16) 472 students are going on a field trip. 120students will be returning home and therest will be spending the night in cabins. Ifa cabin sleeps 8 people, how many cabinsneed to be rented?A) 59 cabins B) 74 cabinsC) 44 cabins D) 4 cabins

K * K > N, because if the square of K is greater than N, it is not possible to add K distinct odd integers to get N.

If you square an integer (multiply it by itself), the result will always be an even number. If K is an odd number, then K * K will be an odd number plus one, which makes it even.

For example, if K = 3, then K * K = 9, which is an even number. If we take the square root of 9, we get 3, which is K. This means that the square of K will always be greater than K itself.

Now, if we want to add K distinct odd integers to get N, then N must be greater than K * K. This is because the sum of K odd numbers will always be less than K * K, and we need N to be greater than this sum.

Therefore, if K * K > N, it means that it is not possible to add K distinct odd integers to get N, because N is smaller than K * K, and the sum of K odd numbers will be smaller than N.

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ANSWER

Radius = 3 yd

Diameter = 6 yd

EXPLANATION

We are given the circle in the figure.

The radius of a circle is defined as the distance between the centre of a circle and its circumference.

Therefore, from the circle given, the radius is 3 yards

The diameter of a circle is defined as the total distance (through the centre) from one end of a circle to another.

It is twice the radius. Therefore, the diameter of the given circle is:

D = 3 * 2

D = 6 yards

The diameter is 6 yards.

Answer:

48

Step-by-step explanation:

Area of a triangle is 1/2(base*height)

Plug in:

1/2(6*16)

1/2(96)

48

Answer: 1,600 cm

~ i really hope that this is correct, have a gr8 day my friend!~

Step-by-step explanation:

The probability that an 18-year-old man selected at random is between 67 and 69 inches tall is 0.2586.

The requirement to solve the probability between z-values is to know that the probability between the z-values is the difference between the probability of the greatest z-value and the lowest z-value.

Here, the heights of 18-year-old men are approximately normally distributed, computing the z-score in this case will be:

P( 67 < x < 69) =

p( (67-68)/3 < z < (69-68)/3)

=p(-0.333 < z < 0.333

Checking the distribution table

= 2(0.1293)

= 0.2586

The value is 0.2586.

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The highest point for the quadratic function for the height of the object, h(t) = -16·t² + 224·t + 816, indicates that the interval over which the height of the object is increasing is; (-∞, 7]

The shape of the graph of a quadratic function is a parabola.

The function for the height of the object in question 3 is; h(t) = -16·t² + 224·t + 816

Where;

t = The time in seconds

The height of the object is increasing in the interval to the left of the highest point, which can be found as follows;

The x-coordinate of the highest point of the quadratic function, f(x) = a·x² + b·x + c is; x = -b/(2·a)

Therefore, the x-coordinates of the highest point of the object is; -224/(2 × (-16)) = 7

Therefore, the height of the object is increasing in the interval; -∞ < t ≤ 7

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The lines of the inequalities are parallel, and the system of inequalities do not have any solution.

The system of inequalities are  given as:

The inequality y ≥ 2x + 1 has the following characteristics:

The inequality y ≤ 2x – 2 has the following characteristics:

See attachment for the graphs of the system of inequalities

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Answer:

2 days

Step-by-step explanation:

On the first day, Adam has 2 dollars and adds 2 dollars to that which is 4. On that same day, Brodie spends 1 dollar and ends up with 7. The next day, Adam adds 2 more dollars and ends up with 6 and Brodie spends another dollar and ends up with 6. On the second day is when they will have the same amount of money.

-7

Step-by-step explanation:

12 + 15 + 20 is 47

40 - 47 = -7

Answer:

-13x. (I think)

Step-by-step explanation:

Answer:

55+3/8 -1/2=55-3×2/8=55-3/4=54.25

Answer:

answer is 11 feet is the correct answer

a) The mean of the data-set is of 2.

b) The range of the data-set is of 4 units, which is of around 4.3 MADs.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.

The dot plot shows how often each observation appears in the data-set, hence the mean of the data-set is obtained as follows:

Mean = (1 x 0 + 5 x 1 + 3 x 2 + 5 x 3 + 1 x 4)/(1 + 5 + 3 + 5 + 1)

Mean = 2.

The range is the difference between the largest observation and the smallest, hence:

4 - 0 = 4.

4/0.93 = 4.3 MADs.

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Answer:

4

Step-by-step explanation:

He made the mistake in step 4

The correct step should be x +2 as two had the sign "-" when it was on the other side

Tom made a mistake in step 4, and to correct the mistake he should add 2 on both sides in step 4.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

Step 1: f(x) = 4x - 2

Step 2: y = 4x - 2

Step 3: x = 4y - 2

Step 4: x + 2 = 4y  (add 2 on both sides)

Thus, Tom made a mistake in step 4, and to correct the mistake he should add 2 on both sides in step 4.

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Answer:

x< -12

Step-by-step explanation:

-1/2x>6
x-2.   x-2

x>-12

Since we multiply by we negative we flip the sign

x< -12

Hopes this helps

Answer:three-fourths

Step-by-step explanation:

because my dad said it was right

The row of tiles would be 24 1/2 inches long.

B:The  row of 10 tiles would be 35 inches long.

A 1. To be able to know the length of the row of tiles, one need to multiply the length of one tile by the number of tiles in the said  row.

So, all tile measures 3 1/2 inches on each side, Hence  the length of one tile is 3 1/2 inches.

Based on the fact that there are 7 tiles in a row, we have to multiply the length of one tile by 7:

Length of the row = 3 1/2 inches/tile x 7 tiles

                              = 24 1/2 inches

So, the row of tiles is 24 1/2 inches long.

B 2. Also, to find the length of a row of 10 tiles, we need to multiply the length of one tile by 10.

Note that:

Length of one tile = 3 1/2 inches

Number of tiles in the row = 10

Hence:

Length of the row = 3 1/2 inches/tile x 10 tiles

                               = 35 inches

So, the row of 10 tiles is 35 inches long.

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Hi there! :)

Answer:

The lines are the same.

Step-by-step explanation:

Begin by converting each equation into its simplest form in slope-intercept form:

-36x + 8y = 16

Move the "x" variable to the right side of the equation:

8y = 36x + 16

Divide all terms by 8:

y = 36/8x + 16/8

y = 9/2x + 2

-------------------------------

-9x + 2y = 4

Move "x" variable:

2y = 9x + 4

Divide both sides by 2:

y = 9/2x + 2

Both of the equations are equivalent, meaning both of the lines are the same.

The side b is approximately 80.02 feet in length. In a right triangle ABC with angle C equal to 90°, if angle B is 37.56° and side a is 49.94 feet, we can solve for side b using the trigonometric function sine.

First, we can label the triangle as follows:

Side a is opposite angle A,

Side b is opposite angle B,

Side c is the hypotenuse.

Let's label the triangle with the given and asked for information. Angle C is the right angle, angle B is 37.56°, side a is 49.94 feet, and side b is the side we are trying to find.

Using the sine function, we have:

sin(B) = opposite/hypotenuse

sin(37.56°) = a/b

Now we can substitute the known values:

sin(37.56°) = 49.94/b

To solve for b, we rearrange the equation:

b = 49.94 / sin(37.56°)

Using a calculator, we find:

b ≈ 80.02 feet.

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Answer:

x=-6

Step-by-step explanation:

For the rational expression, 6x/(x+6) to be undefined, the denominator need to be 0, so x=-6 is the point at which the function is undefined.

The rational expression 6x / (x + 6) is undefined when x equals -6, and it is defined for all other real numbers.

To find the real numbers for which the rational expression 6x / (x + 6) is undefined, we need to identify the values of x that would make the denominator equal to zero. When the denominator is zero, the expression becomes undefined.

In this case, the denominator is (x + 6). Setting the denominator equal to zero, we have:

x + 6 = 0

Solving for x, we subtract 6 from both sides:

x = -6

Therefore, the rational expression 6x / (x + 6) is undefined when x = -6.

When x is equal to -6, the denominator becomes zero, which causes division by zero. Division by zero is undefined in mathematics. Hence, for x = -6, the rational expression is not defined.

For any other real numbers other than x = -6, the expression is defined and can be simplified or evaluated.

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The length οf side x can be any value, as lοng as it is nοt 0.

We can use the trigοnοmetric ratiοs fοr 30°-60°-90° triangles tο sοlve fοr the value οf x.

In a 30°-60°-90° triangle, the sides are in the ratiο:

1 : √3 : 2

In this case, we have the side οppοsite the 60° angle (which is the lοnger leg) equal tο x√3 and the side οppοsite the 30° angle (which is the shοrter leg) equal tο x.

Sο we can set up the fοllοwing equatiοn:

x√3 = 2x sin 60°

Simplifying the right side:

sin 60° = √3/2

2x sin 60° = 2x(√3/2) = x√3

Substituting back intο the equatiοn:

x√3 = x√3

This is true fοr any value οf x, as lοng as x is nοt equal tο 0. Therefοre, the length οf side x can be any value, as lοng as it is nοt 0.

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Answer:12 yes 14 no 16 yes

Step-by-step explanation:its hard to explain

just plug the value in

12.

17 + 5 < 13

22 < 13

false

14.

10/2>6

5>6

false, you are correct

16.

-5 =< 0

it just has to be less OR equal

so it's true, it is a solution

Answer:

18000 m

Step-by-step explanation:

Hey there!

In order to solve this problem, we need to first know how many minutes are in an hour

As you know, there are 60 minutes in an hour so this means in 1 hour, he will climb 9000 meters two times

So 9000 two times is 18000,

Meaning, in 1 hour, Sam will climb 18000 m

Answer:

18,000m in an hour

Step-by-step explanation:

We know this because if its 9000 m in 30 minutes, we can do 9000 x 2 and get 18,000m for an hour.

The value of x in the chord of the circle using the chord-chord power theorem is 0.

The chord-chord power theorem simply state that "If two chords of a circle intersect, then the product of the measures of the parts of one chord is equal or the same as the product of the measures of the parts of the other chord".

From the figure:

The first chord has consist of 2 segments:

Line segment 1 = 27

Line segment 2 = ( x + 16 )

The second chord also consist of 2 sgements:

Line segment 1 = 24

Line segment 2 = ( x + 18 )

Now, usig the Chord-chord power theorem:

27( x + 16 ) = 24( x + 18 )

Solve for x:

27x + 432 = 24x + 432

27x - 24x = 432 - 432

3x = 0

x = 0

Therefore, the value of x is 0.

Option D) 0 is the correct answer.

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A hole exists on the graph of a rational function at any input value that causes both the numerator and denominator of the function to be equal to zero.

Factorize the numerator and denominator.

The common factor in the numerator and denominator is x+10. Equate x+10 with zero and find the value of x, which is the hole of the given function.

The function has only one hole at x = -10.

Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.

The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).

According to the problem, the total interest earned after one year is $519. So we can set up the equation:

0.11x + 0.07(6500 - x) = 519

Simplifying the equation:

0.11x + 455 - 0.07x = 519

0.04x + 455 = 519

0.04x = 64

x = 64 / 0.04

x = 1600

Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

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Answer:

An equation in the slope-intercept form will be:

Step-by-step explanation:

We know The slope-intercept form of the line equation

\(y = mx+b\)

where

Let x represent the time in months

Let y represent the amount of money remaining in the account.

Given that every month Monica withdraws $15 from this account for her contact lenses

Thus, the rate of change or slope = m = 15

Given that after 3 months she has $255 left in her account.

So, we take the point (3, 255)

substituting m = 15, x = 3 and y = 255 in the slope-intercept form to determine the y-intercept

y = mx+b

255 = 15(3) + b

switch sides

15(3) + b = 255

45 + b = 255

b = 255 - 45

b = 210

Now, substituting m = 15 and b = 210 in the slope-intercept form of the line equation

y = mx+b

y = 15x+210

Therefore, an equation in the slope-intercept form will be:

Answer: <BAC is 28.5

Step-by-step explanation:

line AO and Line OB are congruent (both are radius of the circle)

<BAC and <OBA are congruent

<AOB is linear to BOC so 180-57= 123 <AOB is 123

Triangle AOB is Isosceles

2a+123=180

2a=57

a=28.5

The coordinates of p which divides the line AB in ratio 3:1 is (3.75, 3.5).

The section formula provides the coordinates of a point that, either internally or externally, divides the line connecting two locations in a ratio.

P ( x , y ) = ( c ⋅ m + a ⋅ n m + n , d ⋅ m + b ⋅ n m + n ) .

Ratio of line = 3:2

m and n represents the ratios 3:2

let the coordinates of p(x, y).

using Section formula

= [ (3(4) + 1(3) / (3+1), 3(3) + 1(5) / 3+ 1]

= (15/ 4, 14/4)

= (3.75, 3.5)

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Answer:

Area of the shaded polygon= 372