Elizabeth wants to use a sheet of fiberboard 27 inches long to create a skateboard ramp with a 17 ∘ ∘ angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest tenth of an inch if necessary.

Answer:

[tex]{ \rm{rate \: of \: change = \frac{R _{2}(t) - R _{1}(t) }{t _{2} - t _{1}} }} \\ [/tex]

For 0 < t < 10; 226.6 < R(t) < 205.6

[tex]{ \rm{ = \frac{205.6 - 226.6}{10 - 0} }} \\ \\ { \rm{ = - \frac{21}{10} }} \\ \\ = { \rm{ - 2.1}} \\ \\ = 2.1[/tex]

Negative indicates an inverse proportionality, or decrease in temperature

For 30 < t < 50; 157.6 < R(t) < 119.6

[tex] = { \rm{ \frac{119.6 - 157.6}{50 - 30} }} \\ \\ = { \rm{ - \frac{38}{20} }} \\ \\ = { \rm{1.9}}[/tex]

Answer:

Need to know the shape of object (cylinder, cone, etc)

Combinations exist ways to select elements from a collection in mathematics where the order of the selection exists irrelevant. He can choose the question in 28 ways.

Combinations exist mathematical operations that count the number of potential configurations for a set of elements when the order of the selection exists is irrelevant. You can select the components of combos in any order.

The combination formula is used to determine how many options there are for choosing things from a collection so that the order in which they are chosen is irrelevant. Combination, to put it simply, is the choosing of items or things from a bigger group when the order doesn't important.

Given: Number of questions in part A = 10

Number of questions in part B = 10

A student chooses 7 from part A and 4 from part B

Required number of ways = ( 10C7 × 10C4) × ( 10C3 × 10C6)

= 5040 × 24/ 6 × 720

= 28

He can choose the question in 28 ways.

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The latest possible time that Lyle could leave home in order to arrive at his friend’s house on time is 8:30 a.m

Given that Lyle is driving from home to his friend’s house, a distance of 720 km. He plans to drive at an average speed of 80 km per hour, take an hour for lunch, and take two 15- minute breaks and He must arrive at his friend’s house by 7:00 p.m.

The time it takes Lyle to drive to his friend's house is given by t = d/v where

Given that Lyle is driving from home to his friend’s house, a distance of 720 km. He plans to drive at an average speed of 80 km per hour, we have that

Substituting the values of the variables into t, we have

t = d/v

= 720 km/80 km/h

= 9 h

So, it takes Lyle 9 hours to drive.

Now, since Lyle takes an hour for Lunch and two 15 minutes breakes, this extra time is t' = 1 h + 2 × 15 min

= 1 h + 30 min

= 1 h + 30 min/60 min × 1h

= 1 h + 0.5 h

= 1.5 h

So, the total time Lyle takes to reach his friend's house is T = t + t'

= 9 h + 1.5 h

= 10.5 h

Since Lyle must reach his friend's place no later than 7:00 pm, 10.5 hrs from 7:00 pm is 8:30 am.

So, Lyle must leave no later than 8:30 a.m

So, the latest possible time that Lyle could leave home in order to arrive at his friend’s house on time is 8:30 a.m

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The value of A is 3 square unit

A square number is a number multiplied by itself. This can also be called 'a number squared'. The symbol for squared is ².

Formula: s²= s x s

given that, the question is testing the concept of substitution.

A=12s^2

If s=1/2,

Substituting s with 1/2 we get;

A=12(1/2)^2

=12×1/4

=3

The answer is 3 unit squared. There is no fraction in the answer.  

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Answer:

A has a value of 3 square units.

Step-by-step explanation:

Any number multiplied by itself is a square number. This is also referred to as "a number squared." 2 represents the squared sign.

Equation: s2=s x s

As a result, the question is putting the idea of substitution to the test.

A=12s^2

If s=1/2,

Substituting s with 1/2 we get;

A=12(1/2)^2

=12×1/4

=3

The answer is 3 unit squared. There is no fraction in the answer.  

Answer:

No, Dell does not have enough soil to fill the planter.

Step-by-step explanation:

The probability that Alice, David, and Carlene are selected is 1/120.

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.

3 people can be chosen from 10 people in 10C3 ways and Alice, David, and Carlene can be chosen in only one way.

10C3 = 10! / (10 - 3)! 3!

= (10 [tex]*[/tex] 9 [tex]*[/tex] 8 [tex]*[/tex] 7!) / (7! [tex]*[/tex] 3 [tex]*[/tex] 2 [tex]*[/tex] 1)

= 120

So, the number of possible outcomes is 120 and the number of favorable outcomes is 1. Therefore, the probability is 1/120.

The probability that Alice, David, and Carlene are selected is 1/120.

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The squared root of 56 minus the squared root of 189 is -6.26 .

We have given an statement that squared root of 56 minus the squared root of 189  which can be represented in expression as

        [tex]\sqrt{56} -\sqrt{189}[/tex]                    ..(1)

Prime factorization 56 is given by

    [tex]\sqrt{56} =\sqrt{2\times2\times2\times7} \\\sqrt{56} =2\sqrt{14} \\\sqrt{56} =2\times3.74\\\sqrt{56} =7.48[/tex]

Prime factorization 189 is given by

    [tex]\sqrt{189} =\sqrt{3\times3\times3\times7} \\\sqrt{189} =3\sqrt{21} \\\sqrt{189} =3\times4.58\\\sqrt{189} =13.74[/tex]

Putting above values in equation (1) , we get

   [tex]\sqrt{56} -\sqrt{189}=7.48-13.74\\\sqrt{56} -\sqrt{189}=-6.26[/tex]

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Answer:

D

Step-by-step explanation:

If the light build can be 50 and less, the sign needs to be ≤ because it means less than or equal to.

  The value of the geometric mean of the numbers 36 and 24 is.

Gm ( 36, 24) = 12√6

     The definition of geometric mean is a calculation that is performed on a set of numbers which consists of calculating the square root of the product between them, the equation is as follows:

Gm (a,b) = √ab

  Then in our case that we have the values 40 and 15, these are equivalent to the variables a and b

  We substitute and solve for the square root

Gm (36, 24) = √ab = √36×24

Gm (36, 24) = √864

Gm (36, 24) = √6×144

Gm ( 36, 24) = 12√6

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Refer to the graph below for the graphical representation of the given equation y = 49x.

Graph:

Refer to the graph given below for the equation y=49x.

Therefore, the graph of the given equation y=49x is shown below.

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The correct option that proves that angles 1 and 2 are supplementary is; B: Angles 1 and 4 form a Linear Pair and angles 4 and 8 are congruent as corresponding angles.

Supplementary angles are two angles whose measures add up to 180° . The two angles of a linear pair are always supplementary.

Now, looking at the given image, we can see a total of 8 angles formed from the transverse lines.

Angles 1 and 4 can be classified as Linear Pairs because Linear pair of angles are formed when two lines intersect each other at a single point.

Similarly, angle 4 and angle 8 are classified as corresponding angles because Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal

Thus, the correct option that proves that angles 1 and 2 are supplementary is; B: Angles 1 and 4 form a Linear Pair and angles 4 and 8 are congruent as corresponding angles.

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Answer:

Step-by-step explanation:

given: 5^3/5^7

= 1/5^(7-3)

= 1/5^4

= 1/625

final answer: 1/625

Answer:

[tex]5^{-4}[/tex]

Step-by-step explanation:

using the rules of exponents

• [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]

• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

given

[tex]\frac{5^{3} }{5^{7} }[/tex]

= [tex]5^{(3-7)}[/tex]

= [tex]5^{-4}[/tex]

= [tex]\frac{1}{5^{4} }[/tex] ← if required with a positive exponent

Answer:

Step-by-step explanation:

History(H),Economics(E),Literature(L)

1a).To find History(H) only is

H only =H-HE-HL+HEL

H only =60-30-16+10=24

b).E only=50-30-22+10=8

c). L only=48-22-16+10=20

2).no of candidates who sat for the exam is 24+8+20=52

The approximate number of fleas she should expect to remove from the cats on Day 14 is 1

The given parameters are

Function type: exponential function

Day 0 = 87

Day 6 = 14

An exponential function is represented as

y = ab^x

Where

y = a, when x = 0

This means that a = 87

So, we have

y = 87b^x

Day 6 = 14 means that

When x = 6, y = 14

So, we have

87b^6 = 14

This gives

b^6 = 0.161

Take the 6th roots of both sides

So, we have

b = 0.74

Subsitute b = 0.74 in y = 87b^x

y = 87(0.74)^x

On day 14, we have

y = 87(0.74)^14

Evaluate

y = 1.28

Approximate

y = 1

Hence, the approximate number of fleas she should expect to remove from the cats on Day 14 is 1

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Answer:

d=10

d=2r=2·5=10

There is need of total of 9 levels to stack 285 boxes.

A sequence can be taken as the set of numbers having a particular order for all the terms or we can say that arrangement of numbers in some order is known as sequence.

Some examples for sequence are :

2,4,6,8,10,12

3,9,27,81,243

The recursive sequence is the sequence in which any term in the sequence can be find with the help of previous term of that sequence.

In a sequence , first term always known as initial term.

and difference between two terms are known as common difference. It is denoted by d.

General form of sequence is :

[tex]a_1,a_2,a_3,----,a_n[/tex]

where , [tex]a_n[/tex] = last term in sequence.

According to question,

Also, number of boxes at level recursively n =[tex]a_{n-1} + n^2[/tex]

The formula to find number of level for 285 boxes is :

[tex]a_n > =285[/tex]

now, find each level

[tex]a_1 = 1 , a_2 = 1 + 2^2 = 5 , a_3 = 5+3^2 = 14,\\a_4 = 14 + 4^2 = 30\\a_5 = 30 + 5^2 = 55\\a_6 = 55 + 6^2 = 91\\a_7 = 91 + 7^2 = 140\\a_8 = 140 + 8^2 = 204\\a_9 = 204 +9^2 = 285[/tex]

thus, to stack 285 boxes total numbers of level are 9.

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The complete question is :

Suppose you're stacking boxes in levels which make squares. The numbers of boxes in each successive levels make a sequence. The figure show top four levels as view from top or above.

a. How many boxes of same size would need for next lower level?

b. How many boxes of same size would need to add the 3 levels?

c. Suppose you are stacking 285 boxes. Then, how many total levels will you have?

 x = -2 is  input value produces the same output value for the two functions .

What are the function's input values?

The domain of the function is the collection of input values. The range of the function is the collection of output values.

What input and output functions are used?

The fundamental functions for input and output are getchar, putchar, puts, scanf, and printf. To transfer single characters, utilize the first two functions, getchar and putchar.

Which four sorts of functions are there?

Four main categories can be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.

The input  value which produces the same input .

value for two function is  x = -2

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The given geometric sequence, with first term = 4 and ratio = 0.1, has the formula for its nth term: a(n) = 4 . 0.1ⁿ⁻¹. The first five terms are: 4, 0.4, 0.04, 0.004, 0.0004

The formula of the nth term of a geometric sequence is:

a(n) = a₁ . r^(n-1)

with a₁ is the first term and r is the ratio. In a geometric sequence, the ratio is constant and equal to a(n)/a(n-1).

In the given problem,  a₁ =4, r=0.1, therefore:

a(n) = a₁ . r^(n-1)

a(n) = 4 . 0.1ⁿ⁻¹

To find the first five terms, replace n with 1, 2, 3, 4, and 5.

a₁ = 4

a(2) = 4 . 0.1²⁻¹

       = 4 . 0.1¹ = 0.4

a(3) = 4 . 0.1³⁻¹

       = 4 . 0.1² = 0.04

a(4) = 4 . 0.1⁴⁻¹

       = 4 . 0.1³ = 0.004

a(5) = 4 . 0.1⁵⁻¹

       = 4 . 0.1⁴ = 0.0004

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Equation of line B is y=7/2x

A line is simply an object in geometry that is characterized under zero width object that extends on both sides. A straight line is just a line with no curves. So, a line that extends to both sides till infinity and has no curves is called a straight line.

Straight line formulas= y=mx+ c

                                                  = y-y1=m(x-x1)

              slope, m= (y1-y2)/(x1-x2)

given that, B passes through P and parallel to A

so one of the points on the line  is P(2,7)

and one more point is O(0,0) if we extend line B parallelly to A

So we can conclude that B passes through O and P

we know equation of straight line is y-y1=m(x-x1)

on solving we get equation of line B is, y=7/2x

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Answer:

Line B's equation is y=7/2x.

Step-by-step explanation:

An object in geometry known as a line is simply one that extends on all sides and has zero width. Simply put, a straight line is a line devoid of curves. A straight line is one that does not curve and extends to infinity on both sides.

Straight line formulas= y=mx+ c

                                                 = y-y1=m(x-x1)

             slope, m= (y1-y2)/(x1-x2)

given that, B passes through P and parallel to A

so one of the points on the line  is P(2,7)

Moreover, if we stretch line B parallel to A, the final position is O(0,0).

Therefore, we can say that B goes through O and P.

Y-y1=m is the straight line's known equation (x-x1)

After solving, we obtain the equation y=7/2x for line B.

The series that is related to a triangle with 10 cans in the bottom row can be expressed in summation notation as  [tex]\sum\limits^{10}_{n=1} {n}[/tex]

Let us consider the simpler triangle formed by stacking cans as in the attached picture.

As we can see in the picture, if the bottom row contains 3 cans, then the triangle will have 3 rows. The number of cans in each row decreases by 1. We can expand this idea for a triangle with 10 cans in the bottom row.

In this case, there will be 10 rows and the number of cans in each row  decreases by 1.

10th row : 10 cans

9th row : 9 cans

and so on.

We can express the number of all cans in this triangle as a series, starting from the top row (the first row):

1 + 2  + 3 + ... + 10

The explicit formula of the nth term is: a(n) = n.

Hence, in the summation notation, it can be written as:

[tex]\sum\limits^{10}_{n=1} {a(n)} = \sum\limits^{10}_{n=1} {n}[/tex]

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After solving the equation, the value of y = x/4 for the equation 12 y=3 x.

⇒ 12 y=3 x

⇒ y = 3x/12

⇒ y = x/4

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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The difference of squares is a quadratic polynomial of the form is a² - b² = (a + b) · (a - b).

Difference of two squares is a particular case of a second order polynomial whose form is the following:

a² - b² = (a + b) · (a - b)

Now we proceed to demostrate the equivalence between the two expressions:

a² - b² → (a + b) · (a - b)

a² - b²                             Given

(a² - b²) + 0                     Modulative property

(a² - b²) + a · b - a · b      Existence of additive inverse

(a² + a · b) + (- b² - a · b) Associative property

a · (a + b) - b · (a + b)      Definition of power / Distributive property / (- a) · b = - a · b

(a + b) · (a - b)                 Commutative and distributive property /  

(a + b) · (a - b) → a² - b²

(a + b) · (a - b)                 Given

(a + b) · a + (a + b) · (- b) Distributive property

a² + a · b - a · b - b²        Distributive property / (- a) · b = - a · b / Definition of power

(a² - b²) + (a · b - a · b)    Associative property

a² - b²                             Existence of the additive inverse / Modulative property / Result

Hence, the difference of squares is a quadratic polynomial of the form is a² - b² = (a + b) · (a - b).

The statement is incomplete. The complete form is: What is a difference of two squares?

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the correct option is D, the inverse relation is only a function if it passes the vertical line test.

A relation maps elements from one set (called the domain) into elements of another set (called the range).

A relation is a function only if each element in the domain is mapped into only one element of the range. So, there is something called the vertical line test.

It says that if at any part of the graph of the relation you can draw a vertical line that intercepts the graph of the relation more than once, then it is not a function. Passing the vertical line test means that no vertical line intercepts the graph more than once.

Then the correct option is D, the inverse relation is only a function if it passes the vertical line test.

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Answer:

AC is the longest side

Step-by-step explanation:

• the longest side is side opposite largest angle in the triangle

• the shortest side is opposite the smallest angle in the triangle

the largest angle is ∠ B = 68°

the longest side is then AC

Answer:

1 15 degrees

Step-by-step explanation:

Exterior angle is equal to sum of opposite interior angles

We're given:

We can start by isolating one of the variables, like y:

[tex]3x-y=-6\\-y=-3x-6\\y=3x+6[/tex]

Now we can find four solutions by plugging in any number for x:

[tex]y=3x+6\\y=3(1)+6\\y=3+6\\y=9[/tex]

First solution: (1,9)

[tex]y=3x+6\\y=3(2)+6\\y=6+6\\y=12[/tex]

Second solution: (2,12)

[tex]y=3x+6\\y=3(3)+6\\y=9+6\\y=15[/tex]

Third solution: (3,15)

[tex]y=3x+6\\y=3(4)+6\\y=12+6\\y=18[/tex]

Fourth solution: (4,18)

First solution: (1,9)

Second solution: (2,12)

Third solution: (3,15)

Fourth solution: (4,18)