Ted is installing lighting in a new block of 12 apartments. He will need 60 metres of cable for each apartment. Each new spool holds 100 metres of cable. What is the smallest number of new spools that Ted will need for this job ??

Attila the Hun died in 453.

Let x represents the year.

So the inequality for will be 453<x.

Explanation:

Here x will be smaller than 453 because Hun was dead in 453. So 453 and any number smaller than that would be the times in his life that he would have been feared.

Suppose the value of x is greater than 453, then the Romans didn't fear him because after 453 he was dead.

The event "Atleast once" is the complement of event "None".

So, the probability that Marvin teleports atleast once per day will the compliment of probability that he does not teleports during the day. Therefore, first we need to find the probability that Marvin does not teleports during the day.

At Morning, the probability that Marvin does not teleport = 2/3

Likewise, the probability tha Marvin does not teleport during evening is also 2/3.

Since the two events are independent i.e. his choice during morning is not affecting his choice during the evening, the probability that he does not teleports during the day will be the product of both individual probabilities.

So, the probability that Marvin does not teleport during the day = [tex] \frac{2}{3}*\frac{2}{3}=\frac{4}{9} [/tex]

Probability that Marvin teleports atleast once during the day = 1 - Probability that Marvin does not teleport during the day.

Probability that Marvin teleports atleast once during the day = [tex] 1-\frac{4}{9}=\frac{5}{9} [/tex]

Answer:

5/9

Step-by-step explanation:

The chances he teleports in the morning is 2/3

Same for the evening.

so mulitply the two choices 2/3 * 2/3= 4/9

Then add 1 to account for teleports ONCE a day

1+4/9= 5/9

62+x≥85 is the inequality to show how much more money Chantal must save.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

Given that Chantel would like to buy a new pair of running shoes.

The shoes she likes start at $85.

Chantel has already saved $62.

We need to find the inequality to show how much more money Chantal must save.

Let x be the more money needed to purchase the shoes.

62+x≥85

Subtract 62 from both sides

x≥85-62

x≥23

Hence, 62+x≥85 is the inequality to show how much more money Chantal must save.

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Since the given lengths satisfied the Pythagorean theorem then the given triangle is a right angled triangle.

Use the concept of the triangle defined as:

A triangle is a three-sided polygon, which has three vertices and three angles which has a sum of 180 degrees.

And the Pythagoras theorem for a right angled triangle is also defined as:

(Hypotenuse)²= (Perpendicular)² + (Base)²

The given length of sides are:

60 centimeters, 63 centimeters, and 87 centimeters.

Now take,

Hypotenuse = 87 cm

Base = 63 cm

Perpendicular =  60 cm

Apply the Pythagorean theorem,

87² = 60² + 63²

Calculating it,

7569 = 7569

Since the given sides satisfied the Pythagorean theorem,

Hence,

The triangle is a right angled triangle.

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The equation which can be used to determine p, the cost of b cans of beans will be;

⇒ p = 9.5b

What is Equation of line?

The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The values on the x - axis are 0, 2, 4, 6, 8, 10.

The values on the y- axis are 0, 19, 38, 57, 76, and 95.

These points are connected by a line.

The label on the x axis is Number of Cans.

The title on the y axis is Price in dollars.

Now,

Find the equation as;

Let two points from the table are,

⇒ (0, 0) and (2, 19)

So, The equation of line passing through the points (0, 0) and (2, 19) is,

⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)

⇒ y - 0 = (19 - 0) / (2 - 0)  (x - 0)

⇒ y = 19/2x

⇒ y = 9.5x

So, The equation which can be used to determine p, the cost of b cans of beans will be;

⇒ p = 9.5b

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Answer:

[tex]x=50.6cm[/tex]

Step-by-step explanation:

Triangle MAB is similar to triangle MNP

Since the triangles are similar, the corresponding ratios are in the same proportion.

Therefore we can write the relation;

[tex]\frac{|MB|}{|MP|}=\frac{|MA|}{|MN|}[/tex]

[tex]\frac{x}{72.6}=\frac{46.2-14}{46.2}[/tex]

This implies that;

[tex]\frac{x}{72.6}=\frac{32.2}{46.2}[/tex]

We multiply both sides by 72.6 to get

[tex]\frac{x}{72.6}\times 72.6=\frac{32.2}{46.2}\times72.6[/tex]

[tex]\Rightarrow x=50.6[/tex]

Hence the value of [tex]x[/tex] is 50.6 cm

Final answer:

The correct option is (d) 200. By using a proportion based on the sample data where 51 students (25% of the grade) chose summer, it can be predicted that approximately 204 students in total would choose summer. The closest provided option to this calculated number is 200.

Explanation:

Latricia surveyed 25% of the seventh-grade students, and out of this sample, 51 students chose summer as their favorite season. To find the total number who would choose summer, we assume that the sample is representative of the entire grade. If 51 represent 25%, then to find 100% (the whole grade), we use the following proportion:

Sample size (25%) : Number who chose summer in sample (51) = 100% : Total number who would choose summer

To solve the proportion for the total number who would choose summer, we set up a simple equation:

25% / 51 = 100% / x, where x is the total number we want to find.

To find x, we multiply both sides by x and divide by 25%:

x = (51 * 100%) / 25%

x = (51 * 4)

x = 204

Therefore, the most reasonable prediction for the number of seventh-grade students who would choose summer as their favorite season is 204. However, since 204 is not one of the options provided, we will choose the closest option, which is (d) 200.

Answer:

1) 32 bracelets if she cuts the ribbon into a 7 and 1/2 inch.

2) 35 bracelets if she cuts the ribbon into a 6 and 3/4 inch.

Step-by-step explanation:

1) Length of the ribbon = 20 feet = 240 inches

1 foot = 12 inches

Length of the ribbon required to make a bracelet = [tex]7\frac{1}{2}=\frac{15}{2}inches[/tex]

Let the number of bracelets Sally can make from 20 feet ribbon be x.

[tex]x=\frac{240 inches}{\frac{15}{2}inches}=32[/tex]

32 bracelets if she cuts the ribbon into a 7 and 1/2 inch.

2) Length of the ribbon = 20 feet = 240 inches

1 foot = 12 inches

Length of the ribbon required to make a bracelet = [tex]6\frac{3}{4}=\frac{27}{4} inches[/tex]

Let the number of bracelets Sally can make from 20 feet ribbon be x.

[tex]x=\frac{240 inches}{\frac{27}{4}inches}=35.555\approx 35[/tex]

35 bracelets if she cuts the ribbon into a 6 and 3/4 inch.