Find the roc of the volume of a cube with respect to the length of its side s

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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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

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)

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].

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.

Answer:

A black-tailed jackrabbit can hopes 36 in 5 seconds.

Step-by-step explanation:

Consider the provided information.

Black tailed jackrabbit hopes 51 feet in one second.

Therefore, in 5 second Black tailed jackrabbit covers a distance of:

51×5=255  feet

So, in 5 seconds a black-tailed jackrabbit will travel 255 feet.

In one hops Black tailed jackrabbit covers 7 feet.

Now find the number of hops, we need to divide the distance by the length of one hop:

[tex]255\div 7=\frac{255}{7}\approx36[/tex]

Hence, A black-tailed jackrabbit can hopes 36 in 5 seconds.

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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We have that if the sin 30 degrees is 1/2 then the cos __60=1/2.__

Option C

Question Parameters:

The sin 30 degrees is 1/2

Generally, the Trigonometry of a right angle triangle gives values for sin, cos, tan.

Using the triangle we have that

if the sin 30 degrees is 1/2 then the cos60=1/2

Therefore, if the sin 30 degrees is 1/2 then the cos __60=1/2__.

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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.

To find the probability that the average weight of four babies will be more than 7.5 pounds, we calculate the z-score and look it up in the standard normal distribution table. The probability is approximately 0.2843, or 28.43%.

To find the probability that the average weight of four babies will be more than 7.5 pounds, we need to calculate the z-score and look it up in the standard normal distribution table.

First, we convert the weight of 7.5 pounds to ounces: 7.5 pounds * 16 ounces = 120 ounces.

Next, we calculate the z-score using the formula: z = (x - &μ) / &σ, where x is the given weight, &μ is the mean weight, and &σ is the standard deviation. In this case, z = (120 - 112) / 14 = 0.571.

Finally, we can look up the probability using the z-score in the standard normal distribution table. The probability of the average weight of four babies being more than 7.5 pounds is approximately 0.2843, or 28.43%.

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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.