Find the area of the triangle with vertices A(-3, 2), B(1, - 2). and C(1, 3).​

The function that models the graduating ceremony is illustrated below.

First, let's define some variables to make our function more understandable. Let's call the total number of seniors graduating "n", the rate at which seniors walk across the stage "r" (in seniors per minute), and the time it takes for all seniors to walk across the stage "t" (in minutes).

Now, let's also take into account the speaking and music that lasts a total of 25 minutes. We can modify our function to include this by subtracting the time spent on speaking and music from the total time it takes for all seniors to walk across the stage:

function seniors_on_stage_with_music(n, r, t, music_time) {

 return Math.ceil(n / (r * t - music_time));

}

Here, we added an additional argument to our function called music_time, which represents the total time spent on speaking and music. We then subtract this from the total time it takes for all seniors to walk across the stage before dividing the total number of seniors by the result.

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Answer:

No

Step-by-step explanation:

3^5 or using a superscript, 3⁵ means 3 × 3 × 3 × 3 × 3 which is 243

The 5 is an exponent. This format is a shortcut for multiplying. But it means to multiply 3 times itself, over and over again (5 times)

3 × 5 is of course regular multiplication as your learned in elementary school. 3 × 5 is just 15. (regular multiplication like this is a shortcut for adding-- it means to add 3 groups of 5 or 5 groups of 3)

The area of this figure based on the information will be 10cm²

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

From the information, the shape gas sides 5cm and 2cm. The area of this figure will be:

= Length × Width

= 5cm × 2cm

= 10cm²

In conclusion, the area of this figure based on the information will be 10cm²

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A shape has sides 5mm and 2mm. Find the area of the polygon.

16 cm

10 cm

12 cm

24 cm

The equation of the circle will be -

(x - 4)² + (y - 13)² = 64

The general equation of a circle with (h, k) representing the circle's center, and {r} represents the length of its radius is

(x – h)² + (y – k)² = r²

We can write the equation of the circle as -

(x – h)² + (y – k)² = r²

(x - 4)² + (y - 13)² = r²

(x - 4)² + (y - 13)² = r²

(x - 4)² + (y - 13)² = r²

Also -

2πr = 16π

r = 8

So. the equation of the circle will be -

(x - 4)² + (y - 13)² = 64

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Since she travels 183 miles in 3 hours, her speed is:

183 miles / 3 hours = 61 miles per hour

To calculate how long it will take her to drive a total of 366 miles, we can use the formula:

time = distance / speed

Plugging in the values, we get:

time = 366 miles / 61 miles per hour

time = 6 hours

Therefore, it will take Meghann 6 hours to drive a total of 366 miles at a constant speed using cruise control.

Ellis has the following set of numbers ; 20, 9, 14, n, 18. if the median is 18. Then, the two options that could not be n are 20 and 21.

To find out which two of the given options could not be n, we need to first find the value of n.

If the median is 18, then n must also be 18 since the given set has an even number of terms.

So, we have: 20, 9, 14, 18, 18

Now, we can check each option to see if it could be n;

10 - This could be n. The new set would be; 20, 10, 14, 18, 18 and the median would be 18.

18 - This could be n. It is already in the set and the median is 18.

19 - This could be n. The new set would be; 20, 19, 14, 18, 18 and the median would be 18.

20 - This could not be n. If n = 20, then the set would be; 20, 9, 14, 20, 18 and the median would be 14.

21 - This could not be n. If n = 21, then the set would be; 20, 9, 14, 18, 21 and the median would be 18.

Therefore, the two options that could not be n are 20 and 21.

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The area of the park to the nearest unit is 85454 ft²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

A triangle is a 3 sided polygon. The types of triangle are,; equilateral, scalene , isosceles triangle e.t.c

The area of a triangle is expressed as;

A = 1/2 absinC

here, a = 487ft, b= 465ft and C = 49°

therefore;

A = 1/2 × 487 × 465 × sin49°

A = 1/2 × 226455 × 0.755

A = 113227.5 × 0.755

A = 85454 ft² ( nearest unit)

Therefore the area of the park to the nearest unit is 85454ft²

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Answer:

y=-2x-3

Step-by-step explanation:

The point you first stated (0, -3) is the y-intercept of the line given that the x is zero. Parallel lines share a slope. Soooooooooo the equation would be y=-2x-3

Answer: y=-2x-3

hope this helps

Answer:

-5/6

Step-by-step explanation:

y=mx+6

so,

6y=-5x+48

y=-5/6x+48

m=-5/6

The probability that the sum of the cards is greater than 7 is 0. 6 .

To find the probability that the sum of the cards that we picked is greater than 7, first find the total possible cards that we can pick to be:

C(6, 2) = 6! / (2!(6-2)!) = 6! / (2!4!) = (6 × 5) / (2 × 1) = 15

Then find the pairs that would result in a number greater than 7 to be 9 pairs.

The probability would then be:

= Number of pairs greater than 7 / Total number of pairs

= 9 / 15

= 0. 6

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The teacher can pick students for problems 4 and 9 in front of the class in 435 ways.

There are 30 students in the class, and the teacher needs to pick 2 different students to answer problems 4 and 9.

This is a combination problem, and we can use the formula for combinations

n C r = n! / (r! (n - r)!)

where n is the total number of items, r is the number of items to be selected, and ! denotes the factorial function (i.e., the product of all positive integers up to that number).

In this case, we have

n = 30 (total number of students)

r = 2 (number of students to be selected)

So the number of ways the teacher can pick students for the problems is

30 C 2 = 30! / (2! (30 - 2)!) = 435

Therefore, there are 435 ways the teacher can pick students for the problems.

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Step-by-step explanation:

Sure, here's a step-by-step response you can use:

"Hey, that's a good question! Let me explain why (2x + 1)^2 is not equal to 4x^2 + 1.

When we see an expression like (2x + 1)^2, we know that it means we need to multiply (2x + 1) by itself. So let's do that first:

(2x + 1)^2 = (2x + 1) x (2x + 1)

Now we can use the FOIL method to multiply these two expressions together:

(2x + 1) x (2x + 1) = 4x^2 + 2x + 2x + 1

If we simplify the middle terms by adding them together, we get:

(2x + 1) x (2x + 1) = 4x^2 + 4x + 1

So the expression (2x + 1)^2 simplifies to 4x^2 + 4x + 1, not 4x^2 + 1.

I can see why you might have thought the answer was 4x^2 + 1, since that's the first term in the expression we got. But we can't forget about the two middle terms that come from multiplying 2x and 1 together twice.

I hope that helps clear things up! Let me know if you have any more questions."

The value of the stock investment a year ago is $19,200.

A stock is an investment that gives the holder ownership of the company where the stock was purchased. The stock holder receives dividends when declared by the company.

The value of the stock last year would be 20% greater last year than it is today.

Value of the stock last year = value of the stock today x (1 + rate of decline)

= $16,000 x (1 + 20%/100)

= $16,000 x (1 + 0.2)

= $16,000 x 1.2

= $19,200

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Answer:

x=8

Step-by-step explanation:

1/3x+4=-2/3x+12

add 2/3x to both sides

1x+4=12

subtract 4 from both sides

x=8

Hope this helps! :)

If kayaker traveled 4 5/6 miles during his first hour and 1 1/3 more than that his second hour, the kayaker traveled 8 1/18 miles in two hours.

To find out how far the kayaker traveled in two hours, we need to add the distance traveled in the first hour to the distance traveled in the second hour.

First, we need to convert the mixed numbers to improper fractions to make the addition easier:

4 5/6 = (6 x 4 + 5) / 6 = 29/6

1 1/3 = (3 x 1 + 1) / 3 = 4/3

Then, we can add the two fractions:

29/6 + (29/6 + 4/3)

To add these fractions, we need to find a common denominator, which is 6 for the first fraction and 18 for the second fraction:

29/6 + (29/6 + 4/3) = (87/18) + (58/18)

Now we can add the two fractions with the same denominator:

(87/18) + (58/18) = 145/18

Finally, we can simplify the fraction to a mixed number:

145/18 = 8 1/18

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Answer: Spade 3.

Step-by-step explanation: I took this test and after submission it showed the right answer!

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.

In the given question,

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the base, h is the height, and π is approximately 3.14.

Substituting the given values, we get:

V = (1/3) × 3.14 × 3² × 3.8

V ≈ 35.63

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

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Answer:

The denominator is equivalent to the number of segments that the whole is divided into.

The denominator is the bottom number of a fraction.

Answer:

C d e

Step-by-step explanation:

If A computer lab had 1,000 sheets of paper for the printer and last month, 378 sheets of paper were used, the fraction of the sheets that were not used is 0.622 which is 62.2 percent.

To find out what portion of the sheets were not used, we need to subtract the number of sheets used from the total number of sheets and then divide the result by the total number of sheets.

Number of sheets not used = Total number of sheets - Number of sheets used

Number of sheets not used = 1000 - 378 = 622

Now we need to divide the number of sheets not used by the total number of sheets:

A portion of sheets not used = Number of sheets not used / Total number of sheets

Portion of sheets not used = 622 / 1000 = 0.622

Therefore, 0.622 or 62.2% of the sheets were not used.

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The probability that a sample mean is between 137 and 143 is given as follows:

0.754 = 75.40%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 140, \sigma = 47, n = 330, s = \frac{47}{\sqrt{330}} = 2.59[/tex]

The probability that a sample mean is between 137 and 143 is the p-value of Z when X = 143 subtracted by the p-value of Z when X = 137, hence:

X = 143:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (143 - 140)/2.59

Z = 1.16 has a p-value of 0.877.

X = 137:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (137 - 140)/2.59

Z = -1.16 has a p-value of 0.1230.

Hence the probability is of:

0.877 - 0.123 = 0.754 = 75.40%.

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The cost of the hat is £5.

Let's say that the hat costs x pounds.

The cardigan's price might be represented as follows as it is £8 more expensive than the hat according to the problem:

x + £8

The cap and cardigan combined are listed as costing £18. Thus, we may represent an equation as:

x + (x + £8) = £18

Simplifying this equation, we get:

2x + £8 = £18

Subtracting £8 from both sides, we get:

2x = £10

Dividing both sides by 2, we get:

x = £5

Therefore, the hat costs £5.

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There are 8 children share two pics, the number of pics they all are shared is a fraction equals to the [tex] \frac{ 1}{4} [/tex].

Fractions denotes the parts of a whole or collection of things. A fraction has mainly two parts. The number which lie on the top of the line is known as the numerator. It describes how many equal parts of the whole or collection are taken. The number which lies below the line is called the denominator. There are 8 children share 2 pics equally. That is 2 is divided into 8 childrens equally. Then the part of 2 which each one get is represented by the fraction, [tex] \frac{ 2}{8} [/tex]. That is numinator is 2 and denominator is 8. On simplyfication, it is [tex] \frac{ 1}{4} [/tex]. Hence, required value is [tex] \frac{ 1}{4} [/tex].

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The X would be on the line at 1.5cm in first case while in second case it would be at 4.5cm.

A line is a geometric figure that is defined as a straight, continuous arrangement of infinitely many points extending infinitely in both directions. In mathematics, a line is often represented by a straight line with arrows on both ends, indicating its infinite nature.

In mathematics, a point is a precise location in space that has no size or dimension. It is often represented as a dot or a small circle. Points are used as basic elements in geometry and other branches of mathematics to define and describe shapes, lines, curves, and other objects. They are typically named using a single capital letter or a combination of letters and numbers.

a) Since AX:AB = 1:3, we can find the length of AX by dividing the length of AB by 4 (1+3). Thus, AX = (1/4)×AB = (1/4)×6 cm = 1.5 cm. To mark point X on the line, we can start at point A and measure 1.5 cm towards point B and mark that point with a cross.

b) Similarly, since PX:XQ = 1:3, we can find the length of XQ by dividing the length of PX by 4 (1+3). Thus, XQ = (3/4)×PX = (3/4)×6 cm = 4.5 cm. To mark point X on the line, we can start at point P and measure 4.5 cm towards point Q and mark that point with a cross. We can mark the points with red x's for clarity.

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The area of the window that Emily created, given the value of pi and the dimensions is 377. 04 in ².

To find the area, you can divide the shape into two different figures which would be the semi circle and the rectangle.

Area of the rectangle is:

= 12 in  x 22 in

= 264 in ²

Then find the area of the semi circle by the formula :

= Pi x radius x radius

= 3. 14 x 6 x 6

= 3. 14 x 36

= 113. 04 in ²

The area of the window is:

= 264 + 113. 04

= 377. 04 in ²

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The answer of the number simplified in scientific notation is 1 × 10¹.

Scientific notation is a way of expressing very large or very small numbers using powers of 10. In scientific notation, a number is written as a coefficient multiplied by 10 raised to an exponent.

(2 × 10⁻³)/(2 × 10⁻⁴) = 2¹⁻¹ × 10⁻³⁻⁽⁻⁴⁾

(2 × 10⁻³)/(2 × 10⁻⁴) = 2¹⁻¹ × 10⁻³⁺⁴

(2 × 10⁻³)/(2 × 10⁻⁴) = 2⁰ × 10¹

(2 × 10⁻³)/(2 × 10⁻⁴) = 1 × 10¹ {numbers to the power of zero is equal to 1}

Therefore, the answer of the number simplified in scientific notation is 1 × 10¹.

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The actual width of the tent is 72 inches.

Information given in the problem:

Scale: 1 inch : 3 feet

Width of tent on the drawing: 2 inches

The scale is same as

1 inch : 36 inches

2 inches :

Using the proportion from the scale:

Cross multiplying, we get:

1 inch × Actual width of the tent = 2 inches × 36 inches

Actual width of the tent = (2 inches × 36 inches) / 1 inch

Actual width of the tent = 72 inches

hence, the actual width of the tent is 72 inches.

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Answer:

a+ b 2

Step-by-step explanation:

Based on the given diagram, we can see that the angles in a triangle sum up to 180 degrees the value of x is 30 units.

In a triangle, the sum of the three interior angles always adds up to 180 degrees. This is known as the angle sum property of a triangle.

It means that if you add up the measures of the three angles of any triangle, the result will always be 180 degrees.

We can set up an equation:

2x + 50 + 3x - 20 = 180

Simplifying the left side of the equation:

5x + 30 = 180

Subtracting 30 from both sides:

5x = 150

Dividing both sides by 5:

x = 30

Thus, the value of x as per the given angles, is 30 units.

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The dot plot that shows a representative sample of the population is given as follows:

Option C.

A dot plot shows the number of times that each observations appears in the data-set.

Hence a representative sample is a sample in which the observations appear in proportions similar to that of the dot plot of the population, which is given by option C.

The sample is representative as observations 4 and 7 have the highest number of dots, same as for the dot plot of the population.

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