10) There are 5 times as many fiction books in the class library as there are nonfiction books. The number of information books is 7 more than the sum of the number of fiction and nonfiction books. There are 19 information books in the library. How many nonfiction books are there? How many fiction books are there?

From calculations, we can see that the number of smaller boxes to completely fill the larger one are; 250 boxes

The volume of a cuboid is given by the formula;

Volume = Length * Width * Height

Looking at the given dimensions of the larger box in the cuboid image attached, we can calculate the volume as;

Volume = 50 * 30 * 20

Volume = 30000 cm³

The length , width and height of smaller box are 10 cm, 3 cm and 4 cm respectively. Thus, the volume of smaller box is;

volume = 10 * 3 * 4

volume = 120 cm³

Thus, the number of smaller boxes to completely fill the larger one are;

n = 30000/120

n = 250 boxes

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The probability that the jury will make a wrong decision when it reaches a decision by majority rule is 0.033

To solve this, the number of jury that makes the wrong decision can be modeled as a binomial random with parameters n=7 and p=0.2. This jury as a whole will make wrong decision if 4, 5, 6, or 7 make the wrong decision.

We denote these events with A, B, C, D for 4, 5, 6, 7 respectively. The probability of this union is the sum of probabilities, so

P(Jury Error) = P(A)+P(B)+P(C)+P(D)

  = [tex]\left({{7} \atop {4}} \right.)(0.2)^{4} *0.8^{3} +(\left \({7} \atop {5}} \right)(0.2)^{5} *0.8^{2} +(\left{7} \atop {6}} \right.)(0.2)^{6} *0.8^{1} +(\left{7} \atop {7}} \right.)(0.2)^{7} *0.8^{0}[/tex]

   =0.033

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The most appropriate choice for perimeter of rectangle will be given by

It costs $76.16 to buy enough of the border to go around the room.

What is perimeter of a rectangle?

The total length of the outline of a rectangle is called perimeter of rectangle.

If the length of a rectangle is l units and breadth of a rectangle is b units, then perimeter of rectangle will be given by

                                      [tex]2 \times (l+b)[/tex] units

Here,

Length of room = 20 feet

Width of room = 12 feet

Perimeter of room = [tex]2 \times (20 + 12)[/tex]

                               = [tex]2 \times 32[/tex]

                               = [tex]64[/tex] feet

cost of 1 foot of border = $1.19

cost of 64 foot of border = $[tex]1.19 \times 64[/tex]

                                         = $[tex]76.16[/tex]

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New coordinate systems on the plane are frequently defined via coordinate transformations. The transformation's curves are representations of horizontal lines with the form v - constant and vertical lines with the form u - constant, respectively.

Answer the below figure

1. Reflect across y-axis

2.<4,5>  

Answer:

B'''(6, -15), C'''(-3, -12) (-3, -12)

Detailed explanation:

Point B concerns

As for point C,

In order to reflect a point across the x-axis, keep the x coordinate

constant while changing the y coordinate to its opposite.

<1, -3> the following translations: Add 1 to x, take 3 away from y.

Add 3 to both x and y to dilate k=3.

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Hey there!

6(2x - 6) + 2(13 - x) = 10
6(2x) + 6(-6) + 2(13) + 2(-x) = 10

12x - 36 + 26 - 2x = 10

10x - 10 = 10

ADD 10 to BOTH SIDES

10x - 10 + 10 = 10 + 10

SIMPLIFY IT

10x = 10 + 10

10x = 20

DIVIDE 10 to BOTH SIDES

10x/10 = 20/10
SIMPLIFY IT

x = 20/10

x = 2

Therefore, your answer should be:

Option D. x = 2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

After the sixteenth bounce, the basketball would be nearest which is 0.01 meters.

Height after dropping from a height = 3m

Bounce up rate = 75%

Height in first bounce = 2.25m (3 x 0.75)

Height in second bounce = 1.68m (2.25 x 0.75)

Height in third bounce = 1.26m (1.68 x 0.75)

Height in fourth bounce = 0.70m (0.94 x 0.75)

Height in fifth bounce = 0.525m (0.70 x 0.75)

Height in sixth bounce = 0.39m (0.52 x 0.75)

Height in seventh bounce = 0.29m (0.39 x 0.75)

Height in eighth bounce = 0.21m (0.29 x 0.75)

Height in ninth bounce = 0.15m (0.21 x 0.75)

Height in tenth bounce = 0.11m (0.15 x 0.75)

Height in eleventh bounce = 0.08m (0.11 x 0.75)

Height in twelfth bounce = 0.06m (0.08 x 0.75)

Height in thirteenth bounce = 0.04m (0.06 x 0.75)

Height in fourteenth bounce = 0.03m (0.04 x 0.75)

Height in fifteenth bounce = 0.02m (0.03 x 0.75)

Height in sixteenth bounce = 0.01m (0.02 x 0.75)... so on

After the sixteenth bounce, the basketball would be nearest.

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Answer:

91/8

Step-by-step explanation:

[tex]2\frac{4}{5} *4\frac{1}{6}[/tex]

→ Convert to improper fraction

14/5 × 65/16

→ Simplify

7 × 13/8 = 91/8

Answer: 33.7lbs

Step-by-step explanation: One N equals 0.225lb so you do that times 150

Hope this helped!!!!

Zeroes of the equation are i3√3 and -i3√3.

A value (a number) at which the polynomial evaluates to zero is referred to as the "zero of a polynomial." For instance, the zeros of the polynomial x²-3x+2 are 1 and 2. A polynomial's zeros are frequently referred to as its "roots." Every polynomial has a unique multiset of zeros, which is an unordered list. The coefficients of a zero polynomial, which is a constant polynomial, are all equal to 0. The value of the variable that brings a polynomial to zero is referred to as its zero. As a result, any real integer is the zero of the zero polynomial.

Given Data

(x) = -x² - 27

To find zeroes,

m(x) = 0

0 = -x² - 27

x² = -27

As we know,

i² = -1

x² = i²(27)

x² = i (±3√3)

x = i3√3

x = -i3√3

Zeroes of the equation are i3√3 and -i3√3.

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The product of the rational numbers - 5/8 and - 2/15 will be 1 / 20.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction is referred to as the PEMDAS rule. To answer the problem properly and accurately, this rule is applied.

The rational numbers are given below.

- 5/8 and - 2/15

Then the product of the rational numbers - 5/8 and - 2/15 will be given by the multiplication of the rational numbers - 5/8 and - 2/15.

⇒ - 5/8 × - 2/15

⇒ 5/8 × 2/15

⇒ 1/20

The product of the rational numbers - 5/8 and - 2/15 will be 1 / 20.

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The quotient [8a squared b]/[2ab squared] is simplified to 16/b

Algebraic expressions are simply known as arithmetic expressions which are made up of constants, variables, terms, factors and coefficients.

They are also made up of certain operations, arithmetic, mathematical which includes;

Given the expression;

[8a squared b] = x

[2ab squared] = y

Take the quotient of the values

(8a)²b/(2ab)²

Expand the bracket

64a²b/4a²b²

Now, divide the common terms, we have

16/b

Hence, the value is 16/b

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Answer:

Step-by-step explanation:

I hour = 60 minutes

So x hours = 24 minutes

to find x-->

Using the ratio method,

[tex]\frac{1}{60}[/tex] = [tex]\frac{x}{24}[/tex]

where x is the unknown number of hours we have to find.

After solving it, we get 60 * (x) = 24

we get x= 24/60

           x= 0.4 hours

Hence, 24 mins is 4/10 of an hour.

In the simplest form--> x= 2/5

The correct transformation include

The equation of the function is given as

y = |x|

The transformed functions are given as

y = |x| - 4

y = -|x + 4| + 3

The transformation 1

Here, we have

y = |x|

y = |x| - 4

This can be represented as

y = f(x) - 4

The description of the above transformation is:

The function y = |x| is shifted down by 4 units

The transformation 2

Here, we have

y = |x|

y = -|x + 4| + 3

This can be represented as

y = -f(x + 4) + 3

The description of the above transformation is as follows

Next, we graph the functions where the blue line represents y = |x|, the green line represents y = |x| -4 and the orange line represents y = -|x + 4| + 3

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Answer:

-2

Step-by-step explanation:

find two points on the line. You go down 2 units and 1 unit to the right.

The equation that models the situation is 10t + 13s = 25

T-shirts cost $10​ and shorts cost $13​.

The shorts cost $13.

The total amount to be spend is $25.

let

t = number of T-shirt

s = number of shorts

The equation that models the possible combinations of T-shirt t, and shorts  s, is as follows:

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Hence,

10t + 13s = 25

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Before a tax of 22 %, the product has an original price of $ 8032.79.

In this problem we find the case of a product that is sold including a given tax, that is, the price of the product before taxes. The original price can be found by means of the following equation, which is in terms of resulting price and tax rate:

C = C' / (1 + r / 100)

Where:

If we know that C' = $ 9800, r = 22 %, then the original price of the product is:

C = 9800 / (1 + 22 / 100)

C = 9800 / (122 / 100)

C = 9800 / 1.22

C = $ 8032.79

Therefore, the original price of the product, that is, the price before a tax of 22 %, is equal to $ 8032.79.

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The length of the side marked x is 10.2 cm.

We know that it is possible to solve the right angle triangle by the use of the Pythagoras theorem. Also, we could make use of the trigonometric ratios when we have to solve the right angled triangle.

The task here id to find the angle that has been marked x in the image that was shown above.

We are going to use the trigonometric ratios here;

Given that;

Cos θ = adjacent/ hypotenuse

θ = 40 degrees

Adjacent = x

Hypotenuse = 13.4 cm

adjacent = cos 40 * 13.4 cm

adjacent = 10.2 cm

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The lowest possible value for N  is 21.

The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory. The smallest number that can be divided by both numbers is the LCM of two numbers. Finding the lowest common denominator (LCD) of two or more fractions is a key application of LCM. It is crucial when combining, dividing, and contrasting two or more fractions.

Given Data

LCM of 700 and N

is  2²x3x5²x7²

700 and N = 2²x3x5²x7²

700 and N = 14700

N = [tex]\frac{14700}{700}[/tex]

N = 21

The lowest possible value for N  is 21.

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The probability of getting the same number is 1/6.

The ratio of good outcomes to all possible outcomes of an event is known as the probability.

utilizing two ethical six-sided dice.

The likelihood that the dice will produce the same number must be determined.

36 total outcomes were obtained.

The positive results are (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6).

6 good outcomes total.

Therefore, the likelihood of an event is equal to the ratio of good outcomes to all possible outcomes.

Changing the values

Event probability is 6/36, or 1/6.

As a result, there is a 1/6 chance that both dice will reveal the same number.

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Answer:

Complementary angles have a sum of 90°.

(x - 22) + (x - 16) = 90

2x - 38 = 90

2x = 128

x = 64

Substitute x into angle A

A = 64 - 22 = 42°

Answer: $1.25x + $3.50 ≤ $45

Step-by-step explanation:

The total cost for a given number of miles is the initial cost number of miles multiplied by the cost per mile.

So, the expression for the cost is 1.25x+3.50.

Since she has $45 to spend, Jessica can spend no more than this, so the inequality is that in Option 3.

Answer:

Step-by-step explanation:

Answer:

10 times

Step-by-step explanation:

To figure this out, the first thing we will do is to find the LCM (Least Common Multiple). We will do this by making a list of the denominators that we have right now. Right now we have [tex]\frac{20}{4}[/tex] and [tex]\frac{3}{6}[/tex]. We will use 4 and 6 to make a list to find our multiple that is in both lists. (That comes up first)

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32...

Multiples of 6: 6, 12, 18, 24, 30, 36, 42...

Now, we just realized that we have 24 that are in common with both 4 and 6. Now we will multiply both the numerator and denominator by the same number to have the denominator equal 24.

[tex]\frac{20}{4} * \frac{6}{6}[/tex] = [tex]\frac{120}{24}[/tex] & [tex]\frac{3}{6} * \frac{4}{4}[/tex] = [tex]\frac{12}{24}[/tex]

Now that we have [tex]\frac{120}{24}[/tex] and [tex]\frac{12}{24}[/tex]. We will read the question again about how many [tex]\frac{3}{6}[/tex] equal to [tex]\frac{20}{4}[/tex]. Since we have our fractions, we will add [tex]\frac{12}{24}[/tex] multiple times until we get [tex]\frac{120}{24}[/tex].

[tex]\frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} = \frac{120}{24}[/tex]

Therefore, [tex]\frac{3}{6}[/tex] equals to [tex]\frac{20}{4}[/tex] 10 times.

The method and additional information would prove ΔONP and ΔMNL similar by the AA similarity postulate is A. Use a rigid transformation to prove ∠NOP ≅ ∠NML.

The AA Similarity Postulate states that two angles in one triangle must be congruent with two angles in another triangle for the two triangles to be comparable. The AA Similarity Postulate is a shortcut for demonstrating the similarity of two triangles.

In this case, B is incorrect because angles NOP and ONP are not corresponding angles

Also, options (c) and (d) are incorrect, because they prove the similarities by lines segments.

In conclusion, the correct option is A.

The complete question is written below.

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Complete question

Which method and additional information would prove ΔONP and ΔMNL similar by the AA similarity postulate?

A. Use a rigid transformation to prove ∠NOP ≅ ∠NML.

B. Use a rigid transformation to prove ∠NOP ≅ ∠ONP.

C. Use rigid and nonrigid transformations to prove segment LN over segment ON = segment PN over segment MN.

D. Use rigid and nonrigid transformations to prove segment LM over segment ON = segment PN over segment MN

Take a look at the picture below to see how 3/4 looks when represented on a number line.

This is further explained below.

Generally, A image of a graded straight line is what is known as a number line, and its purpose is to provide a visual representation of the actual numbers.

It is generally accepted that a real number may be assigned to each point on a number line and that each real number can be assigned to a point.

In conclusion, consider the image below for the number line representation of 3/4

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slope = 5 or 5 rise over 1 run.

y-intercept = (0,-2)

Answer:

1. 82 2. 82 3. 82 4. 98 5. 123 6. 122 7. 119 8. 60 9. 60 10. 125 11. 35 12. 105

Answer:

The fraction of the shop’s T-shirts are blue T-shirts that are on sale and are size medium is 1/ 8

Step-by-step explanation: