex]\tan\theta=\frac{opp}{adj}[/tex]

The value of tan 30 degrees is [tex]\frac{1}{\sqrt{3} }[/tex]

[tex]\tan30=\frac{h}{98}[/tex]

[tex]\frac{1}{\sqrt{3}}=\frac{h}{98}[/tex]

[tex]h=\frac{98}{\sqrt{3}}[/tex]

[tex]h=56.58[/tex]

Hence, Building is 56.58 feet long.

Answer:

56.58 feet long

Step-by-step explanation:

Consider the provided information.

An aerial photograph from a U-2 spy plane is taken of a building suspected of housing nuclear warheads.

When the photograph is taken, the angle of elevation of the sun is 30°.

By comparing the shadow cast by the building in question to the shadows of other objects of known size in the photograph, scientists determine that the shadow of the building in question is 98 feet long.

As we know:

The value of tan 30 degrees is

Hence, Building is 56.58 feet long.