The Lopez family is looking to rent a large truck for their upcoming move. With Felipe's
Moving, they would pay $90 for the first day plus $1 per additional day. With Springdale
Rent-a-Truck, in comparison, the family would pay $40 for the first day plus $6 per additional
day. Before deciding on which company to use, Mrs. Lopez wants to find out what number of
additional days would make the two choices equivalent with regards to cost. How many
additional days would that be?
Write a system of equations, graph them, and type the solution.
​

Answer:

Let's call the number of 7,000 gallon tank cars "x1", the number of 14,000 gallon tank cars "x2", and the number of 28,000 gallon tank cars "x3".

We can write the following constraints based on the total carrying capacity of the fleet:

7,000x1 + 14,000x2 + 28,000x3 = 532,000

x1 + x2 + x3 = 25

x1, x2, x3 >= 0 (since we can't have a negative number of tank cars)

This is a linear programming problem, which can be solved using simplex method or the graphical method.

By using the graphical method, we find that there are multiple optimal solutions. For example, one solution is x1 = 11, x2 = 7, and x3 = 7. This means that the manufacturer should lease 11 7,000 gallon tank cars, 7 14,000 gallon tank cars, and 7 28,000 gallon tank cars to meet the total carrying capacity requirement of 532,000 gallons.

So, the answer to the question is: There are multiple possible combinations of how the tank cars should be leased. The combinations are obtained from the equations x1 = 11 + 7t, x2 = 7 + 7t, and x3 = 7 + 7t.

To solve the problem we would use tangent as a trigonometric function and find the unknown value.

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

From the given triangle we observe that the given values are:

Angle B, side a and side b.

To find any of the unknows in the three we use the trigonometric function tangent.

Tan α = opposite side / adjacent side

For the given figure:

Tan B = b / a

Hence, to solve the problem we would use tangent as a trigonometric function and find the unknown value.

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The absolute value inequalities for the different lengths are

1) 4.19 ≤  x ≤  4.21

2) 3.3 ≤  x ≤  3.7

What is an absolute value inequality?

The non-negative value of a real number x without regard to its sign is known as its absolute value or modulus in mathematics and is indicated by the symbol |x|.

An expression using absolute functions and inequality signs is known as an absolute value inequality. One example of an absolute value inequality with a larger than symbol is the statement |x + 3| > 1.

1)  length x = 4.2 cm with a tolerance of 0.01 cm

Absolute value inequality is:

|x - 4.2| ≤ 0.01

This can be written as:

           x ≤ 4.21

            x ≥ 4.19

2)  length x =  3.5 cm with a tolerance of 0.2 cm

Absolute value inequality is:

|x - 3.5| ≤ 0.2

This can be written as:

           x ≤ 3.7

            x ≥ 3.3

Therefore the absolute value inequalities for the different lengths are

1) 4.19 ≤  x ≤  4.21

2) 3.3 ≤  x ≤  3.7

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Answer:e

Step-by-step explanation:t

Answer: The momentum of the truck before the collision is given by the formula:

p_i = m_i * v_i, where m_i is the mass of the object and v_i is its velocity.

The momentum of the truck before the collision is:

p_i (truck) = 3000 kg * 10 m/s = 30000 kg m/s

The momentum of the car before the collision is:

p_i (car) = 1000 kg * 0 m/s = 0 kg m/s

The total initial momentum of the system is the sum of the initial momenta of the truck and car:

p_i (total) = p_i (truck) + p_i (car) = 30000 kg m/s + 0 kg m/s = 30000 kg m/s

After the collision, the final momentum of the system is the sum of the final momenta of the truck and car:

p_f (total) = p_f (truck) + p_f (car)

Let's call the velocity of the truck after the collision v_f (truck). The final momentum of the truck is:

p_f (truck) = 3000 kg * v_f (truck)

The final momentum of the car is:

p_f (car) = 1000 kg * 15 m/s = 15000 kg m/s

Using the conservation of momentum, we can write an equation:

p_f (total) = p_i (total)

30000 kg m/s = p_f (truck) + p_f (car)

30000 kg m/s = 3000 kg * v_f (truck) + 15000 kg m/s

30000 kg m/s = 3000 kg * v_f (truck) + 15000 kg m/s

v_f (truck) = (30000 kg m/s - 15000 kg m/s) / 3000 kg = 7.5 m/s

So, the velocity of the truck immediately after the collision is 7.5 m/s.

Step-by-step explanation:

The value of the length /MK/ is 10 units

Recall that in an isosceles reangle, two sides are equal and the base angles are equal

We can use the cosine rule to find the length MK

N² = K²+M² - 2KMCosN

This implies that /MK/² = 5²+5²-2*5*5*cos110

⇒25+25-50*-0.9990

= 50+49.95

=99.95  this can be approximated to 100

the /MK/ = √100= 10 units

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Answer:

A. (f+g)(x)=-2x^2-2x+8

Step-by-step explanation:

You combine like terms by adding

Answer:

≈29.93 [units].

Step-by-step explanation:

according to the attachment the required perimeter is:

P=2*6+4.25*2+3.1415*3=12+8.5+9.4245=29.9245 [units].

Answer:

75

Step-by-step explanation:

Use the arithmetic progression formula:  S =n/2(2a + (n-1)d)

a = 5, d = 5, n = 5

S = 5/2((2(5) + (5-1)(5)) = 75

The measures of the center or variability that are greater than 5 degrees are :

The mean of the data on temperature this week and the last is :

= ( 4 + 10 + 6 + 9 + 6 ) / 5

= 7 degrees Fahrenheit 4+ 10+ 6+9+ 6

The mean of the data on temperature last week and the last is :

= ( 13 + 9 + 5 + 8 + 5 ) / 5

= 8 degrees Fahrenheit

The range of this week's temperature is :

= 10 - 4

= 6 degrees Fahrenheit

All these measures of center are above 6 degrees.

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The full question is:

Temperatures for 5 Days This Week and Last Week

Low Temperatures This Week (Degrees Fahrenheit) 4 10 6 9 6 Low Temperatures Last Week (Degrees Fahrenheit) 13 9 5 8 5 Which measures of center or variability are greater than 5 degrees? Select three choices.

a) the mean of this week’s temperatures

b) the mean of last week’s temperatures

c) the range of this week’s temperatures

d)the mean absolute deviation of this week’s temperatures

e) the mean absolute deviation of last week’s temperatures

Answer:

541.5 ksh

Step-by-step explanation:

Answer:

Step-by-step explanation:

The meaning of the function notations are

G(Jada) = 4 means that the first name Jada has four letters

C(11-15)= chemistry means that the Monday class for 11-15 is chemistry

How to interpret the function notations?

The meaning of the function G

From the question, we have the following parameters that can be used in our computation:

Function G gives the number of letters in the first name for its output.

Next, we have

G(Jada) = 4

Using the meaning of the function, we have

G(Jada) = 4 means that the first name Jada has four letters

The meaning of the function C

From the question, we have the following parameters that can be used in our computation:

Function C gives a student's Monday class for its output.

Next, we have

C(11-15)= chemistry

Using the meaning of the function, we have

C(11-15)= chemistry means that the Monday class for 11-15 is chemistry

The evaluation of the function expressions gives:

(q + f)(5) = 1

(f - q)(2) = -2

(q f)(4) = 9

(f /q)(0) = 1

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

From the graph, when c = 5, q(5) = 0, f(5) = 1. Thus:

(q + f)(5) = 0 + 1 = 1

From the graph, when c = 2, f(2) = 0, q(2) = 2. Thus:

(f - q)(2) = 0 - 2 = -2

From the graph, when c = 4, q(4) = 3, f(4) = 3. Thus:

(q f)(4) = 3 * 3 = 9

From the graph, when c = 0, f(0) = 4, q(0) = 4. Thus:

(f /q)(0) = 4/4 = 1

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Answer:

  y = 1/8x +1/64

Step-by-step explanation:

You want the equation of the line that is tangent to the curve y = x³ -x⁴ in exactly two places.

Since the tangent line is not crossed, the difference between the line and the given curve is a 4th-degree polynomial with two roots, each of multiplicity 2. If those are 'a' and 'b', we can write for line y = mx +p, ...

  mx +p -(x³ -x⁴) = (x -a)²(x -b)² = 0

  x⁴ -x³ +0x² +mx +p = x⁴ -2(a+b)x³ +(a²+4ab+b²)x² -2ab(a+b)x +a²b²

Equating coefficients, we have ...

The coefficient of x³ tells us ...

  a +b = 1/2

The coefficient of x² tells us ...

  0 = (a +b)² +2ab

  0 = (1/2)² +2ab

  ab = -1/8

Using these value, we can find the equation of the line to be ...

  m = -2ab(a+b) = -2(-1/8)(1/2) = 1/8

  p = (ab)² = (-1/8)² = 1/64

The equation of the line is ...

  y = 1/8x +1/64

__

Additional comment

To find the line, we did not need the coordinates of the points of tangency. They are ((1-√3)/4, (3-2√3)/64) and ((1+√3)/4, (3+2√3)/64).

The slope of the line is equal to the slope of the quartic at the point of inflection of its derivative, at x=1/4.

so we're assuming the compounding period is annual, so hmmm let's call our sum "P", how much is it at simple and compound interest anyway?

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &2 \end{cases} \\\\\\ A = P[1+(0.05)(2)] \implies \boxed{A = 1.10P} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annual, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A = P\left(1+\frac{0.05}{1}\right)^{1\cdot 2} \implies \boxed{A = 1.1025P}[/tex]

now, the larger one will be the compound interest one, so, let's subtract the simple interest one from it to get 6.90

[tex]1.1025P~~ - ~~1.10P~~ = ~~6.90\implies 0.0025P=6.90 \\\\\\ P=\cfrac{6.90}{0.0025}\implies {\Large \begin{array}{llll} P=2760 \end{array}}[/tex]

The tropical savanna environment is home to the grass in the picture above.

The two primary types of forests are deciduous or monsoon rainforests and tropical evergreen rainforests, which have leaves all year round (these loose their leaves during the dry season). Human activity causes deforestation because it endangers the local ecosystem's ability to sustain life.

Rainforests are a type of forest habitat that have a dense canopy, great species variety, and high rainfall rates. The Amazon is made up of a variety of ecosystems and plant life, including savannas, deciduous woods, seasonal forests, and rainforests.

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The graph of y = 2 sin(x) + 2 is given by the following option:

Graph A.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For which the parameters are given as follows:

The function in this problem has an amplitude of 2, meaning that before the vertical shift, it oscillates between -2 and 2.

Due to the vertical shift, the function is going to oscillate between 0 and 4, with a period of 2π and no phase shift, crossing the midline of y = 2 at the origin, hence Graph A is the correct graph.

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Answer: The outlier is $95 and the plot is D.

Step-by-step explanation:

          An outlier is the data value that's much larger or much smaller than the other data values. Here, that is $95.

          Excluding this value, our smallest is $15 and the largest is $60. We plot a dot at both of these points.

          The middle dot is the median. To find this, we will arrange the values in order and find the middle value. (We are excluding $95.) After doing this process, we see the middle dot is at 39.

    $15, $20, $38, $60, $45, $40, $35, $50

    $15, $20, $35, $38, $40, $45, $50, $60

    ----, ----, ----, $38, $40, ----, ----, ----

                    [tex]38 + 40 = 78, \;\;78 / 2\;\;\boxed{= 39}[/tex]

          This means we have dots at 15, 39 and 60, leading us to answer D.

Answer:

should" (and any subsequent words) was ignored because we limit queries to 32 words.

When t is any real number, the true statements will be:

A. -t < 0:

B. -t = 0

E. (-t)^2 = -t^2

If t is any real number, then the following statements are true:

A. -t < 0: This statement is true if t > 0, and false if t <= 0.

B. -t = 0: This statement is true if t = 0, and false if t ≠ 0.

C. -t = t: This statement is false for all real numbers t, since the negative of any non-zero real number is not equal to the original number.

D. t|-t: This statement is false for all real numbers t, since the absolute value of any real number is non-negative.

E. (-t)^2 = -t^2: This statement is true for all real numbers t, since squaring a real number gives a non-negative result. Note that the negative sign in front of the square is distributive and can be moved inside the square.

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Answer:

Step-by-step explanation:

Let's call the number of friends "f". Since each friend paid $12.75 for their meal, the cost of the meals can be represented as f * 12.75. And since each friend left the same amount for a tip, the cost of the tips can be represented as t * f.

The total cost of the dinner including the tip was $61, so we can write the following equation:

f * 12.75 + t * f = 61

Expanding the left side of the equation:

12.75f + t * f = 61

Combining like terms:

13.75f + t = 61

Solving for t:

t = 61 - 13.75f

So, the equation that describes the situation is t = 61 - 13.75f.

Answer:

To estimate the number of seventh-graders who attend summer camp, we can use the sample proportion of 30 out of 200 students.

Let's call the population proportion of seventh-graders who attend summer camp "p".

The sample proportion can be estimated as:

p = 30/200 = 0.15

To estimate the number of seventh-graders in the entire school who attend summer camp, we can multiply the population size by the sample proportion:

Estimated number of seventh-graders attending summer camp = p * population size = 0.15 * 780 = 117

So, about 117 seventh-graders in the school are expected to attend summer camp.

Answer:

117 seventh-graders in the school are expected to attend summer camp.

Step-by-step explanation:

On solving the provided question, we can say that equation is 532/13.5 = 39.4 doses.

A mathematical equation is a formula that joins two statements and indicates equality with the equal symbol (=). In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the relationship between the two sentences on either side of a letter. There is frequently only one variable, which also serves as the symbol. For example, 2x - 4 = 2.

the equation is the week * 7 (weekdays) * 24 (hours/day) * 19/6 (MILIGRAMS/HOURS)

532 mg per week (532/13.5 = 39.4 doses)

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By making the discriminant equal to zero, we can see that the quadratic equation has one real solution only for z = 10.

For a general quadratic equation:

a*x^2 + b*x + c = 0

We define the discriminant as:

D = b^2 - 4ac

The quadratic equation will have only one real solution only if the discriminant is equal to zero.

Here the quadratic is:

(z - 5)*x^2 - z*x + 5 = 0

Then the discriminant is:

(-z)^2 - 4*5*(z - 5)

And that must be equal to zero, then we need to solve:

z^2 - 20*(z - 5) = 0

z^2 - 20z + 100 = 0

Using the quadratic formula we will get:

[tex]z = \frac{20 \pm \sqrt{(-20)^2 - 4*1*100} }{2} \\\\z = \frac{20 \pm 0}{2} \\\\z = 10[/tex]

So the quadratic equation has one real solution only for z = 10.

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Explanation:

In this case the median value is more representative of the 'center' of the population. The median is a better measure when the data set is skewed, has fat tails as compared to a normal didtribution, or has outliers. Otherwise you should use the arithmetic mean.

The number of pages in the book is given by the inequality 90 < A < 96 , where A is the number of pages

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the number of pages in the book be A

And , it is more than 90 and less than 96

So , the value of A is { 91 , 92 , 93 , 94 , 95 }

On simplifying , we get

90 < A < 96 , where A is the number of pages

Hence , the inequality is 90 < A < 96

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The effect of "a" in the graph of parabola is value from the quadratic function.

In this question we have four case of parabolas with vertical axes of reference, whose standard formula is:

y = a(x – h)2 + k or x = a(y – k)2 +h

Where:

(h, k) - The vertex of the parabola.

p - Least distance between the vertex and the focus of the parabola.

Given that;

The equation of parabola is f(x) = ax².

Now, Let's look at the graph of f(x) = x^2 + 3x + 1, which is below. The b-value in this equation is 3.

We see that our graph is indeed a parabola. Our parabola is curving up. The x-value of the vertex, the tip of the parabola, is -3 / 2 or -1.5. We can actually calculate this x-value by evaluating the expression -b / 2a, where a and b are the values from the quadratic function.

Therefore, the role of a in parabola is stated.

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The sequence will be aₙ=$1250-118ⁿ⁻¹ where n= place at which a bowler finished.

What exactly is a sequence?

A sequence is a collection of numbers that follows pattern. Olivia, for example, has been offered a position with a beginning monthly pay of $1000 and a yearly raise of $500. To figure out her monthly pay for the first three years? The prices will be $1000, $1500, and $2000. Note that Olivia's income over a number of years creates a sequence as they follow a pattern where the numbers increase by $500 each time.

Now,

given award money for 1, 2, 3 places is given as $1250, $1132 and $1014

that means for the sequence, first term is 1250 and difference between the next terms will be 118 (less)

So, the sequence will be aₙ=$1250-118ⁿ⁻¹

where

n=place at which a bowler is placed.

Hence,

           The sequence will be aₙ=$1250-118ⁿ⁻¹.

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He then constructs a graph to visualize his results,  For a given number of selections, we can use Joseph's graph to find the number of diamonds that he has picked so far is FALSE.

Probability refers to potential. A arbitrary event's circumstance is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to read the liability of colorful events. The degree to which commodity is likely to be is principally what probability means.

You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

We are only interested in finding red card so we can't differentiate between diamond or hearts at any time. Hence,

The false statement is:

For a given number of selections, we can use Josephs graph to find the number of diamonds that he has picked so far.

Option B is correct.

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The fraction that correctly represents the ratio of 5 to 15 in it's simplest form is option C. 1/3.

Fractions are type of numbers which are written in the form p/q, which implies that p parts in a whole of q.

Here p, called the numerator and q, called the denominator, are real numbers.

The given ratio is 5 to 15.

Fraction in simplest form means that, the numerator and denominator cannot be factored by a common factor again.

In order to find the given ratio in simplest form, find the greatest common factor of both 5 and 15.

5 = 5

15 = 3 × 5

5 is the only common factor and so the greatest common factor of both 5 and 15.

5 / 15 = (5 × 1) / (5 × 3)

         = 1/3

Hence 1/3 is the simplest form of the ratio 5 to 15.

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Your question is incomplete. The correct question is as follows.

Chose the fraction that correctly represents the ratio 5 to 15 in simplest form.

A. 2/3

B. 10/30

C. 1/3

D. 1/5