The data set shows the lengths, in minutes, of different musical performances.
36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20
What is the interquartile range (IQR) of the data set?

Answer:

96 cubic inches

Step-by-step explanation:

To calculate the empty space that will be left in the box once the book is inside, we need to find the difference between the volume of the box and the volume of the book.

Volume of the box:

20" x 12" x 2 1/2" = 600 cubic inches

Volume of the book:

18" x 3 1/2" x 8" = 504 cubic inches

Empty space in the box:

600 cubic inches - 504 cubic inches = 96 cubic inches

Therefore, there will be 96 cubic inches of empty space left in the box once Kylie puts the book inside.

The statement that justifies that ΔBAE ≅ Δ DAE is Side-Side-Angle Postulate. The best option from the statements given is "Classify A triangle". That is definition of a triangle.

The Side Side Angle Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Between both triangles, here are the congruent sides and angles:

AB ≅ AD  - Given

AE  = EA - Reflexive Property. Note that AE is shared by both triangles so we have Two congruent sides.

AC ⊥ BD - that means ∠AEB = ∠AED = ∠BEC = ∠CED = 90°

(perpendicular bisector theorem)

A perpendicular bisector is a line segment that cuts another line segment at 90 degrees. A perpendicular bisector, in other terms, meets another line segment at 90° and splits it into two equal halves.

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Answer:

A. the set of all points in a plane that are the same distance from a given point called the center

Step-by-step explanation:

Answer:

Step-by-step explanation:

Note that the substance(s) that Jacob and Natalie should use to make a cold pack that will do the BEST job of keeping food cool is " Sample 1, because it absorbs the most energy" (option A)

In physics, energy is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light.

Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed

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Full Question:

Although part of your question is missing, you might be referring to this full question:

People use self-warming and self-cooling devices for many purposes such as keeping drinks cold or food warm. Medical professionals also use these types of devices to store medicines and other substances that need to stay colder than room temperature. These cooling and warming devices use a chemical reaction to produce their chilling and warming effects. Compounds combine in endothermic (heat absorbing) or exothermic (heat releasing) reactions within these devices to help them keep items cool or warm.

Jacob and Natalie are asked by their science teacher to design a warming or cooling device. They decide to design a cold pack that can be used to help keep food cool. Jacob

and Natalie read about different substances that can be used inside cold packs and learn that most cold packs use endothermic reactions to cool objects. They find the table below while researching.

Which sample uses the substance(s) that Jacob and Natalie should use to make a cold pack that will do the BEST job of keeping food cool?

answer choices

Sample 1, because it absorbs the most energy

Sample 2, because it absorbs the most energy

Sample 3, because it absorbs the least energy

Sample 4, because it absorbs the least energy

The value of the given angle which is N and that is rounded to the nearest hundredth would be =45.58°

To calculate the missing angle N, the sine formula should be used and it is given below;

= a/sin A = b/sin B

Where;

a= 7

A= 90°

b= 5

B= N

That is;

7/sin90°= 5/sinN

sinN= 5×1/7

= 5/7

= 0.714285714

N = Sin-1(0.714285714)

= 45.58°

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Using a rule for exponents, we can simplify the expression and see that the correct option is B, 8.

Remember that when we have the quotient of two powers with the same base (like in this case, where the base is 2) the outcome will be a power of the same base, such that the exponent is equal to the difference between the other two exponents.

The rule is:

[tex]\frac{x^m}{x^n} = x^{m - n}[/tex]

Then we can use that to simplify the expression, we will get:

[tex]\frac{2^6}{2^3} = 2^{6 - 3} = 2^3 = 2*2*2 = 8[/tex]

We can see that the correct option is B.

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Answer:

84°

Step-by-step explanation:

opposite angles in a cyclic quadrilateral (4-sided shape) add up to 180.

c + 96 = 180

c = 180 - 96 = 84°

Answer:

66.6 miles/hour

Step-by-step explanation

50/7.5 = 66.6

Answer:

Step-by-step explanation:

The cylinder contains three areas, the top circle, the bottom circle, and the middle. The surface area of it is the sum of the three;

[tex]As = \pi r^{2} + \pi r^{2} + 2\pi r (h) \\[/tex]

or

[tex]As = 2\pi r^{2} + 2\pi r (h)[/tex]

where h is the height,

104[tex]\pi[/tex] = [tex]2 \pi (4)^{2} + 2\pi (4)(h)[/tex]

h = 9m

Function graph that has y- intercept of 3 is g(x) = 3[tex](\frac{1}{4}) ^{x}[/tex].

y- intercept will be 3 when we will put value of x = 0 and y will be 3 that graph will have y intercept 3

A) h(x) = 5[tex](2)^{x}[/tex]

when x = 0

Any number with zero power is always 1

h(x) = 5

B) h(x) = 5[tex](0.5)^{x}[/tex] + 0.5

when x = 0

h(x) = 5 + 0.5

h(x) = 5.5

C) g(x) = 3[tex](\frac{1}{4}) ^{x}[/tex]

when x = 0

g(x) = 3

Here we get y intercept as 3.

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Answer:

Step-by-step explanation:

Based on the information, tere are 16224000 possible passwords.

There are 52 possible letters for the first two characters (26 uppercase and 26 lowercase).

There are 6 possible special characters for the third character.

There are 10 possible numbers for the last three characters.

We can use the Fundamental Counting Principle to calculate the number of possible passwords. The Fundamental Counting Principle states that if there are n ways to do one thing and m ways to do another thing, then there are n×m ways to do both things.

In this case, there are 52×52=2704 ways to choose the first two characters, 6 ways to choose the third character, and 10×10×10=1000 ways to choose the last three characters.

Therefore, there are 2704×6×1000

=16224000 possible passwords.

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The only relation that is a function is the one in option C.

A relation maps elements from a set called the domain into elements of another set, called the range.

Particularly, if each of the elements in the domain is mapped to a single value in the range, then we have a function.

When we have a graph, we can do the vertical line thest, if a vertical line touches the graph more than once, then it is not a function, with that we can discard the two graphs in the left.

And for option D, we can see that the input 22 is mapped into two different values.

The remaining option, C, is the correct one.

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The equation that could be used to represent the whole pizza is 4/8 + 2/8 = 6/8 = 3/4.

We are given that;

Pizza ate by children= 4/8

Pizza ate by Jonus= 2/8

Now,

4/8 + 2/8 + x = 1

where x is the fraction of the pizza that was saved for later. This equation shows that the sum of the fractions of the pizza that were eaten and saved is equal to 1, which represents the whole pizza. To solve for x, we can simplify the fractions and subtract them from both sides:

4/8 + 2/8 = 6/8 = 3/4

3/4 + x = 1

x = 1 - 3/4

x = 1/4

Therefore, the equation will be 4/8 + 2/8 = 6/8 = 3/4

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Answer:

Three Hundred.

Answer:

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

There are 15 black pens out of total 80.

The probability of a black pen is:

The roots of the cubic function:

f(x)=  x³ + 3x² - x - 3

are x = 1, x= -1, x = -3

We want to find the roots of the function:

f(x)=  x³ + 3x² - x - 3

We know that x = 1 is a root, because f(1) = 0.

Then we can write that function as:

(x - 1)*(x - a)*(x - b)

Where a and b are the other two roots, then we need to solve:

x³ + 3x² - x - 3 = (x - 1)*(x - a)*(x - b)

Expanding the right side, we will get:

x³ + 3x² - x - 3 = x³ + (-a - b - 1)x² + (a + b + ab)x + (-ab)

Comparing like terms, we can see that:

(-a - b - 1) = 3

(a + b + ab) = -1

(-ab) = -3

The third equation gives:

ab = 3

Replacing that in the second one we get:

a + b + 3 = -1

a + b = - 1 - 3 = -4

a + b = -4

a = -4 - b

Replacing that in the relation above:

ab = 3

(-4 - b)*b = 3

-4b - b² = 3

b² + 4b + 3  = 0

The zeros of that function are:

[tex]b = \frac{-4 \pm \sqrt{4^2 -4*3*1} }{2*1} \\\\b = \frac{-4 \pm 2}{2}[/tex]

Then if b is the value when we take the positive sign:

b = (-4 + 2)/2 = -1

the value of a is:

a = -4 - b = -4 + 1 = -3

These are the other two roots.

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The angle between A and B is 90 degrees.

The angle between two vectors A and B, you can use the dot product formula:

A · B = [tex]|A| |B| cos(\theta)[/tex]

where A · B is the dot product of A and B, |A| is the magnitude of A, |B| is the magnitude of B, and theta is the angle between the two vectors.

First, let's calculate the dot product of A and B:

A · B = (3)(4) + (2)(-3) + (-6)(1)

= 12 - 6 - 6

= 0

Next, let's calculate the magnitudes of vectors A and B:

|A| = √((3)² + (2)² + (-6)²)

= √(9 + 4 + 36)

= √(49)

= 7

|B| = √((4)² + (-3)² + (1)²)

= √(16 + 9 + 1)

= √(26)

Now, we can substitute these values into the formula to find the angle theta:

0 = [tex](7)(\sqrt(26)) cos(\theta)[/tex]

Since the dot product is 0, we know that the angle between A and B is either 90 degrees or 270 degrees.

To determine which one it is, we can look at the sign of the dot product. If it's positive, the angle is acute (less than 90 degrees) and if it's negative, the angle is obtuse (greater than 90 degrees).

The dot product is 0, so the angle is orthogonal (perpendicular) and is exactly 90 degrees.

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Answer:

2x^2-5x-12

Step-by-step explanation:

(2x+3)(x-4) can be simplified using the acronym FOIL, which stands for "first, outer, inner, last." This means that you multiply the first terms in each group, the the outer terms, then the inner terms, and lastly the last terms in  each group.

2x*x=2x^2

2x*-4=-8x

3*x=3x

3*-4=-12

Combine those and you get 2x^2-8x+3x-12. Combine like terms, and your final answer is 2x^2-5x-12

Fifty-four and eight tenths" can be expressed in expanded form as the sum of 54 (representing 50 + 4) and 0.8, which represents the decimal part.

To write the number "fifty-four and eight tenths" in expanded form, we can break it down into its individual place values and numerical components.

The number "fifty-four" can be broken down as follows:

The digit 5 represents the value of 50, which is 5 tens.

The digit 4 represents the value of 4, which is 4 ones.

So, "fifty-four" can be expressed as 50 + 4.

Next, we have "eight tenths". This can be expressed as 8/10 or simply 0.8 since each tenth is equal to 0.1.

Putting it all together, the number "fifty-four and eight tenths" can be written in expanded form as:

50 + 4 + 0.8

Simplifying further, we can combine the integer and decimal parts:

54 + 0.8

Therefore, the expanded form of "fifty-four and eight tenths" is 54 + 0.8.

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Answer:

Jurek is 8. His brother is 14

Step-by-step explanation:

let's call Jurek J, and let's call his brother B.

his brother is 6 years older than Jurek.

So, B = J + 6.

B + J = 22

(J + 6) + J = 22

2J + 6 = 22

2J = 16

J = 8

so Jurek is 8

B + J = 22, B = 22 - J = 22 - 8 = 14.

Brother is 14

Answer:

20 square feet

Step-by-step explanation:

area of a triangle = (1/2) base x height

The "base" for this one gigantic triangle is the 'top' of the diagram - - - - it's the entire 3+7 = 10 side. (We can calculate the area of the whole thing at once. We don't have to do the left and the right halves separately!!!)

The height is 4.

So area = (1/2) base x height

= (1/2) * 10 * 4

= 20 square feet

The given supply curve is: Qs = 6700 + 75P

To find how many AirPods Apple would produce at a price of $185, we can substitute P = $185 in the equation and find the corresponding quantity (Qs).

Qs = 6700 + 75P Qs = 6700 + 75($185) Qs = 6700 + 13875 Qs = 20575

Therefore, at a price of $185, Apple would produce 20,575 AirPods according to the given supply curve.

The area of the larger square is 900% of the area of the smaller square.

Let's assume that the side of the smaller square is "s". Therefore, the area of the smaller square will be:

Area of smaller square = s²

Now, the sides of the square are increased by a scale factor of 3, which means that the new side length of the larger square will be 3s. The area of the larger square will be:

Area of larger square = (3s)² = 9s²

To find the percentage of the larger square with respect to the smaller square, we need to divide the area of the larger square by the area of the smaller square, and then multiply by 100:

(9s²/s²) x 100 = 900%

This means that the larger square is 9 times the area of the smaller square.

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Answer:

 y = 4.87x + 2.28 Is the answer

Step-by-step explanation:

( i see a little bit of part b but do not see the FULL QUESTION which is a problem and i cannot answer.. )

using a:

THE ULTIMATE LINEAR REGRESSION CACLAULTOR

yes it is the epic i get:

y = 4.87x + 2.28

Nothing more noting less ikr

y = 4.87x + 2.28 Being the answer

1260° is the sum of all interior angles of the given polygon.

Generally speaking, the measure of the angle at the center of a regular polygon is equal to 360 degrees.

The sum of the interior angles in a polygon can be calculated using the formula:

Sum of interior angles = (n - 2) * 180 degrees

In this formula, "n" represents the number of sides or vertices of the polygon.

In the given problem the number of sides is 9.

Thus,

Sum of all interior angle = (9-2)*180

The sum of all interior angles = 1260°

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Jorge's gross earnings for the week assembling 317 game boards would be $633.

To calculate Jorge's gross earnings for the week, we need to determine how many game boards fall into each pay rate category and then multiply the quantity by the corresponding pay rate. Let's break down the calculation step by step:

Determine the number of game boards that fall into each pay rate category:

First 100 boards: 100 boards (as the rate applies to the first 100 boards).

Next 200 boards: Since Jorge assembled 317 boards in total and the first 100 boards are already accounted for, we subtract 100 from 317 to get 217 boards that fall into this category.

Over 300 boards: We check if the total number of boards exceeds 300. In this case, since Jorge assembled 317 boards, we have

317 - 300 = 17

boards that fall into this category.

Calculate the earnings for each category by multiplying the number of boards by the corresponding pay rate:

Earnings for the first 100 boards:

100 boards * $1.82 per board = $182.

Earnings for the next 200 boards:

217 boards * $1.92 per board = $416.64.

Earnings for the over 300 boards:

17 boards * $2.08 per board = $35.36.

Sum up the earnings from each category to find the gross pay for the week:

Gross pay = Earnings for the first 100 boards + Earnings for the next 200 boards + Earnings for the over 300 boards

Gross pay = $182 + $416.64 + $35.36

Gross pay = $633.

Therefore, Jorge's gross earnings for the week assembling 317 game boards would be $633.

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Answer:

75 points ( more than?? you didn't add the drop-down list ) today's score.

Hope this helps!

Step-by-step explanation:

y = mx + b

y = 5x + b

(50) = 5(6) + b  -> b = 20

y = 5x + 20

If Carlos plays the game today for 0 min, he will get a score of 20 ( odd...  how is that possible )

But tomorrow, he plans to play for an extra 15 min, so he will get a score of 95 ( ( 5 × 15 ) + 20 ). The question asks for how much his score will change so his score will change by 75 points ( 95 - 20 ).

You could also just do 15 × 5 to get 75 :)

The dot product of vectors a and b is option D. 30.

To find the dot product of two vectors, you need to multiply their corresponding components and then sum the results.

Let's calculate the dot product of vectors a = <5, 2> and b = <4, 5>:

a • b = (5 x 4) + (2 x 5)

= 20 + 10

= 30

Therefore, the dot product of vectors a and b is 30.

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