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3 years ago

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The Martins’ van can hold up to 8 passengers. Debbie writes the inequality p < 8, where p is the number of passengers that ca

n fit in the van. Select the choice that provides the best explanation for Debbie’s error and the correct answer in this case. Debbie should have used 8p because 8 passengers can fit in the van. The correct inequality is 8p < 1. Debbie should have switched the inequality symbol to greater than. The correct inequality is p > 8. Debbie should have included 8 as a possible choice. The correct inequality is p < 9. Debbie should have used the not equals sign to compare the two sides of the inequality. The correct answer is p ≠ 8.

1 answer:

Salsk061 [2.6K]3 years ago

4 0

Answer:

Debbie should have included 8 as a possible choice. The correct inequality is p < 9.

Step-by-step explanation:

Given

Passengers = Up to 8

Required

Determine why $p < 8$ is incorrect and make corrections

The inequality $p < 8$ means that the van can hold less than 8 passengers.

To make correction, the digit 8 has to be included in the inequality.

This can be written as:

$p$ or $p \le 8$

<em>Base on the given options, option (c) best answered the question.</em>

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Simply please “picture”

oksian1 [2.3K]

<h3>Answer: (-infinity, 7]</h3>

=====================================

Explanation:

The first interval (-infinity, 3) describes any number less than 3, so we can write x < 3 in short hand (where x is the unknown number).

The second interval (-1, 7] means we start at -1 and stop at 7. We do not include -1 but include 7. So we say that $-1 < x \le 7$ (ie x is between -1 and 7; exclude -1, include 7)

If you were to graph each ona number line, you would see that the too intervals have overlapping parts. The right most edge extends out as far as x = 7. There is no left most edge as it goes onforever that direction.

Therefore, the to intervals combine to get $x \le 7$ which turns into the interval notation answer of (-infinity, 7]

-----------

It might help to think of it like this: x < 3 and $-1 < x \le 7$ say "x is some number that is less than 3, or it is between -1 and 7". So x could be anything less than 7, including 7 itself.

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3 years ago

Help find x out of these 4 questions i can’t find the answer anywheew

babunello [35]

Answer:

Option D. 11√6/2

Step-by-step explanation:

We'll begin by calculating the side opposite to angle 60°.

This is illustrated below:

Angle θ = 60°

Opposite =?

Hypothenus = 11

Using the sine ratio, we can obtain the side opposite to angle 60° as follow:

Sine θ = Opposite/Hypothenus

Sine 60 = Opposite /11

Cross multiply

Opposite = 11 × Sine 60

Sine 60 = √3/2

Opposite = 11 × √3/2

Opposite = 11√3/2

Finally, we shall determine the value of x as follow:

Angle θ = 45°

Opposite = 11√3/2

Hypothenus = x

Using the sine ratio, we can obtain the value of x as shown below:

Sine θ = Opposite/Hypothenus

Sine 45° = 11√3/2 /x

Cross multiply

x × Sine 45° = 11√3/2

Sine 45° = 1/√2

x × 1/√2 = 11√3/2

x/√2 = 11√3/2

Multiply through by √2

x = √2 × 11√3/2

x = 11√6/2

4 0

4 years ago

A box designer has been charged with the task of determining the surface area of various open boxes (no lid) that can be constru

Viktor [21]

Answer:

1) $S = 2\cdot w\cdot l - 8\cdot x^{2}$ , 2) The domain of S is $0 \leq x \leq \frac{\sqrt{w\cdot l}}{2}$ . The range of S is $0 \leq S \leq 2\cdot w \cdot l$ , 3) $S = 176\,in^{2}$ , 4) $x \approx 4.528\,in$ , 5) $S = 164.830\,in^{2}$

Step-by-step explanation:

1) The function of the box is:

$S = 2\cdot (w - 2\cdot x)\cdot x + 2\cdot (l-2\cdot x)\cdot x +(w-2\cdot x)\cdot (l-2\cdot x)$

$S = 2\cdot w\cdot x - 4\cdot x^{2} + 2\cdot l\cdot x - 4\cdot x^{2} + w\cdot l -2\cdot (l + w)\cdot x + l\cdot w$

$S = 2\cdot (w+l)\cdot x - 8\cdpt x^{2} + 2\cdot w \cdot l - 2\cdot (l+w)\cdot x$

$S = 2\cdot w\cdot l - 8\cdot x^{2}$

2) The maximum cutout is:

$2\cdot w \cdot l - 8\cdot x^{2} = 0$

$w\cdot l - 4\cdot x^{2} = 0$

$4\cdot x^{2} = w\cdot l$

$x = \frac{\sqrt{w\cdot l}}{2}$

The domain of S is $0 \leq x \leq \frac{\sqrt{w\cdot l}}{2}$ . The range of S is $0 \leq S \leq 2\cdot w \cdot l$

3) The surface area when a 1'' x 1'' square is cut out is:

$S = 2\cdot (8\,in)\cdot (11.5\,in)-8\cdot (1\,in)^{2}$

$S = 176\,in^{2}$

4) The size is found by solving the following second-order polynomial:

$20\,in^{2} = 2 \cdot (8\,in)\cdot (11.5\,in)-8\cdot x^{2}$

$20\,in^{2} = 184\,in^{2} - 8\cdot x^{2}$

$8\cdot x^{2} - 164\,in^{2} = 0$

$x \approx 4.528\,in$

5) The equation of the box volume is:

$V = (w-2\cdot x)\cdot (l-2\cdot x) \cdot x$

$V = [w\cdot l -2\cdot (w+l)\cdot x + 4\cdot x^{2}]\cdot x$

$V = w\cdot l \cdot x - 2\cdot (w+l)\cdot x^{2} + 4\cdot x^{3}$

$V = (8\,in)\cdot (11.5\,in)\cdot x - 2\cdot (19.5\,in)\cdot x^{2} + 4\cdot x^{3}$

$V = (92\,in^{2})\cdot x - (39\,in)\cdot x^{2} + 4\cdot x^{3}$

The first derivative of the function is:

$V' = 92\,in^{2} - (78\,in)\cdot x + 12\cdot x^{2}$

The critical points are determined by equalizing the derivative to zero:

$12\cdot x^{2}-(78\,in)\cdot x + 92\,in^{2} = 0$

$x_{1} \approx 4.952\,in$

$x_{2}\approx 1.548\,in$

The second derivative is found afterwards:

$V'' = 24\cdot x - 78\,in$

After evaluating each critical point, it follows that $x_{1}$ is an absolute minimum and $x_{2}$ is an absolute maximum. Hence, the value of the cutoff so that volume is maximized is:

$x \approx 1.548\,in$

The surface area of the box is:

$S = 2\cdot (8\,in)\cdot (11.5\,in)-8\cdot (1.548\,in)^{2}$

$S = 164.830\,in^{2}$

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3 years ago

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name me some numbers plz

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4 years ago

Identify the location of the point (-3, -2).

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3 years ago