Devon and Albert are shelving books at a public library. Devon shelves 6 books at a time, whereas Albert shelves 9 at a time. If they end up shelving the same number of books, what is the smallest number of books each could have shelved?

Standard deviation for the given set of data { 6,7,8,9,10} is equal to √2.

As given in the question,

Given set of data is equal to :

{ 6,7,8,9,10}

[tex]x_{i}[/tex] = { 6,7,8,9,10}

Here total number of observation 'N' is equal to 5.

Mean [tex]\bar{x}[/tex] = ∑x / n

            = ( 6+ 7+ 8 + 9 + 10 ) / 5

            = 40 /5

            = 8

[tex]\sum (x_{i} -\bar{x})^{2}[/tex] = ( 6- 8)² + (7-8)² + (8 - 8)²+ ( 9 -8)² + (10 - 8)²

                 = 4 + 1+ 0 + 1+ 4

                 = 10

Standard deviation = [tex]\sqrt{ \frac{\sum (x_{i} -\bar{x})^{2}}{N}[/tex]

                                = √10/5

                                = √2

Therefore, standard deviation for the given set of data { 6,7,8,9,10} is equal to √2.

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Answer:

B

Step-by-step explanation:

1.20x + 3.60 < 9.60

1.20x < 9.60 - 3.60

1.20x < 6

x < 6 ÷ 1.20

x < 5

Answer:

Step-by-step explanation:

The question is asking how many times does 50 go into 425?

or 450/50 = ?

my calculator says it's 9 .  What does your calculator say?

since we now know it's 9 times,   we can just multiply 9 * 10 minutes

by observation of 9*10,  I get the answer,  what answer do you get?

Drake needs 144 ft² (squared feet) of fabric to make the 8 ft long and 18 ft tall sail.

The area (square units) of two lengths is the product of the multiplication of the two lengths.

The area refers to the space occupied by a two-dimensional object or structure.

Areas are stated in square feet to show the squared units occupied by such objects.

The length of a sail = 8 feet

The height of the sail = 18 feet

The square area = 144 ft² (8 x 18)

Thus, Drakes requires a fabric measuring 144 ft² (squared feet) to make the sail.

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As per given data of printing, the total number of pages print by printing center during the week is equal to 39,954 pages.

As given in the  question,

Number of copies of 26 pages article print by printing center is equal to 1,233 copies

Number of copies of 12 page article print by printing center is equal to 658 copies

Total number of pages print by printing center during this one week is equal to

= ( 1233 × 26 ) + ( 658 × 12 )

= 32,058 + 7896

=39,954 pages

Therefore, for the given data of printing, the total number of pages print by printing center during the week is equal to 39,954 pages.

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Answer:

Step-by-step explanation:

define function fg(x) :

Fg(x)  = f(g(x))

         = [tex]\frac{5}{x}[/tex] (4-2x)-1

         = [tex]\frac{20}{x}[/tex] - [tex]\frac{10x}{x}[/tex] - 1

         = 20 - 10x -1

         = 20 - 1 - 10x

         = 19 - 10x

Answer:

x= 2.7,-11.7 (sorry if im wrong) :'C

Answer:

$47.76

Step-by-step explanation:

77 : 100 = x : 207.65

x = (207.65 * 77)/100

x = 159.8905

final price = 207.65 - 159.8905 = 47.7595= $47.76

The interest amount is $120 when given principal amount $2000, rate of interest per year is 3% and time period is 2 years.

Given that,

p = $2,000, r = 3%, and t = 2 yr.

We have to find the i when i=prt.

Here,

i is interest amount.

p is principal amount.

r is rate of interest per year.

t is time period.

So,

Formula for finding interest amount is

i=prt

So,

i=2000(3/100)(2)

i=20×3×2

i=120

Therefore, The interest amount is $120 when given principal amount $2000, rate of interest per year is 3% and time period is 2 years.

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The ratio of green apples to all apples in the basket is 5:14 and the ratio of red apples to all apples in the basket is 9:14.

According to the question,

We have the following information:

There are five green apples and nine red apples in a basket.

Now, total apples in the basket are (5+9) which is 14.

Now, the ratio of green apples to all apples in the basket:

Number of green apples : total apples in the basket

5:14

Now, the ratio of red apples to all apples in the basket:

Number of red apples : total apples in the basket

9:14

Hence, the ratio of green apples to all apples in the basket is 5:14 and the ratio of red apples to all apples in the basket is 9:14.

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Answer:

  B.) 4x^2 - 15x - 54

Step-by-step explanation:

You want the product f(x)·g(x) when f(x) = 4x+9 and g(x) = x-6.

The distributive property can be used to find the product. Each term of one binomial is multiplied by every term of the other, and like terms are combined.

  f(x)·g(x) = (4x +9)·(x -6)

  = 4x(x -6) +9(x -6)

  = 4x² -24x +9x -54 = 4x² +(-24 +9)x -54

  f(x)·g(x) = 4x² -15x -54 . . . . . . . . . . matches choice B

__

Additional comment

The product of two binomials is sometimes described using the mnemonic FOIL, for First, Outer, Inner, Last. These refer to the locations of the terms involved in the four products

These products are the same as the ones we show above.

The FOIL mnemonic is only helpful for two binomials. Any polynomials can be multiplied using the distributive property.

Answer:

Slope = - 2

Explanation step by step:

Answer:

x= -3/5

Step-by-step explanation:

2x+21/5=3

2x+21/5-21/5=3-21/5           (subtract 21/5 from both sides)

2x=3-21/5                            (L.C.M=5)

2x= 15-21/5

2x= -6/5

2x/2=-6/5/2                        (divide both sides by 2)

x= -6/5x1/2                          (reciprocal)

x= -6/10

simplify:

x= -3/5

Answer: [tex]\frac{7}{3}[/tex]

Step-by-step explanation:

The two points found on the graph are:

The slope can be calculated as:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-3-4}{-1-2} =\frac{-7}{-3} =\frac{7}{3}[/tex]

1. The number of sides of the polygon is of: 12 sides.

2. The missing exterior angles are of: α = 48.5º.

3. The size of the exterior angle is of 20º, hence the polygon has 18 sides.

A regular polygon is a polygon in which all the sides have the same length.

The relation between the measure of the exterior angles of a regular polygon and the number of sides is given as follows:

Measure of each angle = 360º/number of sides.

For item a, the measure of each angle is of 24º, hence the number of sides is obtained as follows:

24º = 360º/number of sides.

24n = 360

n = 360/24

n = 12 sides.

The sum of the measures of the external angles of a polygon is always of 360º.

Hence, for item 2, the missing angles are obtained as follows:

2α + 90 + 55 + 40 + 78 = 360

2α + 263 = 360

2α = 97

α = 97/2

α = 48.5º.

An interior angle and it's exterior angle are supplementary, hence, for item 13, the measure of the exterior angle is of:

Exterior angle = 180º - 160º = 20º.

Then the number of sides of  the polygon is obtained as follows:

20n = 360

n = 360/20

n = 18 sides.

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The total bill that will be paid by the friends is $88.27.

Cost of meal = $72.50

Sales tax = 6.75%

The amount on tax will be:

= 6.75% × $72.50

= $4.89

Tip = 15% × $72.50

Tip = $10.88

The total bill will be:

= Cost of bill + Tax + Tip

= $72.50 + $4.89 + $10.88

= $88.27

The cost is $88.27.

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Answer:

$5

Step-by-step explanation:

Since $10 for 6 avocados and 3 = half of 6,

You would half $10 too = $5

Answer:

$5

Step-by-step explanation:

divide both numbers by 2 and there is your answer

Answer:

1/2

Step-by-step explanation:

Because the y is going up by 0.5 which in a fraction form is 1/2 and it isn't negative 1/2 because the number is growing and is not decreasing.

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

1) Find the difference between  and y

2) Find the pattern between the numbers

As we can see there is a pattern of subtract [tex]\frac{1}{2}[/tex] between every number

To find this just subtract each number by the other

As 0.5 is equal to [tex]\frac{1}{2}[/tex] the answer to the solution would be [tex]\frac{1}{2}[/tex]

Hope this helps, have a great day!!

Step-by-step explanation:

10 + x = 30

or, x = 30 - 10

x = 20

Answer:

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Answer:

Subtract 3 3/4 from 10 1/2.  Note that the LCD is 4, so 10 1/2 = 10 2/4.

What is    10 2/4

              -  3 3/4

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

                    ?

Since 2/4 is smaller than 3/4, you must borrow 1 from that 10.

Now your problem looks like   9 6/4

                                              -3 3/4

                                            ----------

                                                6 3/4   (answer)

The remnant of the board is 6 3/4 feet long.

Step-by-step explanation:

The Fourier series representation of the output y(t) is;

(a) y(t) = 0.097 cos(3πt - 67)

(b) y(t) = 0.097 sin(3πt - 67) + 0.051 cos(6πt + π/4 -78)

Given;

A causal continuous-time LTI system whose input x(t) and output y(t) are related by the following differential equation;

[tex]\frac{d}{dt}y(t) + 4y(t) = x(t)[/tex]

By taking Laplace's Transform;

sY(s) + 4Y(s) = X(s)

Y(s)/X(s) = H(s) = 1/(s + 4)

(a) When input x(t) = cos3πt

∵ ω = 3π

H(jω) = 1/(jω + 4)

H(jω₁) = 1/[tex]\sqrt{w^2+4^2}[/tex] = 0.097

∠H(jω) = -tan⁻¹(ω/4) = -67° = Ф₁

y(t) = H(jω₁)*cos(3πt + Ф₁)

→ y(t) = 0.097 cos(3πt - 67)

(b) When input x(t) = sin3πt + cos(6πt + π/4)

∵ ω = 6π

H(jω) = 1/(jω + 4)

H(jω₂) = 1/[tex]\sqrt{w^2+4^2}[/tex] = 0.051

∠H(jω) = -tan⁻¹(ω/4) = -78° = Ф₂

y(t) = H(jω₁) * sin(3πt + Ф₁) +  H(jω₂) * cos(6πt + π/4 + Ф₂)

→  y(t) = 0.097 sin(3πt - 67) + 0.051 cos(6πt + π/4 -78)

The Fourier series representation of the output y(t) is;

y(t) = 0.097 cos(3πt - 67)

y(t) = 0.097 sin(3πt - 67) + 0.051 cos(6πt + π/4 -78)

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The probability that a dart hits one of the shaded areas is 1/6 when a dart is thrown at a regular hexagon dartboard with the design shown.

The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions.

Here,

angle of hexagon=360/6=60°

using trigonometric ratios,

area of triangle=bh/2

=(h*h√3/2)/2

=h²√3/4

area of hexagon=6*area of triangle

=6*(h²√3/4)

=3√3*h²/2

area of rectangle=bh

=h*h√3

=h²√3

area of shaded region,

=3√3*h²/2-h²√3

=h²√3/2

area of 1 shaded region=(h²√3/2)/2

=h²√3/4

Probability of hitting one shaded area,

=(h²√3/4)/(h²3√3/2)

=1/6

When a dart is thrown at a standard hexagonal dartboard with the pattern shown, the likelihood that it will land in one of the shaded areas is 1/6.

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A population has a standard deviation of 10 and a mean of 75.

The sample mean has a standard deviation of 5 and an expectation of 100.The empirical rule states that there is a 68% probability of being between 95 and 105 (within one standard deviation of its expected value) if it is approximately normal.

What is meant by a standard deviation?

A measure of how dispersed the data are in relation to the mean is called the standard deviation (or ).Data with a low standard deviation are grouped around the mean, while data with a high standard deviation are more dispersed.

How can I determine the standard deviation?

Step 1: Locate the mean. Step 2: Find the square of the distance from the mean for each data point. Step 3: Sum the results of Step 2's values. Step 4: Divide by how many data points there are.

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Answer:

Bottom left

Step-by-step explanation:

Let's look at it as (1/3)^x first. This function would have a y-intercept of (0,1) (because (1/3)^0 is 1), and would then become (1/3) times smaller for every 1 unit increment of x. This would look like the top left graph in these options. However, we are given (1/3)^-x, which means, in terms of transformations, that the graph is flipped across the y-axis. Algebraically, this looks like (1/3)^(-x) which equals to  [tex]\frac{1}{(1/3)^x}[/tex], which simplifies down to 3^x, which would look like the bottom left graph.

Answer:

slope = 10

Step-by-step explanation:

Solve the equation for "y". In other words, isolate "y":

y + 7 = 10(x - 4)

y = 10(x - 4) - 7

y = 10x - 40 - 7

y = 10x - 47

Above is a linear expression in slope-intercept form "y = mx + b", where "m=slope" and "b=y-intercept". "m=10", so 10 is the slope

Answer:

3 feet

Step-by-step explanation:

All 4 sides are equal so 12/4=3