four numbers that are evenly divisible by 2, 3, and 5.

We are asked to determine the total number of students in a school. To do that we need to add the number of students in each of the year classes. Beginning with the 9th class we have:

Now, the number of students in the 10th year class is 20% more, this means:

Now, the number of students in the 11th year class is:

The 12th year class is:

Now we add all the students in each class:

Therefore, there are about 1610 students in Townsend High School.

Answer:

A: 428.75/ 24.5 = $17.50 per sq foot

B: 62.50*24.50 = $1,531.25

C: 428.75 + 1,531.25 + 137.50 = $2,097.50 for the total replacement

Step-by-step explanation:

Answer:

Q1: \(\sqrt{361} =19\)

Q2: ±\(\sqrt{1.96} =\)± \(1.4\)

Q3: \(-\sqrt{\frac{9}{16} }\)= \(-\frac{3}{4}\)

Q4: It cannot be simplified, since it is impossible to square root a negative number. A number cannot be multiplied by itself to get a negative answer.

Q5: \(m^{2} =0.04\)

±\(\sqrt{0.04}\) = ±\(0.2\)

\(m=\) ±\(0.2\)

Q6: \(\sqrt[3]{343} = 7\)

Q7: \(\sqrt[3]{-512} =-8\)

Q8: \(s^{3} =91.125\)

\(s=\sqrt[3]{91.125}\)

\(s=4.5\)

Q9: \(\sqrt{196} =14\)

Q10: \(p^{3}=-0.027\)

\(p=\sqrt[3]{-0.027}\)

\(p=-0.3\)

Q11:

Length of one square: x

Area: \(6x*x=6x^{2}\)

\(6x^{2} =96\)

\(x^{2} =16\)

\(x=4\)

Length of the path: \(6*4=24\)

Q12:

Length of one photo: y

Area: \(7y*y=7y^{2}\)

\(7y^{2} =567\)

\(y^{2} =81\)

\(y=9\)

Length of collage:

\(9*7=63\)

Q13:

\(\sqrt[3]{8}=2\) but \(\sqrt{8}\) = \(2.8284271...\) (goes on forever and cannot be expressed as a fraction)

Q14:

Let's say you have 70 tables and you want to make a square formation.

\(\sqrt{70}=8.3666...\)

It's clearly impossible to have 8.3666... tables, so we round down to 8.

Even though you didn't use all 70 tables, you still made a square with the most numbers of table possible.

I don't have an answer to the question...but:

The triangle having sides - 4, 5, and 6 is a right triangle, 11, 12, and 15 is an acute triangle and 30, 40, and 50 are also a right triangle.

To determine the type of triangle, we can use the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Here,6²  = 4² + 5², which simplifies to 36 = 16 + 25. Since the Pythagorean theorem holds, we know that this is a right triangle.

Therefore, the triangle with sides 4, 5, and 6 is a right triangle.

8.) 11, 12, 15:

We can use the Law of Cosines to determine the type of triangle, which states that for any triangle with sides a, b, and c and angle C opposite side c, c² = a²+ b²- 2ab cos(C).

Using this formula, we get:

15² = 11² + 12² - 2(11)(12) cos(C)

225 = 265 - 264cos(C)

264cos(C) = 40

cos(C) = 40/264

C = cos⁻¹(40/264) ≈ 81.87°

Since all angles of a triangle add up to 180°, we know that the remaining angles must be less than 90° (acute). Therefore, the triangle with sides 11, 12, and 15 is an acute triangle.

9.) 30, 40, 50:

Using the Law of Cosines, we get:

50² = 30² + 40² - 2(30)(40) cos(C)

2500 = 2500 - 2400cos(C)

cos(C) = 0

C = cos⁻¹(0) = 90°

Since one angle of the triangle is a right angle, we know that this is a right triangle.

Therefore, the triangle with sides 30, 40, and 50 is a right triangle.

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The above question is a mathematical proof of the relationship between Lines and angles related to a Rhombus. See the proof below.

We know,

A Rhombus is a parallelogram with four sides (that is a quadrilateral). It's sides however are all of equal length.

we have,

∠DEC ≅ ∠BFC  Reason = All Right Angles with Equal dimensions are congruent.

∠C ≅ ∠C  Reason = It is the same angle for the two Right angles above which are congruent, hence Reflexive Property.

Δ DEC ≅ Δ BFC  Reason = Angle Angle Side. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

 ≅   Reason = The corresponding parts of congruent triangles are congruent. Also, it is a parallelogram with all congruent sides.

ABCD is a Rhombus Reason = Its sides are all congruent.

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complete question:

Given: ABCD is a parallelogram, FC is congruent to EC, DE bisects BC and BF bisects DC Prove: ABCD is a rhombus

Answer:

5.5p-17.6

Step-by-step explanation:

-3.1p + 2(4.3p – 8.8)=-3.1p+8.6p-17.6=5.5p-17.6

Answer:

103%

Step-by-step explanation:

each little box is 1%

The intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

To show that a1 ≤ a2 ≤ ... ≤ an ≤ ..., we need to use the fact that the sequence of intervals is nested, meaning that each interval is contained within the next one.

First, we know that I1 contains I2, so every point in I2 is also in I1. That means that a1 ≤ a2 and b1 ≥ b2.

Now consider I2 and I3. Again, every point in I3 is also in I2, so a2 ≤ a3 and b2 ≥ b3.

We can continue this process for all the intervals in the sequence, until we reach In. So we have:

a1 ≤ a2 ≤ ... ≤ an-1 ≤ an

and

b1 ≥ b2 ≥ ... ≥ bn-1 ≥ bn

This shows that the endpoints of the intervals are ordered in the same way.

Given that I₁ ⊇ I₂ ⊇ ... In ⊇ ... is a nested sequence of intervals and In = [an; bn], we can show that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... as follows:

Since the intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

Continuing this pattern for all intervals in the sequence, we can conclude that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... .

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Answer:

12

Step-by-step explanation:

12 x 12 = 144

Answer:

12

Step-by-step explanation:

\(\sqrt{144}\)=12

Intro:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

This is the slope formula \(y=mx+b\) if you know what each letter stands for you know which one is slope.

Each Letter Meanings:

y stands for the y-value in the order pairs on the line.

m stands for the rate of change, AKA the slope of the line.

x stands for the x-value in the order pairs on the line.

b stands for the y-intercept.

_________________________________________________________

So now you should have figured out that \(\frac{1}{3}\) is the slope of the line.

Answer:

slope is 1/3

first point y intercept is 1/7

its a non linear function

(-3/7,0) (0,1/7)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Its number line 2.

Answer:

64

Step-by-step explanation:

You need to substitute the value of each number into its corresponding variable

2(3 + 3(6) + 4(1)+ 7)

You multiply to get this

2(3+18+4+7)

You then add all of the numbers up to get this

2(32)

Then, multiply 2 by 32 to get 64

John initially had Php 132 and Mary initially had Php 252 (384 - 132).

Let's start by setting up the equations to solve for this problem.

Let x be the amount of money John had initially.

Then, Mary had (384 - x) initially.

After John gave Php 36 to Mary, John had (x - 36) left and Mary had (384 - x + 36) = (420 - x).

We are told that Mary had three times as much money as John after this transaction, so we can write:

3(x - 36) = 420 - x

Simplifying this equation gives:

3x - 108 = 420 - x

4x = 528

x = 132

Therefore, John initially had Php 132 and Mary initially had Php 252 (384 - 132).

Answer: Mary had Php 252 at first.

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Answer:  C(10,7)

Reason:

We can numerically compute both C(10, 3) and C(10, 7) and we would get 120 for each result.

Use the nCr combination formula

\(nCr = \frac{n!}{r!(n-r)!}\)

In general we have the rule C(n, r) = C(n, n-r)

To find the average cost of producing 400 units of plywood, we need information about the cost function. If we have the cost function per unit, we can calculate the total cost of producing 400 units and then divide it by 400 to find the average cost per unit.

Let's assume the cost function for producing x units of plywood is given by C(x), where C(x) represents the cost in dollars. We can then calculate the total cost of producing 400 units as follows:

Total Cost = C(x) * Number of Units

Total Cost = C(400) * 400

Once we have the total cost, we can find the average cost per unit by dividing the total cost by the number of units:

Average Cost per Unit = Total Cost / Number of Units

Average Cost per Unit = (C(400) * 400) / 400

Average Cost per Unit = C(400)

Therefore, to find the average cost of producing 400 units, we need to know the cost function C(x) specifically for producing 400 units of plywood. Without that information, we cannot provide an exact value for the average cost.

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If the cost per unit is to produce x units of plywood. find the average cost of producing 400 units.

Answer:

60x8=6x8=48x10=480

Step-by-step explanation:

Answer:

166.68

Step by Step:

166.678

The bolded number is greater than 5 meaning you have to round up.

so 166.678 is rounded to 166.68.

Hope this helped.

Answer:

a= 12

Step-by-step explanation:

Use pythagorean theorem

a^2 + b^2 = c^2 where c is the hypotenuse

so 9^2 + a^2 = 15^2

81 + a^2 = 225

a^2 = 144

square root both sides to get a = 12

Answer:

164 degree is the answer

Answer:

Step-by-step explanation:

Chord PM and PN are equal

arc PM = arc PN

164=5x+4

x=32

arc PN = 5x+4 = 5(32)+4=164

Answer:

8 cm

Step-by-step explanation:

24 ÷ 3

The solution are,

2x^2+ 12 x = 0

3.6x^2 + 8 = 0

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

Quadratic equations are those with the variable to the power of 2

2x^2+ 12 x = 0

3.6x^2 + 8 = 0

now, we get,

None of the other equations have the variable raised to the power of 2.

Hence, The solution are,

2x^2+ 12 x = 0

3.6x^2 + 8 = 0

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Answer:

BC = 28

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are in proportion, that is

\(\frac{BC}{EF}\) = \(\frac{AB}{DE}\) ( substitute values )

\(\frac{BC}{7}\) = \(\frac{16}{4}\) = 4 ( multiply both sides by 7 to clear the fraction )

BC = 4 × 7 = 28

To find the derivative of the given function f(x) = 6√(5x-8)(-5x²-3x), we can use the product rule and the chain rule. Let's break it down step by step.

First, applying the product rule, we have:

\(f'(x) = (6\sqrt{5x-8})'(-5x^2-3x) + (6\sqrt{5x-8})'(-5x^2-3x)'\)

Next, we apply the chain rule to the square root term:

\(f'(x) = (6\sqrt{5x-8})'(-5x^2-3x) + (6\sqrt{5x-8})'(-5x^2-3x)'\)

Now, let's find the derivatives of the individual terms:

\(\left(\sqrt{5x-8}\right)' = \frac{1}{2}(5x-8)^{-\frac{1}{2}}(5)\)

\((-5x^2-3x)' = -10x - 3\)

Now, substituting these derivatives back into the equation, we have:

\(f'(x) = 6\left(\frac{1}{2}\right)(5x-8)^{-\frac{1}{2}}(5) + 6\sqrt{5x-8}(-10x - 3)\)

Simplifying further, we have:

\(f'(x) = 3\left(\sqrt{5x-8}\right)^{-1/2}(-5x^2-3x) - 6\sqrt{5x-8}(10x+3)\)

In short, the derivative of

\(f(x) = 6\sqrt{5x-8}(-5x^2-3x)\\f'(x) = 3\left(\sqrt{5x-8}\right)^{-1/2}(-5x^2-3x) - 6\sqrt{5x-8}(10x+3)\)

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A reasonable value for the actual percentage of the population that prefers candidate A, taking into account the margin of error of 2.5%, would be between 28.5% and 33.5%. This range reflects the potential variability in the survey results and provides a reasonable estimate of the true population preference.

We have that the survey was conducted on a random sample of voters in the United States and the percentage who preferred candidate A was 31%, a reasonable value for the actual percentage of the population that prefers candidate A can be estimated by taking into account the margin of error.

Since the margin of error was 2.5%, we can consider a range around the observed percentage of 31%.

A reasonable value for the actual percentage of the population that prefers candidate A would be within the range of 28.5% (31% - 2.5%) to 33.5% (31% + 2.5%).

This range takes into account the margin of error and provides a reasonable estimate of the true population preference for candidate A.

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Here, we use the property of multiplication of exponential expression which states when we multiply two exponential expressions with the same base, we keep the base and add the exponents.

Therefore,

\(x^(3+5) = x^8\)

Now,

\(x^(3+5) = x^8\)

is of the form:

\(x^b = x^p\)

When we have two equal expressions on either side of the equation, the power of the base remains the same. Therefore,

p = 8

There we have it. The value of p is 8. The full solution is shown below:

\(x^3 × x^5 \\= x^px^8\\ = x^p\)

We can see that the base of the exponential expression on either side is equal.

Therefore, the power of the base must be equal as well. In other words

,p = 8.

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Answer:

Hats cost $15, T-Shirts cost $25, Jackets cost $45

If this was helpful please mark brainliest, have a great day!

Driving from North Carolina to Florida at an average speed of 70 mph takes about 7 hours and 12 minutes.

Velocity is a term used to describe how fast an object is moving in a particular direction. It is measured as distance traveled in a period of time and is usually expressed in units of meters per second (m/s). Velocity is an important concept in physics and is used to calculate how fast an object moves in a given environment. Velocity is related to speed, which is the rate of change of distance in a particular direction. Speed ​​is an important factor in many sports and activities such as running, cycling and driving. It is also used in different ways in our daily life. For example, it is used to determine how fast a car can go from A to B, or how long it will take to walk to a destination.

Speed = Distance/Time

55 = Distance/9

Distance = 495 miles

When speed is 70 mph:

70 = 495/Time

Time = 495/70

Time = 7 hours and 12 minutes

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Answer:

0.625

Step-by-step explanation:

Just take a calculator and devide it

Answer: 1 usd to thai baht is 33.44 thai baht or 33 thai baht

Step-by-step explanation:
There's no need for an explanation for this as you can just search this on the internet.