156 students at summer camp There are 13 cabins an equal number of students sleep in each cabin how many students stay in each cabin

Answer:

OOk

Step-by-step explanation:

Answer:

Options (1), (3) and (5)

Step-by-step explanation:

Equation that represents the relationship between the three sides of a triangle is,

a² + b² = c²

Where c = longest side of the triangle

If the length of the given sides satisfy the equation, triangle formed by the sides will be a right triangle.

Option A.

27 in, 36 in, 45 in

(45)² = (27)² + (36)²

2025 = 729 + 1296

2025 = 2025

True.

Option 2.

18 in, 22 in, 28 in

(28)² = (18)² + (22)²

784 = 324 + 484

784 = 808

False.

Option 3

10 in, 24 in, 26 in

(26)² = (10)² + (24)²

676 = 100 + 576

676 = 676

True.

Option 4

20 in, 21 in, 31 in

(31)² = (20)² + (21)²

961 = 400 + 441

961 = 841

False.

Option 5

28 in, 45 in, 53 in

(53)² = (28)² + (45)²

2809 = 784 + 2025

2809 = 2809

True.

Therefore, Options (1), (3) and (5) will be the correct options.

Answer:

Step-by-step explanation:

P(-2,-1) and Q(4,3)

average of x-coordinates = (-2+4)/2 = 1

average of y-coordinates = (-1+3)/2 = 1

midpoint of PQ: (1,1)

distance between midpoint and Q = √((4-1)²+(3-1)²) = √13

(x-1)² + (y-1)² = 13

The equation of the circle is \((x - 1)^{2} + (y - 1)^{2} = \frac{52}{4}\)

A circle is a shape consisting of all points in a plane that are at a given distance from a given point (the Centre) Equivalently .

Equation of circle

The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle.

The equation of circle represents all the points that lie on the circumference of the circle .

The standard equation of a circle with center at \((h , k )\) and radius r is

  \((x - h)^{2} + (y - k)^{2} = r^{2}\)

The distance formula in coordinate geometry is used to calculate the distance between two given points.

The formula says the distance between two points (\(x_{1} ,y_{1}\)), and (\(x_{2} , y_{2}\))

\(Distance(D) = \sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} }\)

The Midpoint Formula:

The midpoint of two ends coordinates points,  (\(x_{1} ,y_{1}\)), and (\(x_{2} , y_{2}\)) is the point M can be found by using:

\(M = \frac{x_{1} + x_{2}}{2}, \ \ \frac{y_{1} + y_{2}}{2}\)

According to the question

P = (-2,-1) and Q = (4,3) are the

endpoints of the diameter of a circle

Therefore, distance between point P and Q which is diameter of circle is

 \(Distance(D) = \sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} }\)

P(-2,-1) =  (\(x_{1} ,y_{1}\))

Q (4,3) =  (\(x_{2} , y_{2}\))

Now,

Diameter of circle = \(\sqrt{(4 - (-2) )^{2} + (3 - (-1) )^{2} }\)

                             = \(\sqrt{(6 )^{2} + (4 )^{2} }\)

                             = \(\sqrt{(36 + 16) }\)

                             = \(\sqrt{52}\)

As , radius  =  \(\frac{diameter }{2}\)

       radius (r) =  \(\frac{\sqrt{52}}{2}\)          

As we know The center of the circle separates the diameter into two equal segments called radii and radii are equal in a circle .

i.e mid point of coordinates of diameter are coordinates of circle .

\(M = \frac{x_{1} + x_{2}}{2}, \ \ \frac{y_{1} + y_{2}}{2}\)

\(Centre of circle (h,k) = \frac{x_{1} + x_{2}}{2}, \ \ \frac{y_{1} + y_{2}}{2}\)

\(h = \frac{x_{1} + x_{2}}{2}, \ \ k = \frac{y_{1} + y_{2}}{2}\)

\(h = \frac{ -2 + 4}{2}, \ \ k = \frac{-1 + 3}{2}\)

\(h = 1, \ \ k = 1\)

Now , substitute the value in the equation of circle

\((x - h)^{2} + (y - k)^{2} = r^{2}\)

\((x - 1)^{2} + (y - 1)^{2} = \frac{52}{4}\)

Hence, the equation of the circle is \((x - 1)^{2} + (y - 1)^{2} = \frac{52}{4}\)

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Answer:

30ft.

your welcome. ...................

The sales tax rate of a 7190 purchase is 1.25%.

This question relates to a percentage. A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, a sales tax of $90 is paid on a good of $7190. The percentage will be:

= 90 / 7190 × 100

= 1.25%

The tax rate is 1.25%.

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Complete question

What is the sales tax rate of a 7190 purchase if a sales tax of $90 is paid on a good of $7190

Answer:

Step-by-step explanation:

The unknown number, represented by the variable b, is 1/2, which satisfies the equation "Five more than the product of a number and 8 equals 9."

To solve the equation "Five more than the product of a number and 8 equals 9" using the variable b for the unknown number, we can express this statement as an equation:

8b + 5 = 9

To solve for b, we need to isolate the variable on one side of the equation. Let's simplify the equation step by step:

Subtract 5 from both sides to get rid of the constant term:

8b + 5 - 5 = 9 - 5

8b = 4

Divide both sides of the equation by 8 to solve for b:

8b/8 = 4/8

b = 1/2

Therefore, the solution to the equation is b = 1/2. This means that when we substitute b = 1/2 into the equation, the equation will hold true:

8(1/2) + 5 = 9

4 + 5 = 9

Both sides of the equation are equal, confirming that b = 1/2 is the solution.

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Answer:

CAB is 37 degrees

Step-by-step explanation:

90 + 53 = 143

180 - 143 = 37

Answer:

100

Step-by-step explanation:

the room is square this means each wall equal 25 .4 walls *25 =100 square feet

Answer:120

Step-by-step explanation:

Exponential growth is a type of growth that occurs when the rate of increase is proportional to the current amount.

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The possible formula for the polynomial in discuss whose roots are described as; having roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 is; P(x) = x^5 -5x⁴-6x³+18x².

The polynomial which is as described in the task content whose roots are as given can be written in its factorised form as follows;

P(x) = (x-3) (x-3) (x) (x) (x+1)

The expanded form is therefore;

P(x) = x^5 - 5x⁴- 6x³+ 18x².

Therefore, the polynomial having roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 is P(x) = x^5 - 5x⁴- 6x³+ 18x².

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To find f(g(x)), we substitute g(x) in place of x in the function f(x).

f(g(x)) = f(5x/(1-x)) = (5x/(1-x)) / (5 + (5x/(1-x))) = 5x / (1-x+5-5x) = 5x / 6 - 4x/6 = x/6

To find g(f(x)), we substitute f(x) in place of x in the function g(x).

g(f(x)) = g(x/(5+x)) = (5(x/(5+x))) / (1 - (x/(5+x))) = 5x / (5+x-x) = 5x/5 = x

Therefore, f(g(x)) = x/6 and g(f(x)) = x.

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Answer:

SI = $810

Amount = $3,810

Step-by-step explanation:

Given that ,

We can use the formula of SI to find the interest as ,

=> SI = P × R × T / 100

=> SI = $ 3000 × 5.4 × 5 / 100

=> SI = $ 30 × 5.4 × 5

=> SI = $ 810 .

=> Amount = SI + P

=> Amount = $ 810 + $ 3,000

=> Amount = $ 3,810

Answer:

Step-by-step explanation:

3000*(.054)(5)= $810

Answer:

Step-by-step explanation:

Perimeter:  

     \(P=(x+y+z) \ cm\)

Semi-perimeter:

     \(SP=\frac{1}{2} (x+y+z) \ cm\)

Answer:

constant is - 19

Step-by-step explanation:

the constant is the term in an expression with no variable attached to it.

12r + \(\frac{r}{2}\) - 19

the only term without the variable r attached to it is - 19

then the constant term is - 19

answerr:

2 ≤ 2x or 2x ≥ x + 5

x ≤ 1  or x ≥ 2.5

Answer:

80 mm²

Step-by-step explanation:

Even for slanted triangles, the area is base x half height! The base is 10 mm, half the height is 8 mm, so the area is 8x10=80 mm.

Answer:

the set of all real numbers -1≤y≤1

Step-by-step explanation:

according to the definition of 'sin'-function, the max value of it is '+1' and the min is '-1'. Finally, the correct answer is B. the set of all real numbers -1≤y≤+1.

Answer:

AC = 3 + 2√15

Step-by-step explanation:

Call the center of the circle O.

(OB)² = 2² + 3²

(OB)² = 13

OD = OB

(OD)² + (DC)² = (CO)²

13 + 51 = (CO)²

(CO)² = 64

(CX)² + 2² = (CO)²

(CX)² = 64 - 4

(CX)² = 60

CX = √60 = 2√15

AX = BX = 3

AC = AX + CX

AC = 3 + 2√15

The period of \(f(x)\) is \(\boxed{2\pi}\).

Recall that \(\sin(x)\) and \(\cos(x)\) both have periods of \(2\pi\). This means

\(\sin(x + 2\pi) = \sin(x)\)

\(\cos(x + 2\pi) = \cos(x)\)

Replacing \(x\) with \(3x\), we have

\(\sin(3x + 2\pi) = \sin\left(3 \left(x + \dfrac{2\pi}3\right)\right) = \sin(3x)\)

In other words, if we change \(x\) by some multiple of \(\frac{2\pi}3\), we end up with the same output. So \(\sin(3x)\) has period \(\frac{2\pi}3\).

Similarly, \(\cos(5x)\) has a period of \(\frac{2\pi}5\),

\(\cos(5x + 2\pi) = \cos\left(5 \left(x + \dfrac{2\pi}5\right)\right) = \cos(5x)\)

We want to find the period \(p\) of \(f(x)\), such that

\(f(x + p) = f(x)\)

\( \implies \sin(3x + p) + \cos(5x + p) = \sin(3x) + \cos(5x)\)

On the left side, we have

\(\sin(3x + p) = \sin(3x + 2\pi + p - 2\pi) \\\\ ~~~~~~~~ = \sin(3x+2\pi) \cos(p-2\pi) + \cos(3x+2\pi) \sin(p-2\pi) \\\\ ~~~~~~~~ = \sin(3x) \cos(p-2\pi) + \cos(3x) \sin(p - 2\pi)\)

and

\(\cos(5x + p) = \cos(5x + 2\pi + p - 2\pi) \\\\ ~~~~~~~~ = \cos(5x+2\pi) \cos(p-2\pi) - \sin(5x+2\pi) \sin(p-2\pi) \\\\ ~~~~~~~~ = \cos(5x) \cos(p-2\pi) - \sin(5x) \sin(p-2\pi)\)

So, in terms of its period, we have

\(f(x) = \sin(3x) \cos(p - 2\pi) + \cos(3x) \sin(p - 2\pi) \\\\ ~~~~~~~~ ~~~~+ \cos(5x) \cos(p - 2\pi) - \sin(5x) \sin(p - 2\pi)\)

and we need to find the smallest positive \(p\) such that

\(\begin{cases} \cos(p - 2\pi) = 1 \\ \sin(p - 2\pi) = 0 \end{cases}\)

which points to \(p=2\pi\), since

\(\cos(2\pi-2\pi) = \cos(0) = 1\)

\(\sin(2\pi - 2\pi) = \sin(0) = 0\)

The expressions are illustrations of algebraic expressions, and the simplified expressions are \(\frac{x^{5}y^{3}}{7}\), \(\frac{7y^{11}}{4z^{4}}\), \(8y^{2}\), \(\frac{6}{x^5w^3}\), \(64w^{15}\\\) and \(y^3\)

\((a)\ \frac{xy}{7x^{-4}y^{-2}}\)

Apply the quotient rule of indices

\(\frac{x^{1 + 4}y^{1 + 2}}{7}\)

Simplify the exponents

\(\frac{x^{5}y^{3}}{7}\)

Hence, the simplified expression is \(\frac{x^{5}y^{3}}{7}\)

\((b)\ \frac{7y^6}{4y^{-5}z^{4}}\)

Apply the quotient rule of indices

\(\frac{7y^{6+5}}{4z^{4}}\)

Simplify the exponents

\(\frac{7y^{11}}{4z^{4}}\)

Hence, the simplified expression is \(\frac{7y^{11}}{4z^{4}}\)

\((c)\ (x^3y^{-5})(2x^{-4}y^2)(4xy^5)\)

Apply the product rule of indices

\(4 * 2x^{-4+3+1}y^{2-5+5}\)

Simplify the exponents

\(8x^{0}y^{2}\)

Further, simplify

\(8y^{2}\)

Hence, the simplified expression is \(8y^{2}\)

\((d)\ (xw)(6x^{-6}w^{-4})\)

Apply the product rule of indices

\(6x^{-6+1}w^{-4+1}\)

Simplify the exponents

\(6x^{-5}w^{-3}\)

Rewrite as:

\(\frac{6}{x^5w^3}\)

Hence, the simplified expression is \(\frac{6}{x^5w^3}\)

\((e)\ (w \cdot 4w^2\cdot w^2)^3\)

Apply the product rule of indices

\((4w^{1+2+2})^3\)

Simplify the exponents

\((4w^{5})^3\)

Expand

\(4^3w^{5*3}\)

Further, simplify

\(64w^{15}\)

Hence, the simplified expression is \(64w^{15}\\\)

\((f)\ (\frac{y^2}{y})^3\)

Apply the quotient rule of indices

\((y^{2 - 1})^3\)

Simplify the exponents

\((y)^3\)

Remove the bracket

\(y^3\)

Hence, the simplified expression is \(y^3\)

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90 people

We are told that;

Total number of seats = 10

Number of people in each seat  = 2 Total duration of the Ferris wheel  = 30 minutes

Number of people to ride for the first 15 minutes = 15 × 2 = 30 people

This means that 2 seats will pass per minute and thus;

Number of people to ride for 15 minutes at this double speed = 15 × 2(2) = 60

2(2) was used because a seat can take 2 people.

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Answer:

A

Step-by-step explanation:

DE is the shortest side because it's is opposite to the smallest angle (<F)

180 - 60 = 3X +2X + 5,

X = 23

<F = 2*(23) +5 = 51

Chenelle can travel at most 160 miles without exceeding her spending limit of $300.

We have,

To determine the maximum number of miles Chenelle can travel without exceeding her spending limit of $300, we need to subtract the flat rate from her budget and divide the remaining amount by the cost per mile.

So,

Subtract the flat rate from Chenelle's budget:

Budget after subtracting the flat rate.

= $300 - $19.95

= $280.05

Divide the remaining budget by the cost per mile to find the maximum number of miles:

Maximum miles = Budget after subtracting the flat rate / Cost per mile

= $280.05 / $1.75

Using division.

Maximum miles = 160.028571

Therefore,

Chenelle can travel at most 160 miles without exceeding her spending limit of $300.

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Answer:

64x^12 / y^20

Step-by-step explanation:

(4x^3y^-5)^4

Distribute the exponential value of 4 to all terms in the parentheses.

4^4 * x^(3*4) * y^(-5*4)

Multiply each exponent.

64x^12 * y^-20

Make the negative exponent positive by making it a fraction.

64x^12 / y^20

Answer: 10

Step-by-step explanation:

2.5 times 4

Haleema would have approximately £3947.46 in her account after 2 years and 11 months, considering the monthly compounding interest of 5%.

To calculate the amount of money in Haleema's account after 2 years and 11 months, we need to consider the monthly compounding interest on the account.

The interest rate is given as 5% per year, which means the monthly interest rate is (5%/12) = 0.4167%.

Let's calculate the final amount using the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, P = £3700, r = 0.004167, n = 12 (monthly compounding), and t = 2.917 (2 years and 11 months).

Plugging these values into the formula, we get:

A = £3700(1 + 0.004167/12)^(12*2.917)

A ≈ £3947.46

The amount of money in Haleema's account after 2 years and 11 months would be approximately £3947.46.

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Answer:

Input     Output

  0             1

  2              2

 -8            -3

100           51

Step-by-step explanation:

Given

The rule: input ⇒ ÷2+1 ⇒ output

Solve

0 ⇒ 0÷2+1 ⇒ 1

2 ⇒ 2÷2+1 ⇒ 2

-8 ⇒ -8÷2+1 ⇒ -3

100 ⇒ 100÷2+1 ⇒ 51

Hope this helps!! :)

Please let me know if you have any questions

The zeros and the multiplicities are

from the question, we have the following parameters that can be used in our computation:

f(x) = (x + 6)³(x - 11)²(x - 6)(x + 5)³

The power of each factor are the multiplicities

So, we have

Zero(s) of multiplicity one:

x - 6 = 0

Zero(s) of multiplicity two:

x - 11 = 0

Zero(s) of multiplicity three:

x + 6 = 0 and x + 5 = 0

When evaluated, we have

Zero(s) of multiplicity one:

x = 6

Zero(s) of multiplicity two:

x = 11

Zero(s) of multiplicity three:

x = -6 and x = -5

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