The choir director wants to divde the choir into groups. There ar 24 Altos and 36 Tenors. Each group must have the same amount of each Alto and Tenors. What is the greates amount of groups the choir director could make?

Answer:

[tex]13.5cm[/tex]

Step-by-step explanation:

You just need to subtract to find your answer!

The information we are given:

We have a 16cm glue stick.

Christina used 2.5cm of it.

Subtracting:

16 - 2.5 = 13.5

Now, dont forget your units :D

[tex]13.5 -- > 13.5cm[/tex]

~~~Harsha~~~

The desired sketch is attached below.

To sketch the scenario where BC intersects KT at point F, with F being the midpoint of BC but not KT, you can follow these steps:

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Answer:The least number by which 125 be multiplied to make it a perfect square is 5.125 = 5 × 5 × 5

The question deals with solving an equation pertaining to natural numbers and their squares. The solution involves finding the square root of 125 divided by 5, which gives us 5. Thus, the natural number whose square multiplied by 5 equals 125 is 5.

The subject of this question is Mathematics, specifically working with natural numbers and their squares. Here, you're given that 'when the square of a natural number is multiplied by 5, the product is 125'.

It's a simple application of the basic arithmetic operations. We have to try and find the square root of 125 divided by 5 because multiplication is inverse of division.

The calculation would be: √(125/5) = √25 = 5.

Thus, the natural number in question is 5, as 5 squared (25) times 5 is equal to 125.

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If in a large population, about 70% of families have a pet. A researcher takes a random sample of 6 families and surveys whether they have a pet. The probability of families that have a pet is: 0.0595.

Number of trial=  6

Probability of success = 0.7

Probability of failure = 1 - 0.7 = 0.3

Probability that exactly 2 of the families have a pet

Let make us of binomial distribution formula to determine the probability

P(X = 2) = (6 choose 2) * 0.7² *[tex]0.3^{4}[/tex]

= 15 * 0.49 * 0.0081

= 0.0595

Therefore the probability  is 0.0595.

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The derivative of the function is solved and f' ( 1 ) = 0.183

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = sinh⁻¹ ( √ (2x + 3 )

On taking the derivative of the function , we get

f' ( x ) = 1/ ( √2x + 4 ) ( √ ( 2x + 3 ) )

On simplifying , we get

when x = 1

f ( 1 ) = 1 / ( √6 ) ( √5 )

f ( 1 ) = 1/√30

f ( 1 ) = 0.18257

f ( 1 ) = 0.183

Hence , the function is solved

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The description of the given bearing with the towns and a similar drawing of bearing is given below:

The directions to draw the diagram that shows the relative position of the towns is given below:

Town R is at the center of the coordinate system.

Town C is 27km away on a bearing of 060°. Start at R, move 27km at 060° to find C towards east-southeast.

Town T is 19 km away from R on a ring of 3400.

T is on a circular path of radius of 3400 units.

To plot T, draw a circle at R with a 3400 unit radius. Put T on the circle, 19 km from R. Diagram: R center, C ESE, T on a circular path with a 3400 unit radius around R.

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The solution to the system of linear equations is (14, 16/3).

To find the solution to the given system of linear equations, we can use the method of substitution. First, we can solve the second equation for y by dividing both sides by 3, which gives us y = 16/3. .

We can then substitute this value of y into the first equation and solve for x. This gives us x - 3(16/3) = -2, which simplifies to x = 14. This point represents the intersection of the two lines, where they cross over each other on the coordinate plane.

The other answer choices given in the question are not valid solutions to the system of equations.

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Answer:

C

Step-by-step explanation:

The equation of line that passes through and is perpendicular toy = (7/5)x + 6 is  [tex]y = -\frac{5}{7}x - \frac{32}{7}[/tex].

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the original line:
y = (7/5)x + 6

Using the slope intercept, slope m is 5/2

Slope m = 7/5

Note: the equation of a perpendicular line to y = (7/5)x + 6 must have a slope that is the negative reciprocal of the original slope.

Slope of perpendicular line = -1 / ( 7/5 )

Slope of perpendicular line = -5/7

Plug the slope m = -5/7 and point (2,-6) into point-slope formula and simplify.

( y - y₁ ) = m( x - x₁ )

[tex]( y - (-6) = -\frac{5}{7}( x - 2 ) \\\\y + 6 = -\frac{5}{7}x + \frac{10}{7} \\\\y = -\frac{5}{7}x + \frac{10}{7} - 6\\\\y = -\frac{5}{7}x - \frac{32}{7}[/tex]

Therefore, the equation of the line is [tex]y = -\frac{5}{7}x - \frac{32}{7}[/tex].

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Answer:

Sure, I can help you with that.

To calculate the density of Saturn, we can use the following formula:

Density = Mass / Volume

We know the mass of Saturn is 5.68 x 1026 kg, and we can calculate the volume of Saturn using the following formula:

Volume = (4/3)πr³

where π is approximately equal to 3.14159 and r is the radius of Saturn, which is 5.6 x 107 m.

Plugging in these values, we get the following:

Density = 5.68 x 1026 kg / (4/3)π(5.6 x 107 m)³

Density = 0.687 kg/m³

Therefore, the density of Saturn is 0.687 kg/m³, which is less than the density of water (997 kg/m³). This means that Saturn would float on water.

Step-by-step explanation:

Using a calculator, the trigonometric ratio of sin 98 is approximately 0.9848.

One of the trigonometric ratio we have in mathematics is the sine ratio. We can use calculator to find the sine of an angle without making use of tables. To do this on your calculator, enter the sine function followed by the degree of the angle you want to find its sine. You will get your answer.

Using a calculator, we can find the sine of 98 degrees as follows:

sin 98° ≈ 0.9848

Rounding this to four decimal places, we get:

sin 98° ≈ 0.9848

Therefore, sin 98° is approximately equal to 0.9848.

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The correct statements that apply to the given limits are:

Option A: Multiply by (√(x + 2) + 3)/(√(x + 2) + 3)

Option D: "Divide out a common factor of x - 7."

Option E: The limit of the given expression is 1/6.

Option: We generally multiply by the conjugate of the expression to eliminate square roots in simplification. Thus, option A applies.

Option B: Get x - 1 in the numerator:

This statement is not correct. The expression does not involve x - 1 in the numerator.

Option C: Get (x - 7)(√(x + 2) - 3) in the denominator:

This statement is not correct due to the fact that we want to simplify the expression, and not introduce a more complex denominator.

Option D: Divide out a common factor of x - 7:

This statement is correct because by factoring out (x - 7) from both the numerator and denominator, we can cancel out the common factor.

Option E: Calculate the limit as 1/6:

After canceling out the common factor of x - 7, the simplified expression becomes:

lim x -> 7 (√(x + 2) - 3)/(x - 7)

= lim x -> 7 1/(√(x + 2) + 3)

To find the limit, we substitute the value x = 7 into the simplified expression:

lim x -> 7 1/(√(7 + 2) + 3) = 1/(√(9) + 3) = 1/(3 + 3) = 1/6

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The equivalent equations of 4(2-5x)=6-3(1-3x)​ are 4(2 - 5x) = 6 - 3(1 - 3x), 8 - 20x = 6 - 3 + 9x and 29x = 5

From the question, we have the following parameters that can be used in our computation:

4(2-5x)=6-3(1-3x)​

Express properly

So, we have

4(2 - 5x) = 6 - 3(1 - 3x)

Open the brackets

So, we have

8 - 20x = 6 - 3 + 9x

Evaluate the like terms

This gives

29x = 5

This means that the equivalent equations are 4(2 - 5x) = 6 - 3(1 - 3x), 8 - 20x = 6 - 3 + 9x and 29x = 5

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Answer:

1/4, 4/7, 2/3, 1/2

Step-by-step explanation:

125 workers can produce approximately 102.94 cars in 7 hours.Additionally, this assumes that the constant of Proportionality remains the same for different numbers of workers and hours worked.

We are given that the number of cars manufactured at an automobile plant varies jointly as the number of workers and the time they work. This can be expressed as:

C = kWT

where C is the number of cars produced, W is the number of workers, T is the time they work, and k is a constant of proportionality

We can use this formula to solve the problem. We are given that 85 workers can produce 136 cars in 8 hours, so we can set up an equation using this information:

136 = k(85)(8)

Solving for k, we get:

k = 2/17

Now we can use the formula to find the number of cars that 125 workers can produce in 7 hours:

C = (2/17)(125)(7)

C = 102.94

Therefore, 125 workers can produce approximately 102.94 cars in 7 hours.

It's important to note that this is an approximation since we have rounded the answer to two decimal places. Additionally, this assumes that the constant of proportionality remains the same for different numbers of workers and hours worked.

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625 as a fraction of 1000 in its lowest terms is 5/8.

Express 625 as a fraction of 1000 in its lowest terms. Here's a step-by-step explanation:
1. Write the given numbers as a fraction: 625/1000
2. Find the greatest common divisor (GCD) of the numerator (625) and the denominator (1000). The GCD of 625 and 1000 is 125.
3. Divide both the numerator and the denominator by the GCD: (625 ÷ 125) / (1000 ÷ 125)
4. Simplify the fraction: 5/8
So, 625 as a fraction of 1000 in its lowest terms is 5/8.

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Answer:

To find the z-score of a data value, we use the following formula:

z = (x - μ) / σ

where z is the z-score, x is the data value, μ is the mean of the distribution, and σ is the standard deviation.

Given a normal distribution with a mean (μ) of 146 and a standard deviation (σ) of 4, and a data value (x) of 153, we can plug these values into the formula:

z = (153 - 146) / 4

z = 7 / 4

z = 1.75

Thus, the z-score of the data value 153 is 1.75.

The solution to the equations are

1/3(2x - 3/7) + 1/6x = 4/7 is x = 6/7

7/8 x + 3/4 x + 7/16 x - 1/16 = 5/8 is x = 1/3

1 1/5 y + 3/10 y - 1/2 y = 1/3 y + 2/5 is y = 6/10

3/4 * (1/6 x + 16) = 3/7 * (4 3/8  x - 21) is x = 12

4/3x + 9/2y

1. To solve this equation, we can start by simplifying

1/3(2x - 3/7) + 1/6x = 4/7

2/3x - 1/7 + 1/6x = 4/7

Multiplying both sides by the lcm of the denominators which is 42

28x - 6 + 7x = 24

35x = 30

x = 6/7

2. 7/8x + 3/4x + 7/16x - 1/16 = 5/8

Multiplying both sides by the lcm of the denominators which is 16

14x + 12x + 7x - 1 = 10

33x = 11

x = 1/3

3.

6/5 y + 3/10 y - 1/2 y = 1/3 y + 2/5

2/3 y= 2/5

y = 2/5 * 3/2

y = 6/10

4.

3/4 * (1/6 x + 16) = 3/7 * (4 3/8 x - 21)

opening the parenthesis

1/8 x + 12 = 15/8 x - 9

1/8 x - 15/8 x= -12 - 9

-7/4 x = -21

x = 12

5.

2x - 2/3 x + 3 y + 1 1/2 y

4/3 x + 9/2 y

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Triangle- m ∠ 2 m ∠ 3 m ∠ 5 =  180 °( by the Triangle Sum Theorem)          

The statements are true. still, grounded on the given options, three statements that are always true regarding any triangle are . The sum of the angles of a triangle is always equal to 180 degrees.

This statement is true because the total degrees of any triangle is 180 degrees.

This is known as the Triangle Sum Theorem.

2. The  surface angle of a triangle is equal to the sum of its interior  contrary angles.  This statement is true for any triangle. The  surface angle is the angle formed by extending one side of the triangle. The  contrary innards angles are the two angles inside the triangle that don't partake a vertex with the  surface angle.  

3. The measure of each angle of an equilateral triangle is 60 degrees.  This statement is true for any equilateral triangle. An equilateral triangle has three equal sides and three equal angles, each measuring 60 degrees.  thus, grounded on the given options,

the three statements that are always true regarding the  illustration could be  

- m ∠ 3 m ∠ 4 m ∠ 5 =  180 °( by the Triangle Sum Theorem)

- m ∠ 5 m ∠ 6 =  180 °( by the sum of the angles of a straight line)

- m ∠ 2 m ∠ 3 m ∠ 5 =  180 °( by the Triangle Sum Theorem)

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Answer:

Step-by-step explanation:

5.6

Michio answer was wrong. The correct answer for x in the expression 2(3)ˣ = 34 is 2.5789

To know if Michio is correct or not, we shall determine the value of x in the algebraic expression. This is shown below:

2(3)ˣ = 34

Divide both sides by 2

3ˣ = 34 / 2

3ˣ = 17

Take the Log of both sides

Log 3ˣ = Log 17

Recall

Log Aⁿ = nLogA

Thus, we have

xLog 3 = Log 17

Divide both sides by Log 3

x = Log 17 / Log 3

x = 2.5789

From the above calculation, we see that Michio was wrong as the correct value of x in the expression is 2.5789

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Step-by-step explanation:

7 yr 11 mos = 95 mos

8 yr 11 mos = 107 mos

(x + y + z) / 3 = 95   mos              z is youngest

(x+y)/2 = 107         or      x+y = 214    <=====sub into first equation

(214  + z ) / 3 = 95      solve for 'z'

214+ z = 285

z = 71 months =  5 yrs 11 months  

Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{40}\\ a=\stackrel{adjacent}{ST}\\ o=\stackrel{opposite}{24} \end{cases} \\\\\\ ST=\sqrt{ 40^2 - 24^2}\implies ST=\sqrt{ 1600 - 576 } \implies ST=\sqrt{ 1024 }\implies ST=32 \\\\[-0.35em] ~\dotfill\\\\ \tan(S )=\cfrac{\stackrel{opposite}{24}}{\underset{adjacent}{32}} \implies \tan(S )=\cfrac{3}{4}[/tex]

The value of the given limit expression is 1.

Given is limit expression [tex]\lim _{x\to \infty }\left(x^{\frac{1}{3x}}\right)[/tex], we need to use L’Hôpital’s Rule to solve it,

So,

[tex]\lim _{x\to \infty \:}\left(x^{\frac{1}{3x}}\right)[/tex]

Using the exponent rule,

[tex]=\lim _{x\to \infty \:}\left(e^{\frac{1}{3x}\ln \left(x\right)}\right)[/tex]

Applying the chain rule,

[tex]\lim _{x\to \infty \:}\left(e^{\frac{1}{3x}\ln \left(x\right)}\right) = 1[/tex]

Hence the value of the given limit expression is 1.

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The area of the shaded region, to the nearest hundredth can be calculated as approximately: 1,195.71 mm².

The area of the shaded region can be found using the area of circle, which is: Area = πr²

Therefore, area of the shaded region = area of larger circle - area of smaller circle.

Area of larger circle:

radius (r) = 14 + 6.6 = 20.6 mm

Area of larger circle = 3.14 * 20.6² = 1,332.4904 mm²

Area of smaller circle:

radius (r) = 6.6 mm

Area of larger circle = 3.14 * 6.6² = 136.7784 mm²

Area of the shaded region = 1,332.4904 - 136.7784 = 1,195.71 mm².

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Bill's share = $56 Therefore, Bill received $56.

Let's start by setting up some equations based on the given information:

David's share = 1/7 * (Alex's share + Bill's share + Carl's share)

Alex's share = 3/4 * (Bill's share + Carl's share)

Bill's share = 2/5 * Carl's share

The sum of all four shares is $168.

We can use the fourth equation to solve for one of the shares in terms of the others:

Alex's share + Bill's share + Carl's share + David's share = $168

Alex's share + Bill's share + Carl's share = $168 - David's share

Substituting the other equations into this expression, we get:

Alex's share + (2/5 * Carl's share) + Carl's share + (1/7 * (Alex's share + (2/5 * Carl's share) + Carl's share)) = $168

Simplifying this equation, we get:

(8/7) * Alex's share + (22/35) * Carl's share = $168

Now we can use the other equations to solve for Carl's share, and then for Bill's share:

From Bill's share = 2/5 * Carl's share, we get Carl's share = (5/2) * Bill's share

From Alex's share = 3/4 * (Bill's share + Carl's share), we get Alex's share = (3/4) * ((7/2) * Bill's share) = (21/8) * Bill's share

Substituting these expressions into the equation we derived earlier, we get:

(8/7) * (21/8) * Bill's share + (22/35) * (5/2) * Bill's share = $168

3 * Bill's share = $168

Bill's share = $56

Therefore, Bill received $56.

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The distance of bird away from the tower is  4.04 miles.

Given that,

Distance between A and B = 10 miles

To solve this problem,

Use the law of tangents and basic trigonometry.

Let  the distance from tower A to the bird = x

Then,

tan(180° - 64°) = x / (10 - d)

(where d is the distance from tower B to the bird)

tan(42°) = x / d

We can rearrange the first equation to get,

10 - d = x / tan(116°)

Substituting this into the second equation, we get:

⇒ tan(42°) = x / (x / tan(116°))

⇒ tan(42°) = tan(116°) x / x

⇒  x = 10 tan(42°) / (tan(116°) - tan(42°))

Plugging this into a calculator, we get:

x ≈ 4.04 miles

Therefore,

The exotic bird is approximately 4.04 miles away from tower A.

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The measure of the arc angles which subtends angles at the center are: MN = 72°, NQR = 180°, NQ = 108°, MRP = 193°, QR = 72, MR = 108, QMR = 288°, PQ = 13°, PRN = 265°, and MQN = 288°.

The angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.

So;

arc angle MN = 72° {vertical angles}

arc angle NQR = 95 + 13 + 72 = 180°

arc angle NQ = 95 + 13 = 108°

arc angle MRP = 108 + 72 + 13 = 193°

arc angle QR = 72

arc angle MR = 95 + 13 = 108 {vertical angles}

arc angle QMR = 180 + 108 = 288°

arc angle PQ = 13° {sum of angles on a straight line}

arc angle PRN = 85 + 108 + 72 = 265°

arc angle MQN = 180 + 12 + 95 = 288°.

Therefore, the following are measures of the arc angles which subtends angles at the center: MN = 72°, NQR = 180°, NQ = 108°, MRP = 193°, QR = 72, MR = 108, QMR = 288°, PQ = 13°, PRN = 265°, and MQN = 288°.

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Under the units-of-activity method, the depreciation expense per mile for Bus #3 is $0.4616.

The units-of-activity method is one of the depreciation methods in use.

Under the units-of-activity method, the depreciation expense per unit is determined by dividing the depreciable amount by the total units of activity.

The depreciation amount (the value of the asset subject to depreciation) is the net of the total cost less the salvage value.

Depreciable amount of Bus #3 = $57,700 ($66,500 - $8,800)

Expected total miles for Bus #3 = 125,000

Depreciation expense per mile for Bus #3 = $0.4616 ($57,700 ÷ 125,000)

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Bus    Acquired    Cost    Salvage    Useful Life     Depreciation
                                          Value         in Years          Method

1          1/1/12      $99,100   $7,900           4             Straight-line

2         1/1/12      128,000     11,000          4             Declining- balance

3         1/1/13       66,350      8,800          5             Unit-of-activity