Amanda has a job transporting soft drinks by truck. Her truck is filled with cans that weigh 14 ounces each and bottles that weigh 70 ounces each. There is a combined total of 930 cans and bottles in her truck. Let x be the number of 14 -ounce cans in her truck. Write an expression for the combined total weight (in ounces) of the cans and bottles in her truck.

The total revenue (R) can be expressed as a function of the price (p) per item by multiplying the price by the quantity demanded (q). Given the demand equation q = -5p + 500, the total revenue equation is R(p) = -5p^2 + 500p.

The total revenue (R) can be expressed as a function of the price (p) per item by multiplying the price by the quantity demanded (q).

Given the demand equation q = -5p + 500, we can substitute q in the total revenue equation with -5p + 500:

R(p) = p * (-5p + 500)

Simplifying, we distribute p to both terms inside the parenthesis:

R(p) = -5p^2 + 500p

So, the total revenue (R) as a function of price (p) is R(p) = -5p^2 + 500p.

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The first four terms of the sequence defined by n squared plus 5 are 6, 9, 14, and 21.

The first four terms of the sequence defined by the expression n squared plus 5, which can be represented mathematically as n^2 + 5.

To find the terms, we simply substitute the first four positive integers (1, 2, 3, 4) for n and calculate:

For n = 1: 1^2 + 5 = 1 + 5 = 6

For n = 2: 2^2 + 5 = 4 + 5 = 9

For n = 3: 3^2 + 5 = 9 + 5 = 14

For n = 4: 4^2 + 5 = 16 + 5 = 21

The required probability is 0.55 while selecting a group that has an average value of at least $26.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

John has six bills of paper money in the following denominations $1, $5, $10, $20, $50, and $100.

The total number of possible combinations = [tex]^6c_3[/tex] = 6!/313! = 20

Combinations for which the average value is at least $26:

(1.5.100), (1,10,100), (1.20,100). (1.50,100), (5,10,100), (5,20,100), (5,50,100), (10,20,100), (10,20,50), (10,50,100), (20,50,100)

Number of favorable combinations = 11

So, required probability = 11/20 = 0.55

Thus, the required probability is 0.55 while selecting a group that has an average value of at least $26.

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By substituting the x-values into the linear function g(x) = 4x - 5, we find g(2) = 3 and g(-4) = -21. Therefore, the value of g(2) is larger than the value of g(-4).

To determine the values of g(2) and g(-4) for the function g(x) = 4x - 5, we simply substitute the x-values into the function.

For g(2):

For g(-4):

Now, we can compare the two values:

The value of g(2), which is 3, is larger than the value of g(-4), which is -21.

The statement that is true concerning [tex]\( g(2) \)[/tex] and [tex]\( g(-4) \)[/tex] is option a) : The value of [tex]\( g(2) \)[/tex] is larger than the value of [tex]\( g(-4) \)[/tex].

To compare and contrast [tex]\( g(2) \)[/tex] and [tex]\( g(-4) \)[/tex] for the function [tex]\( g(x) = 4x - 5 \)[/tex]:

1. Calculate [tex]\( g(2) \)[/tex] :

 [tex]\[ g(2) = 4 \cdot 2 - 5 = 8 - 5 = 3 \][/tex]

2. Calculate [tex]\( g(-4) \)[/tex] :

 [tex]\[ g(-4) = 4 \cdot (-4) - 5 = -16 - 5 = -21 \][/tex]

Now, let's analyze the values:

- [tex]\( g(2) = 3 \)[/tex]

- [tex]\( g(-4) = -21 \)[/tex]

Comparing these values:

- [tex]\( g(2) \)[/tex] is positive (3).

- [tex]\( g(-4) \)[/tex] is negative (-21).

Therefore, [tex]\( g(2) \)[/tex] is greater than [tex]\( g(-4) \)[/tex]. This means:

[tex]\[ \text{The value of } g(2) \text{ is larger than the value of } g(-4). \][/tex]

Explanation:

The function [tex]\( g(x) = 4x - 5 \)[/tex] calculates a linear relationship where [tex]\( g(2) \)[/tex] evaluates to 3 and [tex]\( g(-4) \)[/tex] evaluates to -21. This comparison clearly shows that [tex]\( g(2) \)[/tex] yields a larger value than [tex]\( g(-4) \)[/tex]. This result stems from the fact that when x = 2 , [tex]\( g(x) \)[/tex] outputs a positive value, while for x = -4 , [tex]\( g(x) \)[/tex]outputs a larger negative value. Therefore, option:

Complete question : Given the function g(x) = 4x −5, compare and contrast g(2) and g(−4). Choose the statement that is true concerning these two values.

a The value of g(2) is larger than the value of g(−4).

b The value of g(2) is smaller than the value of g(−4).

c The value of g(2) is the same as the value of g(−4).

d The values of g(2) and g(−4) cannot be compared.

Answer:  The correct option is (B) [tex](3x-4).[/tex]

Step-by-step explanation:  Given that Sam decides to build a square garden whose area is as follows:

[tex]A=9x^2-24x+16~\textup{square feet}.[/tex]

We are to find the length of one side of the garden.

Since the given garden is of a square shape, so the length of each side is same.

That is, the area of the garden must be a perfect square trinomial.

We have

[tex]A\\\\=9x^2-24x+16\\\\=(3x)^2-2\times 3x\times 4+4^2\\\\=(3x-4)^2.[/tex]

Since the area of a square is (length)², so the length of one side of the garden is [tex](3x-4)~\textup{feet}.[/tex]

Thus, (B) is the correct option.

Converting 35°C to degrees Fahrenheit is equal to 95°F.

Option D is the correct answer.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Using the formula F = (9/5)C + 32, where C is the temperature in Celsius and F is the temperature in Fahrenheit.

Substituting C = 35°C into the formula:

F = (9/5) × 35 + 32

F = 63 + 32

F = 95°F

Therefore,

35°C is equal to 95°F.

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The graph resembles a "V" shape with its vertex at the origin.

The function f(x) = |x| - 1 is a piecewise function that represents the absolute value of x minus 1.

The absolute value function  |x| returns the distance of x from the origin on the number line.

When x is positive or zero, |x| = x , and when x is negative, |x| = -x.

Thus, f(x) = |x| - 1behaves differently for positive and negative values of x .

For [tex]\( x \geq 0 \)[/tex], the function is f(x) = x - 1, and for x < 0, the function is f(x) = -x - 1.

The graph of  f(x)  consists of two straight lines intersecting at the point (0, -1), with a slope of 1 for [tex]\( x \geq 0 \)[/tex] and a slope of -1 for x < 0.

The graph resembles a "V" shape with its vertex at the origin.

The function modeling the total area of the four pens is [tex]A(w) = w * ((750 - 3w) / 2)[/tex]. The maximum area can be found by taking the derivative of this function, setting it to zero, and solving for w.

The subject in question is Mathematics, specifically calculus and problem-solving involving areas. The rancher with 750 ft of fencing intends to make a rectangular area divided into four pens. Let's define w to be the width and l to be the length of the rectangle.

1] Since the total length of the fence is 750 ft and it will be divided into 3 parts for the width and 2 parts for the length, the function for calculating length will be [tex]l = (750 - 3w) / 2[/tex]. Since the area of a rectangle is given by A=w*l, we can substitute our equation for l into our Area function. Therefore, our function will be [tex]A(w) = w * ((750 - 3w) / 2).[/tex]

2] To find the maximum area of the rectangles, you would need to find the derivative of the Area function and solve for w. After that, plug the value of w into the area function to get maximum area. The exact calculation requires calculus skills and could be taught in a high school Calculus course.

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Answer:

A. 1

B. 2

Step-by-step explanation:

We have been given an image of a triangle. We are asked to find remote interior angles of angle 5 for our given triangle.

We can see that angle 5 is an exterior angle. We know that remote interior angles are those, which are inside the triangle and opposite to exterior angle.

We can see that angle 2 and angle 1 are are opposite angles of angle 5 and they are inside our given triangle.

Therefore, option A and B are correct choices.

Final answer:

Remote interior angles are non-adjacent angles within the same triangle. Relative to angle 5, angle 1 and angle 2 are remote interior angles because they are inside the triangle and do not share a vertex with angle 5.

Explanation:

In this mathematics problem, we are asked to find the remote interior angles of a given angle, which are angles that are inside the triangle and non-adjacent to the exterior angle being considered. For example, if we have a triangle with angles labeled 1, 2, 3, 4, 5, and 6, and we want to find the remote interior angles relative to angle 5, we would look for the angles inside the triangle that do not share a vertex with angle 5.

From the available options:

Therefore, options A (1) and B (2) are the correct answers to this problem.

Answer: 0.99483

Step-by-step explanation:

Given : A box contains four 40-W bulbs, five 60-W  bulbs, and six 75-W bulbs.

Total bulbs : 4+5+6=15

The probability of selecting a 75-W bulb :[tex]p=\dfrac{6}{15}=0.4[/tex]

Using the binomial probability :-

[tex]P(X)= ^nC_xp^x(1-p)^{n-x}[/tex], where P(x) is the probability of getting success in x trials , p is the probability of getting success in each trial and n is the total number of trials.

We have,

The  probability that at least two bulbs must be  selected to obtain one that is rated 75W :-

[tex]P(x\geq2)=1-(P(x<2))\\\\=1-(P(x=0)+P(x=1))\\\\=1-(^{15}C_0(0.4)^0(0.6)^{15}+^{15}C_{1}(0.4)^1(0.6)^{14})\\\\=1-((1)(0.6)^{15}+(15)(0.4)(0.6)^{14})\ \ [\because\ ^nC_0=1\ \&\ ^nC_1=n]\\\\\approx1-(0.00047+0.00470)\\\\=1-0.00517=0.99483[/tex]

Hence, the required probability = 0.99483

Final answer:

To find the number of cars George needs to sell in the next month to have a mean of 24, calculate the total number of cars he has sold in the past seven months. Subtract that total from 24 multiplied by 8 (including the past seven months and the next month). Divide the result by 1 to get the number of cars George needs to sell in the next month.

Explanation:

To find the number of cars George needs to sell in the next month to have a mean (average) number of sales per month of 24, we need to calculate the total number of cars he has sold in the past seven months. Then, we can subtract that total from 24 multiplied by 8 (as George wants a mean of 24 sales per month for a total of 8 months, including the past seven months and the next month). Finally, we divide the result by 1 to get the number of cars George needs to sell in the next month.

In this case, the total number of cars George has sold in the past seven months is 18 + 22 + 26 + 12 + 25 + 20 + 19 = 142.

So, to determine the number of cars George needs to sell in the next month to have a mean of 24, we perform the following calculation:

(24 * 8) - 142 = 192 - 142 = 50.

Therefore, George needs to sell 50 cars in the next month to have a mean number of sales per month of 24.

Answer:

8.10

Step-by-step explanation:

The student's question involves counting the number of spirals in a cactus, which corresponds to two consecutive numbers in the Fibonacci sequence. The exact answer would depend on the actual count, which cannot be determined without the photograph.

The question asks about the phenomenon related to the Fibonacci sequence observed in natural patterns, specifically in plant architecture such as cacti spirals. The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. It is often observable in nature, for example, in the arrangement of leaves or the spirals on sunflower heads and cacti.

In order to answer the question, one would need to physically count the number of left-handed and right-handed spirals on the cactus. The Fibonacci sequence relevant to this context begins with 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on. Since the given answer choices are consecutive terms from this sequence, the correct numbers would be identified based on the actual spiral counts which are expected to be consecutive Fibonacci numbers.

Without the photograph, it is impossible to provide the specific numeric answer, but we can understand that the two numbers representing the left-handed and right-handed spirals on the cactus would be consecutive Fibonacci numbers as indicated by the options provided: A) 34 and 55, B) 5 and 8, C) 8 and 13, D) 21 and 34, e) 13 and 21.

Answer:

Step-by-step explanation: Taking into account that they are all like terms they can be combined, therefore there would only be one term. For example:

5x-3x+6x-x+2x=

Combine the like terms

2x+6x-x+2x=

It can be simplified further

8x-x+2x=

7x+2x=

9x