PLEASE HELP
Mrs. Williams is deciding between two field trips for her class. The Science Center charges $80 plus $5 per student. The Dino Discovery Museum simply charges $7 per student. For how many students will the Science Center charge less than the Dino Discovery Museum charges?

fewer than 40 students
78 or fewer students
78 or more students
more than 40 students

1. The growth rate equation has a general form of:

y = A (r)^t

The function is growth when r≥1, and it is a decay when r<1. Therefore:

y=200(0.5)^2t                    --> Decay

y=1/2(2.5)^t/6                  --> Growth

y=(0.65)^t/4                       --> Decay

2. We rewrite the given equation (1/3)^d−5 = 81

Take the log of both sides:

(d – 5) log(1/3) = log 81

d – 5 = log 81 / log(1/3)

d – 5 = - 4

Multiply both sides by negative 1:

- d + 5 = 4

So the answer is D

Answer:

The answer is A. OR   3 5/6

Longer childhoods are closely linked to brain development, enhancing cognitive abilities by allowing more complex neuronal connections and greater adaptation to environmental stimuli. Extended brain development is also associated with increased brain plasticity, leading to better adaptability and higher complex problem-solving skills.

Research has found a significant relationship between longer childhoods and brain development. Humans have one of the longest childhoods among species, a period during which our brains continue to develop and mature significantly. This extended period of growth allows for more complex neuronal connections and adaptation to environmental stimuli, thus enhancing cognitive abilities.

A long childhood provides ample opportunities for learning and skill acquisition, and it is during this period that the brain is especially receptive to picking up new information. More prolonged brain development during childhood also tends to be associated with increased brain plasticity, meaning the brain's ability to change and adapt as a result of experiences. This plasticity aids in the formation of our identities and equips us to handle complex tasks and challenges as we grow.

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Answer: The number of granola bars in one pack = 8

The number of fruit rolls in one pack = 12

Step-by-step explanation:

Let x be the number of granola bars in each pack and y be the number of fruit rolls in each pack .

Then according to the question we have the following system of equations :

[tex]10x+6y=152.....................(1)\\7x+12y=200.......................(2)[/tex]

Multiply equation (1) by 2 we get

[tex]20x+12y=304......................(3)[/tex]

Subtract equation (2) from equation (3), we get

[tex]13x=104\\\\\Rigtarrow x=8[/tex]

Substitute x=8 in (1), we get

[tex]10(8)+6y=152\\\\\Rightarrow6y=152-80\\\\\Rightarrow\ 6y=72\\\Rightarrow y=12[/tex]

Hence, the number of granola bars in one pack = 8

The number of fruit rolls in one pack = 12

To find the square root of an improper fraction, simplify the fraction if possible, convert it into perfect squares, or use the properties of exponents. If it is already in simple form like 49/100, directly find the square roots of the numerator and denominator separately. Otherwise, use multiplication to manipulate the fraction into a more manageable form for taking square roots.

To find the square root of an improper fraction, the process involves several steps, similar to finding the square root of any number. First, simplify the fraction if possible. In some cases, this may involve multiplying the numerator and denominator by the same factor to make the radical easier to simplify. For instance, if you have an improper fraction like 49/100, you can easily identify that both the numerator and the denominator are square numbers. So, the square root of 49/100 equals the square root of 49 divided by the square root of 100, which simplifies to 7/10.

When the fraction cannot be simplified easily, a different approach is by converting the numerator and denominator into perfect squares, simplifying the expression within the radical, or using properties of exponents to re-express the square root. For example, if you have a fraction like 1/2, you can multiply both the numerator and denominator by 2 to get 2/4. Then you would rewrite the square root as the square root of 2 over the square root of 4, which simplifies to the square root of 2 over 2.

It is important for us to simplify rational expressions before multiplying or dividing because it makes our calculations easier.

The rational expression is in its simplest form when there is no common factor between the numerator and the denominator.

A rational number is a number that can be written in the form of p/q where q is not equal to zero.

We have,

Some examples of rational numbers are:

38/44 or 39/63

We can divide this rational number into a decimal number but it is easier for us if we can simplify it in its simplest form.

There is no common factor between numerator and the denominator in its simplest form.

The simplest form of 38/44.

= 38/44

= 2 x 19 / 2 x 22

= 19/22

The simplest form of 39/62 is

= 39/63

= 3 x 13 / 3 x 21

= 13/21

Thus,

It is important for us to simplify rational expressions before multiplying or dividing because it makes our calculations easier.

The rational expression is in its simplest form when there is no common factor between the numerator and the denominator.

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3 inside angles need to = 180, since it is a right triangle, the bottom left angle = 80 so the other 2 angles need to equal 90 degrees

 so you have:

(8x+2) + (9x+3) = 90

 combine like terms to get:

17x+5 = 90

subtract 5 from both sides:

17x = 85

 divide both sides by 17

x = 85/17 = 5

x = 5

Final answer:

Tom would need to rent the basketball court 15 times for the gym membership to be more cost-effective than paying the non-member rental fee.

Explanation:

To determine how many times Tom would need to rent the basketball court to make the membership cheaper than being a non-member, we can set up a cost equation and find the breakeven point. Let's assume that Tom rents the court x times. For a non-member, the cost is $11 each time, which results in 11x dollars. For a member, the cost includes the one-time membership fee of $135 plus $2 each time the court is rented, summing to 135 + 2x dollars.

To find the breakeven point, we equate the two costs and solve for x:

11x = 135 + 2x

9x = 135

x = 135 / 9

x = 15

Thus, Tom would need to rent the court 15 times for the membership cost to be cheaper than paying as a non-member.

The ordered pairs that satisfy the given inequality is required.

The points that are solutions are [tex](-4,2),(-2,1),(1,-1)[/tex]

The given inequality is [tex]y-4x\geq -5[/tex]

Let us substitute each point in the inequality

[tex](5,-2)[/tex]

[tex]y-4x\\ =-2-4\times 5\\ =-22\ngeq -5[/tex]

[tex](1,-1)[/tex]

[tex]-1-4\times 1\\ =-5\geq -5[/tex]

[tex](-4,2)[/tex]

[tex]2-4\times -4\\ =18\geq -5[/tex]

[tex](4,0)[/tex]

[tex]0-4\times 4=-16\ngeq -5[/tex]

[tex](-2,1)[/tex]

[tex]1-4\times -2=7\geq -5[/tex]

The points that are solutions are [tex](-4,2),(-2,1),(1,-1)[/tex]

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The algebraic expression representing the words "6 less than the product of 3 and a number" is shown as 3x - 6.

An algebraic expression is a combination of terms separated by mathematical operations (+, -, *, /).

A term is a combination of numerals and variables where variables are raised to integral powers.

In the question, we are asked to write the algebraic expression that represents the words "6 less than the product of 3 and a number".

Assuming the number to be x.

We first try to make the terms.

The term that will be formed using the words the product of 3 and a number is 3 * x = 3x.

The term using the word 6 is 6.

Now, to complete the expression, we combine the terms.

The words less than implies the difference. Thus the expression can be written as 3x - 6.

Thus, the algebraic expression representing the words "6 less than the product of 3 and a number" is shown as 3x - 6.

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Answer:

(C) [tex]{\angle}MOP=61^{\circ}[/tex]

Step-by-step explanation:

Given: It is given that angle MON is a straight angle and OP is bisects angle MOQ.

To find: The measure of the angle MOP.

Solution: It is given that angle MON is a straight angle and OP is bisects angle MOQ.

Thus, using the straight line property, we get

[tex]{\angle}MOP+{\angle}POQ+{\angle}QON=180^{\circ}[/tex]

[tex]2{\angle}MOP+{\angle}QON=180^{\circ}[/tex]

Substituting the given values, we get

[tex]2{\angle}MOP+58^{\circ}=180^{\circ}[/tex]

[tex]2{\angle}MOP=122^{\circ}[/tex]

[tex]{\angle}MOP=61^{\circ}[/tex]

Hence, option (C) is correct.

Answer: C - 61°

Step-by-step explanation: edge

Final answer:

Two functions are inverses if, when composed, they return the original input value (identity function). For example, an exponential function and its inverse, the natural log, undo each other. This can be checked with the equations by rearranging and setting equal to isolate constants or applying the functions one after the other.

Explanation:

How to Determine if Two Functions Are Inverses

To determine if two functions, F and G, are inverses of each other, you can compose the functions and see if the result is the identity function. The composition of two inverse functions will output the original input value, meaning that if you take a value x, apply function F to get F(x), and then apply function G to this result, i.e., G(F(x)), you should get x back if F and G are true inverses. The same must hold true in the reverse order, where G is applied first, followed by F: F(G(x)) = x.

To illustrate this concept, let's consider the exponential function and its inverse function, the natural log.Exponential functions are undone by their inverses, natural logs, according to the relation[tex]eln(x) = ln(ex)[/tex]to see this is with the equations involving a constant A, for instance, these can be rearranged to isolate ln A and set them equal to obtain an identity.

Another familiar context is the square and square root functions. To "undo" a square, you take the square root and vice versa. This "undoing" operation is a key characteristic of inverse functions.

Remember that not all functions have inverses, only those that are one-to-one, meaning for each x there is a unique y and vice versa, have inverses that can be defined over their entire domain.

The number goes on top tells line changes in the y direction and how much it rises.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

As, The top number indicates how much the line rises or moves in the y direction.

Given that the number is a 1 and is positive, we can infer that the line rises or moves up by one.

Hence, line changes in the y direction and how much it rises.

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