Describe when you would need to solve a system of linear equations, instead of a single linear equation. (Site 1)

Final answer:

The surface area of an open-top box with a length of 7 cm, width of 6 cm, and height of 3 cm is calculated using the formula and comes out to be 120 cm².

Explanation:

To find the surface area of an open-top box with given dimensions, we use the formula: A= 2LH + 2WH + LW. Substituting in the provided lengths for length (L), width (W), and height (H):

A = 2(7 cm)(3 cm) + 2(6 cm)(3 cm) + (7 cm)(6 cm)

A = 2(21 cm²) + 2(18 cm²) + 42 cm²

A = 42 cm² + 36 cm² + 42 cm²

A = 120 cm²

This gives us the total surface area of the open-top box which is 120 cm².

The number .50 in the context of this question represents the proportion (or probability) of people in the sample who have brown eyes. It's calculated by dividing the count of individuals with brown eyes by the total number of individuals in the sample.

In this context, the number .50 represents the proportion or probability of people with brown eyes in the sample. This number is obtained by dividing the number of people with brown eyes (25) by the total number of people in the sample (50).

Hence, .50 means there is a 50% chance that a randomly selected person from the sample will have brown eyes. This is often used in the field of statistics where proportions are utilized to represent probabilities of outcomes.

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The probability is 0.187 or 18.7% that the restaurant chosen at random is in the north east and is located in a city with a population over 500,000.

To find the likelihood that a haphazardly picked eatery from the 588 outlets situated in a city with a populace more than 500,000 is in the north east, we really want to know the quantity of cafés that meet these two rules and are situated in the north east.

Let's look for this information using the table:

Northeast Midwest South West More than 500,000 Over 500,000 110 95 178 66 Less than 500,000 53 39 38 9 The table indicates that 110 restaurants are located in the north east of the United States in cities with more than 500,000 residents. In this manner, the likelihood that a haphazardly picked eatery from the 588 outlets situated in a city with a populace more than 500,000 is in the north east is:

P(Northeast and North of 500,000) = 110/588 = 0.187

Thus, the likelihood is 0.187 or 18.7% that the café picked aimlessly is in the north east and is situated in a city with a populace more than 500,000.

Answer:  The required probability that the child took a green marble is 40%.

Step-by-step explanation:  Given that there are 9 red and 6 green marbles in a bag and a child reaches in the bag and randomly takes one marble.

We are to find the probability that the child took a green marble.

Let S denote the sample space of choosing a marble from the bag and A be the event of choosing a green marble.

Then,

n(S) = 9 + 6 = 15   and   n(A) = 6.

Therefore, the probability of event A will be

[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{6}{15}=\dfrac{2}{5}\times 100\%=40\%.[/tex]

Thus, the required probability that the child took a green marble is 40%.

To find out how many servings are in a 15 cup bag of pasta when serving size is 3/4 cup per person, divide 15 by 3/4, which equals 20 servings.

Firstly, convert the mixed fraction into an improper fraction for easier division: 3/4 remains the same since it is already a proper fraction.

Now, carry out the division: 15 ÷ (3/4)
= 15 × (4/3) (You multiply by the reciprocal of 3/4)

Then, multiply the numbers:
= 15 × 4 ÷ 3
= 60 ÷ 3
= 20

Therefore, there are 20 servings in a 15 cup bag of pasta when the serving size is 3/4 cup per person.

The sum of three consecutive integers is 90. So you know that 3 numbers that are next to each other in numerical order equals 90.

First step: Make an equation:

Let's take x as the smallest of the three numbers.

[tex]x +(x+1)+(x+2)=90[/tex]

2nd step: Open the brackets:

[tex]x+x+1+x+2=90[/tex]

3rd step: Simplify:

[tex]3x+3=90[/tex]

4th step: Keep similar integers on one side of the equation

[tex]3x+3-3=90-3[/tex]

5th step: Solve for x:

[tex]3x=87[/tex]

[tex]\frac{3x}{3} =\frac{87}{3}[/tex]

[tex]x=29[/tex]

So if the numbers are consecutive, they have to be next to each other.

Answer: 29, 30, 31

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The point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1) is [tex]\( \boxed{A) y + 6 = -1(x - 5)} \)[/tex].

To find the point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1), we first need to calculate the slope (m) using the formula:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

Given points:

[tex]\((-5, 6)\) and \((0, 1)\)[/tex]

Calculate the slope m:

[tex]\[ m = \frac{1 - 6}{0 - (-5)} = \frac{-5}{5} = -1 \][/tex]

Now that we have the slope m = -1, we can use the point-slope form of the equation of a line, which is:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

Choose one of the points, let's use [tex]\((-5, 6)\) as \((x_1, y_1)\)[/tex]:

[tex]\[ y - 6 = -1(x + 5) \][/tex]

Now, simplify and compare with the given options:

[tex]\[ y - 6 = -1(x + 5) \][/tex]

So, the point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1) is [tex]\( \boxed{A) y + 6 = -1(x - 5)} \)[/tex].

The expected number of ticket holders that will fail to show for the flight is 11.

Given that,

Based on the above information,

= 276%

= 2.76

Now the number of ticket holders who fail for presenting the flight should be

[tex]= 2.76\times 4[/tex]

= 11

Therefore we can conclude that the expected number of ticket holders that will fail to show for the flight is 11.

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(7^2)x = 1

7^2 = 49

49x = 1

x = 1/49

(7^0)x=1

7^0 = 1 (anything raised to 0 = 1)

1x = 1

x = 1

Answer:

So, the maximum of C is 15 at (3,0) and the minimum value is 0 at (0,0)

Step-by-step explanation:

When you graph all of the constraint functions, the vertices of the shape that is made are at the points above. Now you plug those points into the function equation C=5x-4y and see where you get a max or min.

(0,1)

(1.5,1.5)

(0,0)

(3,0)

(1,1)=C=1

(1.5,1.5)=C=1.5

(0,0)=C=0

(3,0)=C=15

So, the maximum of C is 15 at (3,0) and the minimum value is 0 at (0,0)

6 rolls of dimes = $30.

6 rolls of quarters = $60.

Answer:

7 roll of quarter and 4 roll of dimes.

Step-by-step explanation:

Let x be the number of rolls of quarters and y be the number of rolls of dimes,

Given,

Total rolls = 11

⇒ x + y = 11 ------(1),

Also, the total value of $ 90 in which Each roll of quarters has a value of $10 and each roll of dimes has a value of $5.

⇒ 10x + 5y = 90 ------(2),

Equation (2) - 5 × Equation (1),

We get,

5x = 90 - 55

⇒ 5x = 35 ⇒ x = 7

From equation (1),

7 + y = 11 ⇒ y = 4

Hence, the number of roll of quarters = 7,

And, the number of roll of dimes = 4

The angle between a side of a polygon and the extension of its adjacent side is the exterior angle at that vertex, forming a linear pair with the adjacent interior angle.

Angle between a side of a polygon and the extension of its adjacent side: When considering a polygon, the angle between a side and the extension of its adjacent side is equal to the exterior angle of the polygon at that vertex. This angle forms a linear pair with the adjacent interior angle of the polygon.