Rebecca is playing a video game that involves planting and cutting down trees. She moves up an energy level for each tree she plants, and she moves down a level for each tree she cuts. If Rebecca reaches energy level 10, she will earn bonus points.

Rebecca is currently at energy level 4. The results of her next 3 turns are:
Turn 1: 6 trees cut
Turn 2: 8 trees planted
Turn 3: 1 tree cut

Answer the questions to find out whether Rebecca earned bonus points in the next 3 turns. Use the number line to help you add.

A number line from -5 to 10.
1. Using only addition, write an expression that represents Rebecca's score after these three turns. (Remember that she starts at an energy level of 4.). (2 points)

2. What is Rebecca's energy level after Turn 1? (2 points)

3. What is Rebecca's energy level after Turn 2? (3 points)

4. What is Rebecca's energy level after Turn 3? Will she earn bonus points after Turn 3? Explain why or why not. (3 points)

Step-by-step explanation:

The area of a circle is radius²· π​

12x12=144

So the answer is 144π​.

Answer:

37.71428571425567788

The sample space is given as: S = { MEV, MEH, MSV, MSH, AEV, AEH, ASV, ASH }

The total number of sample points is 8

A sample point is one of the experiment's potential outcomes in a probabilistic experiment. Sample space is the collection of all sample points.

There are two results when you toss a coin: head (H) or tail (T) (T). There are four possible results when tossing two coins: HH, HT, TH, and TT, where the first letter denotes the result of the first toss and the second, that of the second. Each result is referred to as a sample point.

The list of all potential outcomes of an experiment is referred to as the sample space. Regardless of the number of ways an event might occur, each potential result is represented by a single point in the sample space.

For more questions on Sample space and sample points

https://brainly.com/question/24652200

#SPJ4

If JK has endpoints (-10, 1) and K(2, -2). Point L divides JK into two parts with lengths in a ratio of 2:1 then the possible locations of L is at (-7, 0.25)

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0

L divides JK into two parts with lengths in a ratio of 2:1

so JL:LK is either 2:1 or 1:2

Let us solve the midpoint of JK

Midpoint=(-10+2/2, 1-2/2)

M=(-4,-1/2)

Midpoint of JM is (-10-4/2, 1-1/2/2)

L: (-7, 1/4)

Hence, the possible locations of L is at (-7, 0.25)

To learn more on Ratios click:

https://brainly.com/question/13419413

#SPJ1

Step-by-step explanation:

the slope-intercept form is

y = ax + b

"a" being the slope, "b" being the y-intercept (the y-value when x = 0).

we see that with every increase of x by 1 y increases by 3.

so, the slope "a" is 3.

to get b we use one of the given points, e.g. (1, 5) :

5 = 3×1 + b = 3 + b

b = 2

so, our function is

y = 3x + 2

Answer:

|x| = x if x >= 0, -x if x < 0

Step-by-step explanation:

A collection of six objects can be chosen from one of 120 possibilities. These six configurations comprise BDF, BFD, DBF, DFB, FBD, and FDB.

A permutation is what? The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a mutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.

Out of the six things A, B, C, D, E, and F, rotations of items B, D, and F (a total of three items) must be listed.

Simply said, we must find every configuration for these three elements.

The three objects can be placed in three ways, which equals (3x2x1) ways, or six.

These six configurations are BDF, BFD, DBF, DFB, FBD, and FDB.

To know more about Permutations visit:

https://brainly.com/question/1216161

#SPJ4

Answer:

19 tables, f(19) = $280

1 table, f(1) = $33

Step-by-step explanation:

Let f(x) be the money Serenity makes each day, where x is the number of tables she serves.

Her saily income includes a fixed injcome of $20/day, plus $13/table in tips.

We can write f(x) = $20 + $13x

When x = 19, f(19) = $280

When x = 1, f(1) = $33

El número A = 52 es una solución del sistema de ecuaciones lineales.

En esta pregunta tenemos un sistema de dos ecuaciones lineales con dos incógnitas, de modo que existe la posibilidad de una solución única. Primero, escriba el sistema de ecuaciones descrito en el enunciado de la pregunta:

A / 4 = B / 9

A + B = 169

Segundo, despeje la variable A de la segunda ecuación del sistema de ecuaciones:

B = 169 - A

Tercero, elimine la variable B en la primera ecuación del sistema de ecuaciones y despeje la variable A:

A / 4 = (169 - A) / 9

9 · A = 4 · (169 - A)

9 · A = 676 - 4 · A

13 · A = 676

A = 52

Para aprender más sobre sistemas de ecuaciones lineales: https://brainly.com/question/20178040

#SPJ1

The exact value of the trigonometric expression [tex]\frac{tan-(2\pi/3) }{sin(7\pi /4)} - sec(-\pi )[/tex] in the simplified radical form is √6  +  1.

[tex]\frac{tan-(2\pi/3) }{sin(7\pi /4)} - sec(-\pi )[/tex]

We have the angle,

-2π/3  =  -120° = (360 - 120)°  = 240° = 60°

Put the value of -2π/3 in tan -2π/3, we get

tan -2π/3 =  tan (60)  = √3

7π/4 × 180/π  =  7 × (180/4)  =  7 × 45  =  315° =  45°

Put the value of 7π/4 in sin 7π/4, and we get

sin 7π/4 = sin (45°) = √2/2

sec (-π)  =  sec (π)  = -1

Now, substitute all the values in the given equation,

= {√3/(√2/2)} - (-1)

= (2√3/√2) + 1

= (2√3 × √2/√2 × √2) +1

= (2√6/2) + 1

= √6 + 1

--The given question is incorrect, the correct question is

''What is the exact value of the trigonometric expression? [tex]\frac{tan-(2\pi/3) }{sin(7\pi /4)} - sec(-\pi )[/tex] State your answer in simplified radical form."--

To know more about trigonometric expression, here

https://brainly.com/question/11659262

#SPJ4

Answer:

Mar Apr May

Receipts $1,155 $1,250 $

Expenses $1,100 $990 $900

Net Cash Flow $55 $ $45

Cumulative Balance $ $315 $360

The value of the equation is y = 0.75x , where y is the total cost of the ticket and x is the original cost of the ticket

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the original cost of the ticket be represented as x

Let the discounted price of the ticket be y

Now , the percentage of discount = 35 %

So , the discounted price of the ticket y = original cost of the ticket - ( 35/100 ) x original cost of the ticket

Substituting the values in the equation , we get

The discounted price of the ticket y = x - 0.35x

On simplifying the equation , we get

The discounted price of the ticket y = 0.75x

y = 0.75x   be equation (1)

Now , the cost of the ticket cannot be a negative value so it should lie in the first quadrant

Hence , the equation is y = 0.75x

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

The monomial that completes the expression hence it is the square of a binomial is given as follows:

9p².

The square of a binomial is modeled as follows, considering that the binomial can be either a sum or a subtraction.

The expression for this problem is given as follows:

x - 42pq + 49q².

In which x is the monomial.

Hence the system of equations to obtain the values of the parameters a and b are given as follows:

Hence the parameter b is obtained as follows:

[tex]b = \sqrt{49q^2}[/tex]

b = 7q.

The parameter a is obtained as follows:

2ab = 42pq

14aq = 42pq

14a = 42p

a = 42p/14

a = 3p.

Hence monomial that makes the expression that square of a binomial is given as follows:

a² = (3p)² = 9p².

More can be learned about the square of a binomial at https://brainly.com/question/12336181

#SPJ1

Answer:

Step-by-step explanation:

X=32

where M is we can see that those 3 sections add up to make 180.

Therefore 180-96=84 and 84/2=42 so the angles by 84 on both side is 42 since we know that LM and MN is the same we can then determine that the angles in the middle triangle add up to make 180.  By looking at the proofs at the top NO and LM are the same so both the bottom angles in each triangle is 42. So we know that 84 is the addition of both the bottom angles 180 - 84 is 96. We set that equal to 3x. 3x=96 Divide both sides by 3 x is equal to 32.

Answer:

Step-by-step explanation:

Answer:

D = (2x + 3)² + (x-2)(2x + 3)

Factoring D, we get:

D = (2x + 3)² + (x-2)(2x + 3)

= (2x + 3)(2x + 3 + x-2)

= (2x + 3)(3x - 2)

The volume of the pentagonal right pyramid with base area 30 square metres and height 5 metre is 50 m³.

Therefore the answer is 50 m³.

To find the volume of a pentagonal pyramid, we can use the formula:

V = (Bh)/3

where V is the volume, B is the area of the base and h is the height.

Area of the base is given, B = 30 m². From figure it is evident that the height of the pentagonal right pyramid is 5m. Therefore the volume of the figure is

V = 30 × 5/ 3

V = 50 m³

--The question is incomplete, answering to the question below--

"This pentagonal right pyramid has a base area of 30 m². What is the volume of the figure?"

To know more on volume of pyramid

https://brainly.com/question/17615619

#SPJ4

Four lines be chosen from four horizontal lines and four vertical lines in a plane such that a rectangular region is enclosed in 36 ways.

The four horizontal lines can be chosen in 4 choose 2 = 6 ways because we have to pick 2 out of 4, and the four vertical lines can be chosen in 4 choose 2 = 6 ways as well as

4C2 = 4!/ (2!×2!)

4C2 = 6

The total number of ways to pick four lines that enclose a rectangular region is 6×6 = 36, where each combination of two horizontal lines and two vertical lines forms a rectangle.

It's important to notice that the order of choosing the lines doesn't matter, so we use the combination formula (nCr) instead of permutation formula (nPr).

To know more on combination problem

https://brainly.com/question/29110744

#SPJ4

The pair of equations y = 0 and y = -5 has no solutions.

The pair of equations y = 0 and y = -5 can be written as:

y = 0

y = -5

Since both equations have the same value of y, 0 and -5, the equations are not equal and therefore there is no solution.

The pair of equations y = 0 and y = -5 have no solutions. This is because the equations have the same value of y, 0 and -5, which means that the equations are not equal. Therefore, there is no solution to this pair of equations. To determine if the pair of equations has a solution, you must check to see if the equations are equal. If the equations are not equal, then there is no solution. In this case, the equations are not equal, and thus there is no solution.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

The total surface area of the prism will be 290.125 Square units.

The surface area of a rectangular prism is the measure of how much-exposed area a prism has. Surface area is expressed in square units.

The surface area of a rectangular prism is given by:

SA = 2 (lh +wh + lw )

where

l = 3

w = 4.25

h = 18.25

SA = 2 (3x18.25 + 4.25x18.25 + 3x4.25)

SA = 2 (54.75 + 77.5625 + 12.75)

SA = 2 (146.0625)

SA = 290.125 square units

Learn more about surface area of the prism here: https://brainly.com/question/26889653

#SPJ1

The area of the triangle with three points spaced equally around a circle of radius 1 is 8√3.

The area of the triangle can be calculated using Heron's formula:

Area = √(s(s-a)(s-b)(s-c))

where s is the semiperimeter of the triangle and a, b, c are the side lengths.

The semiperimeter can be calculated as follows:

s = (a + b + c)/2

For this triangle, the side lengths are:

2, 2√2, and 2

Therefore, the semiperimeter is

s = (2 + 2√2 + 2)/2 = 4√2

The area of the triangle is then:

Area = √(4√2(4√2-2)(4√2-2√2)(4√2-2))

    = √(4√2*2√2*2*2)

    = 8√3

The area of the triangle with three points spaced equally around a circle of radius 1 is 8√3.

Learn more about triangle here

https://brainly.com/question/2773823

#SPJ4

The following are the valid bases for an exponential function:

An exponential function has the form f(x) = ab^x, where a and b are constants, and b is greater than 0 but not equal to 1. In this case, C, D, E, F, and G all have the correct form of an exponential function.

Options A, B and H are incorrect because:

The options C, D, E, F, and G are valid exponential functions because they have the correct form of f(x) = ab^x, where a and b are constants, and b is greater than 0 but not equal to 1.

The base can be negative or fractional, but as long as it's a constant, it's still a valid exponential function.

Learn more about exponential function here: brainly.com/question/2456547

#SPJ4

Answer:

[tex]\frac{5x-3}{4}[/tex]

Step-by-step explanation:

[tex]x=\frac{4y+3}{5} \\ 5x=4y+3\\ 5x-3=4y\\ \frac{5x-3}{4} =y[/tex]

Answer:

[tex]\boxed{a_5 = 40.5}[/tex]  

Step-by-step explanation:

Common ratio r of a geometric sequence is the ratio of each term to the previous term and is a constant

Thus if you have a sequence a₁, a₂, a₃, a,...
[tex]r = \dfrac{a_2}{a_1} = \dfrac{a_3}{a_2} = \dfrac{a_4}{a_3} \cdots[/tex]

For a geometric sequence with common ratio [tex]r[/tex] and a starting value of [tex]a_1[/tex]the nth term is given by the formula:
[tex]a_n = a_1r^{n-1}[/tex]

Here [tex]a_1 = 8, r = 1.5[/tex]

and we are asked to find the 5th term

[tex]a_5 = 8 \times 1.5^{(5-1)}\\\\= 8 \times 1.5^4\\\\=40.5\\\\[/tex]ANSWER

The terms of the sequence are
8, 12, 18, 27, 40.5 with 8 being the first term and 40.5 the 5th term

In the given figure, where triangle QPS = triangle SRQ, the value of

a. x = 47°

b. ∠PQS = 32°

c. ∠PSR = 74°

A triangle is a 3-sided polygon that is occasionally (though not very frequently) referred to as the trigon. Every triangle has three sides and three angles, some of which might be the same.

In a right triangle, the two sides opposite the right angle are referred to as the hypotenuse, and the other two sides are referred to as the legs. All triangles are bicentric and convex. The triangle's interior is that part of the plane it encloses; the exterior is the rest.

Given that  ∆QPS ≈ ∆SRQ

a) ∠QPS = ∠QRS

106° = 2x + 12

106° - 12 = 2x

2x = 94°

x = 47°

b) ∠RSQ = ∠PQS

∠SQR + ∠SRQ + ∠RSQ = 180°

42° + 2(47°) + 12 + ∠RSQ = 180°

148 + ∠RSQ = 180°

∠RSQ = 180° - 148°

∠RSQ = 32°

∠PQS = 32°

c) ∠PSR = ∠PSQ + ∠RSQ

[ ∠PSQ = 42° = ∠SQR ; ∠RSQ = 32°]

∠PSR = 42° + 32°

∠PSR = 74°

Thus, In the given figure, where triangle QPS = triangle SRQ, the value of x = 47°, ∠PQS = 32°, ∠PSR = 74°.

Learn more about triangle

https://brainly.com/question/2773823

#SPJ1

Answer:

6y - 14

Step-by-step explanation:

simplify the expression

2y - 6 + 4 (y -2)

Distribute the 4 to each term in the parentheses.

2y - 6 + 4y -8

Combine like terms

2y+4y-6-8

6y - 14

Answer:

[tex] \sf \: 6y - 14 [/tex]

Step-by-step explanation:

Given expression,

→ 2y - 6 + 4(y - 2)

Let's simplify the expression,

→ 2y - 6 + 4(y - 2)

→ 2y - 6 + 4(y) - 4(2)

→ 2y - 6 + 4y - 8

→ (2y + 4y) + (-6 - 8)

→ (6y) + (-14)

→ 6y - 14

Hence, the answer is 6y - 14.

The project team is conducting a quality check of randomly selected products against the quality plan.

What is probability ?

Probability is a branch of mathematics that deals with the likelihood of events occurring. It is a number between 0 and 1 that represents the chance of an event happening. An event with a probability of 0 cannot happen, while an event with a probability of 1 is certain to happen.

The project team is undertaking quality control activities. Specifically, they are conducting a quality check by evaluating 100 randomly selected products against the quality plan. This is done to ensure that the products meet the required standards and specifications outlined in the quality plan, and that they are fit for their intended use. Quality control is an ongoing process that is performed throughout the project to identify and correct any defects or issues in the products before they are delivered to the customer.

The project team is conducting a quality check of randomly selected products against the quality plan.

To learn more about probability visit : brainly.com/question/30034780

#SPJ4

The distance between the two people is changing at a rate of 3.2 mi/hr.

The distance between the two people can be calculated by using the Pythagorean theorem.

Let one person be at the origin (0, 0) and the other person be at (x, y). After 15 minutes, the first person will be at (3*15, 0) and the second person will be at (2*15*cos45, 2*15*sin45).

Using the Pythagorean theorem, the distance between them can be calculated as:

d = sqrt((3*15 - 2*15*cos45)^2 + (2*15*sin45)^2) = sqrt(225 + 225) = sqrt(450) = 21.213

The rate of change of distance is given by the formula d/t, where d is the distance and t is the time.

Therefore, the rate of change of distance between the two people after 15 minutes is 21.213/15 = 3.2 mi/hr.

Learn more about distance here

https://brainly.com/question/28956738

#SPJ4

Answer:

10.75 miles

Step-by-step explanation:

[tex]\frac{40}{100}[/tex]×x=4.3

40x=430

x=10.75

Answer:

The tablecloth overhang is the amount of tablecloth that hangs over the edges of the table.

The area of the square table is 1.3m * 1.3m = 1.69m^2.

The area of the round tablecloth is pi * (diameter/2)^2 = pi * (2/2)^2 = pi * 1^2 = pi * 1 = pi m^2.

The overhang is the difference between the area of the round tablecloth and the square table.

Overhang = pi m^2 - 1.69m^2 = pi - 1.69

To find the percentage of the tablecloth that overhangs the table, we can divide the overhang by the area of the tablecloth and multiply by 100.

Overhang % = (pi - 1.69) / pi * 100 = (pi - 1.69) / pi * 100 = (3.14 - 1.69) / 3.14 * 100 = 1.45 / 3.14 * 100 = 46.14%.

So, the percentage of the tablecloth that overhangs the table is 46.14%.