Ninety one students signed up for the skating club. Coach Link wants to form teams with the same number of members on each team, but says that is impossible: the only teams he can make are 91 teams of 1 or 1 team of 91. Is coach Link correct. Explain why or why not.

Answer:

the answer is the option C

[tex]KJ=3\sqrt{5}\ units[/tex]

Step-by-step explanation:

we know that

The triangle KMJ is a righ triangle

so

Applying the Pythagoras Theorem

[tex]KJ^{2}=KM^{2}+MJ^{2}[/tex]

in this problem we have

[tex]KM=6\ units[/tex]

[tex]MJ=3\ units[/tex]

substitute

[tex]KJ^{2}=6^{2}+3^{2}[/tex]

[tex]KJ^{2}=45[/tex]

[tex]KJ=\sqrt{45}=3\sqrt{5}\ units[/tex]

Answer: 32 quarts

Step-by-step explanation:

We know that there area 4 quarts in one gallon.

i.e.[tex]1\text{ gallon}=4\text{ quarts}[/tex]

Now, to convert 8 gallons into quart we need to apply unitary method.

Using unitary method , to convert 8 gallons into quart , multiply 8 to 4 , we get

[tex]8\text{ gallon}=8\times4\text{ quarts}\\\\\Rightarrow\ 8\text{ gallon}=32\text{ quarts}[/tex]

Hence there are 32 quarts in 8 gallons.

There are 32 quarts in 8 gallons of quantity.

The given quantity is 8 gallons.

We know that, 1 gallon = 4 quarts

Here, 8 gallons = 8×4

= 32 quarts

Therefore, there are 32 quarts in 8 gallons of quantity.

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Final answer:

The composition h = f о g is only guaranteed to be an odd function if both g and f are odd functions. If f is an even function or neither odd nor even, h will not necessarily be an odd function. The property of the composition depends on the nature of both functions involved.

Explanation:

Whether the composition of functions h = f о g is always an odd function when g is an odd function depends on the nature of f. If g(x) is an odd function, it follows that g(-x) = -g(x). However, for h to also be odd, f must satisfy the condition h(-x) = -h(x). This can only be the case if f is also an odd function.

If f were an even function, then f(g(-x)) = f(-g(x)) would equal f(g(x)) due to the even property of f. In this scenario, h would not be an odd function since h(-x) = f(g(-x)) = f(g(x)) = h(x), which violates the definition of an odd function.

When an odd function and an even function are multiplied, the result is an odd function, as exemplified by g(x) = x³ - 3x and h(x) = x². But when composing functions, the outer function's properties dominate the result. Therefore, the composition h = f о g can only be assured to be odd if f itself is odd.

1 mile = 5280 feet

1 hour = 3600 seconds

72 * 5280 = 380160 feet per hour

380160/ 3600 = 105.6 feet per second ( round answer if needed)

The domain will consist of all non-negative real numbers (x ≥ 0).

And, the range will consist of all real numbers (-∞, +∞).

Given that;

The function is,

c (x) = 10x - 50

Now for the domain and range of the function c(x) = 10x - 50,

Since the domain refers to all the possible input values (x) for the function.

In this case, since c(x) represents the profit from selling candles, x would represent the number of candles sold.

The number of candles sold cannot be negative, as it wouldn't make sense to sell a negative number of candles.

So, the domain will consist of all non-negative real numbers (x ≥ 0).

And, The range refers to all the possible output values (c(x)) of the function.

In this case, c(x) represents the profit. The profit can be any real number because it can be positive, negative, or zero.

Therefore, the range will consist of all real numbers (-∞, +∞).

Thus, Domain: All non-negative real numbers (x ≥ 0).

Range: All real numbers (-∞, +∞).

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To find 60% off of $33.00, you multiply 33 by 60, then divide the product by 100. The result is $19.80, which is the discount amount. So after the discount, the cost is $13.20.

To find out what 60% off of $33.00 is, you need to multiply 33.00 by 60 and then divide that product by 100, as percentages are always out of 100. Here's the process:

So, 60% off of $33.00 equals $19.80. Hence, after a 60% discount, you would pay $13.20 (33 - 19.80), as this is the remaining cost after the discount has been applied.

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The required three consecutive even integers are 56, 58, and 60.

Given that,
The sum of three consecutive even integers is 174 what are integers is to be determined?

Arithmetic progression is the series of numbers that have common differences between adjacent values

Here,
Let the three even integers be 2x, 2x+ 2 and 2x + 4
Now, accoding to the question,

2x + 2x + 2 + 2x + 4 = 174
6x + 6 = 174
x = 28

Now,
2x =28 * 2 = 56

2x + 2 = 56 + 2 = 58
2x + 4 = 56 + 4 = 60

Thus, the required three consecutive even integers are 56, 58, and 60.

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To find the parallel line's equation through the point (6, -5), we identify the slope of 9x - 2y = 7 as (9/2), and then use the point-slope form with the given point to derive the new line's equation. The final general form of this equation is 9x - 2y - 64 = 0.

To find the general form of an equation of the line that is parallel to the line 9x - 2y = 7 and passes through point a(6, -5), we first need to identify the slope of the given line. The slope-intercept form of the line can be found by rearranging the equation into y = mx + b, where m is the slope. For the given equation 9x - 2y = 7, we solve for y to get the slope:

2y = 9x - 7

y = (9/2)x - 7/2

The slope of the given line is (9/2). Since parallel lines have the same slope, our new line will also have a slope of (9/2). Using the point-slope form of a line's equation, we can insert the slope and the coordinates of point a to determine the equation of our new line:

y - y₁ = m(x - x₁)

y - (-5) = (9/2)(x - 6)

y + 5 = (9/2)x - 27

Finally, we rearrange this equation to its general form, Ax + By + C = 0:

(9/2)x - y - 32 = 0

or

9x - 2y - 64 = 0

This is the general form of the equation of the line that is parallel to 9x - 2y = 7 and passes through point (6, -5).

To calculate the total miles, first convert 50000 inches to feet, then convert the result to miles. Approximately 0.790 miles are in 50000 inches.

To answer your question, "How many miles are in 50000 inches?" We need to convert inches to miles. We have to use the given conversion rates: 1 foot = 12 inches and 1 mile = 5280 feet.

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The required number, whose sum with its square is 210, is -15 and 14.

Given that,
The sum of a number and its square is 210. To determine the​ number(s).

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Let the number be x,
according to the question,
x + x² = 210
x² + x -210 = 0
x² + 15x - 14x  - 210 = 0
x(x + 15) -14 (x + 15) = 0
(x + 15)(x - 14) = 0
x = -15 and 14

Thus, the required number, whose sum with its square is 210, is -15 and 14.

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First, let's define the number we are looking for as n.

So "half a number" is (1/2)×n

Therefore, "four less than" this would be: ((12)×n)−4

And if this is or, in other words, = to #17 we can write the equation:

((12)×n)−4=17

Solving for n while keeping the equation balanced gives:

((12)×n)−4+4=17+4

(12)×n=21

(21)×(12)×n=21×(21)

((21)×(12))×n=421

1×n=42

n=42

Answer:

C. 9

Step-by-step explanation:

Ron is five years older than twice his cousin's age. Lets assume that Pat's age is 'x' years.

So Ron's age is [tex]2\times x+5=2x+5[/tex]

The question says:

[tex]x+2x+5<35[/tex]

[tex]3x+5<35[/tex]

[tex]3x<35-5[/tex]

[tex]3x<30[/tex]

[tex]x<10[/tex]

Pat's age [tex](x)[/tex] should be less than 10. Therefore, the greatest age (in integer) that Pat can be is 9 years.