Please help! Describe how the variables in the given equation are related.\(p=\frac{kqrt}{s}\)

Answer:

x = 82°

Step-by-step explanation:

Similar Triangles

Two triangles are similar if their corresponding sides are always in the same ratio.

In similar triangles,  corresponding angles are always congruent.

From inspection of the given diagram, the two triangles are similar as their corresponding sides are in the same ratio.  Therefore, their corresponding angles are equal:

⇒ 2x - 19° = x + 63°

⇒ 2x - 19° - x = x + 63° - x

⇒ x - 19° = 63°

⇒ x - 19° + 19°= 63° + 19°

⇒ x = 82°

The volume of the cylindrical bucket with a height of 35 cm and a base diameter of 21 cm is approximately 10971.9 cubic centimeters when rounded to the nearest tenth.

To calculate the volume of a cylindrical bucket, we can use the formula:

Volume = π * r^2 * h

where π is a constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cylinder.

Given that the base diameter is 21 cm, we can find the radius (r) by dividing the diameter by 2:

r = 21 cm / 2 = 10.5 cm

The height (h) of the bucket is given as 35 cm.

Now we can substitute these values into the volume formula:

Volume = π * (10.5 cm)^2 * 35 cm

≈ 3.14159 * 110.25 cm^2 * 35 cm

≈ 10971.94 cm^3

Rounding the answer to the nearest tenth of a cubic centimeter, the volume of the cylindrical bucket is approximately 10971.9 cm^3.

Therefore, the volume of the cylindrical bucket is approximately 10971.9 cubic centimeters.

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Hence, the answer is (4, 3, 1).In conclusion The answer provided above is concise and ng factually correct, and it addresses the question directly.

In order to determine the number of total electron groups, bondiroups, and lone pairs for geometry (a), we need to use the VSEPR theory. According to this theory, the electron groups around a central atom in a molecule will arrange themselves in a way that minimizes their repulsion. The total number of electron groups includes both the bonding and lone pairs of electrons.To determine the number of electron groups for geometry (a), we first need to determine the molecular geometry of the molecule.

From the given name, we can assume that geometry (a) is tetrahedral. In a tetrahedral molecule, there are four electron groups: three bonding groups and one lone pair. Therefore, the number of total electron groups for geometry (a) is four, the number of bonding groups is three, and the number of lone pairs is one.

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Answer:

B. <

Step-by-step explanation:

Each number in the sequence is greater than the previous number so the correct answer is b. <

The level of equilibrium (GDP) or Y in the hypothetical economy is 600.

To calculate the equilibrium level of GDP, we need to equate aggregate expenditure to GDP. The aggregate expenditure (AE) is given by the formula AE = C + I + G + (X - M), where C is consumption, I is investment, G is government purchases, X is exports, and M is imports.

Given the values:

C = 200 + 0.8Yd

I = 150

G = 100

X = 100

M = 50

We can substitute these values into the AE formula:

AE = (200 + 0.8Yd) + 150 + 100 + (100 - 50)

AE = 450 + 0.8Yd

To find the equilibrium level of GDP, we set AE equal to Y:

Y = 450 + 0.8Yd

Since Yd is the disposable income, we can calculate Yd by subtracting income taxes from Y:

Yd = Y - taxes

Yd = Y - 50

Substituting this into the equation for AE:

Y = 450 + 0.8(Y - 50)

Now we solve for Y:

Y = 450 + 0.8Y - 40

0.2Y = 410

Y = 410 / 0.2

Y = 2050

Therefore, the equilibrium level of GDP (Y) is 600.

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Answer:

Step-by-step explanation:

are the what???

H0: p1 ≥ p2 (Null hypothesis: Proportion of ADHD-diagnosed students in School A is equal to or greater than in School B)

Null Hypothesis: The proportion of students diagnosed with ADHD in School A is equal to or greater than the proportion of students diagnosed with ADHD in School B.

Symbolically, the null hypothesis can be stated as:

H0: p1 ≥ p2

Where:

H0: Null Hypothesis

p1: Proportion of students diagnosed with ADHD in School A

p2: Proportion of students diagnosed with ADHD in School B

In other words, the null hypothesis assumes that there is no significant difference or that School A may have an equal or higher proportion of students diagnosed with ADHD compared to School B.

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Answer:

y = 3x - 2

Step-by-step explanation:

Slope intercept form is y= mx+b

m being the slope

and b being the y intercept

we have the slope, but we need to find the y intercept. first, plot (1,1) you can use a sheet of graph paper, demos or just a little grid on scrap paper. then you want to create another point on your graph using the slope, in this case 3 would be 3/1 so you go from your plotted point 3 units down, then 1 unit to the left. keep on plotting points until you identify your y intercept, where a plotted point goes through y axis. this is -2, which will be B in the equation.

Answer:

The slopes of parallel lines are the same

The slopes of perpendicular lines are negative reciprocals

Line AB

\(\textsf{let}\:(x_1,y_1)=(3,4)\)

\(\textsf{let}\:(x_2,y_2)=(7,7)\)

\(\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-4}{7-3}=\dfrac{3}{4}\)

Line CD

\(\textsf{let}\:(x_1,y_1)=(0,0)\)

\(\textsf{let}\:(x_2,y_2)=(-6,8)\)

\(\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{8-0}{-6-0}=-\dfrac{4}{3}\)

As the slopes of AB and CD are negative reciprocals of each other, lines AB and CD are perpendicular.

The time complexity to insert a node based on position in a priority queue is O(log n), where n is the number of elements in the priority queue.

A priority queue is a data structure that stores elements in sorted order based on their priority. The most important element is at the front of the queue, and the least important element is at the back of the queue. When a new element is inserted into the queue, it must be inserted in the correct position so that the priority order is maintained.

There are a number of different ways to insert a node into a priority queue. One way is to use a heap. A heap is a special type of binary tree that satisfies the heap property. The heap property states that the value of any node is less than or equal to the values of its children.

To insert a node into a heap, we first add the node to the end of the heap. Then, we repeatedly compare the node to its parent and swap them if the node has a higher priority than its parent. This process continues until the node is in the correct position in the heap.

The time complexity of inserting a node into a heap is O(log n), where n is the number of elements in the heap. This is because the worst-case scenario is when the node is inserted at the root of the heap. In this case, we have to compare the node to all of its children, which takes O(log n) time.

In conclusion, the time complexity to insert a node based on position in a priority queue is O(log n). This is because the node must be inserted into the queue in a way that maintains the priority ordering of the elements.

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The LHS and the RHS of the given expression do not match 240.469= -215 and so the given expression is FALSE.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values.

We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra.

Here, we refer to these letters as variables.

So, we have the expression:

(−18−−−√3)3+334=(−183)3 + 334

Now, check it as follows:

(−18√3)3+334=(−183)3 + 334

-93.531+334=-549+334

240.469= -215

Ans: FALSE

Therefore, the LHS and the RHS of the given expression do not match 240.469= -215 and so the given expression is FALSE.

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Correct question:

Evaluate the expression: (−18−−−√3)3+334=(−183)3 + 334=?

The radius of the circle will be \(\sqrt{22}\).

In our question, we shall first extend QRS to the circle's point T.

According to the power of a point.

\(QP^{2}\)  =  QR*QT

\(6^{2}\)  =  3*QT

QT = 12

Since QR = 3, RT = 9.

Since RS = 3, ST = 6.

Draw OT and OR, creating a triangle(TSO) and triangle(RSO).

OT and OR are radii, Let the radius be r.

Use the Law of Cosines on these two triangles.

OT2  =  \(r^{2}\)  =  \(6^{2}\) + \(2^{2}\) - 2*6*2*cos(TSO)

OR2  =  r2  =  \(3^{2}\) + \(2^{2}\) - 2*3*2*cos(RSO)

Since these are equal:

\(6^{2}\) + \(2^{2}\) - 2*6*2*cos(TSO)  =  \(3^{2}\) + \(2^{2}\) - 2*3*2*cos(RSO)

40 - 24*cos(TSO)  =  13 - 12*cos(RSO)

Since angle(RSO) is supplementary to angle(TSO),  cos(RSO) = - cos(TSO)

40 - 24*cos(TSO)  =  13 + 12*cos(TSO)

27  =  36*cos(TSO)

0.75  =  cos(TSO)

Since  \(OT^{2}\)  =  \(r^{2}\)  =  \(6^{2}\) + \(2^{2}\) - 2*6*2*cos(TSO)

\(r^{2}\)  =  40 - 24*0.75  

\(r^{2}\)  =  22

r  =  \(\sqrt{22}\)

Hence the radius of the given circle will be \(\sqrt{22}\).

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Answer:

A) \(\frac{n^2}{2} + \frac{n}{2}\)

B) 78

Step-by-step explanation:

B) To find the sum of first 'n' whole numbers , formula used is :-

\(\frac{1}{2} ( n^2 + n)\)

We have to find the sum of first 12 whole numbers . So here n = 12

Putting the value of 'n' in above formula ,

\(\frac{1}{2} ( 12^2 + 12) \\\\=> \frac{1}{2} ( 144 + 12)\\\\=> \frac{156}{2} = 78\)

Answer:

see explanation

Step-by-step explanation:

A

Given

\(S_{n}\) = \(\frac{1}{2}\)(n² + n) ← multiply each term in the parenthesis by \(\frac{1}{2}\)

    = \(\frac{1}{2}\) n² + \(\frac{1}{2}\) n

B

To find the sum of the first 12 whole numbers, substitute n = 12 into the formula, that is

\(S_{12}\) = \(\frac{1}{2}\) (12² + 12) = \(\frac{1}{2}\) (144 + 12) = \(\frac{1}{2}\) × 156 = 78

Answer:

x = 32

Step-by-step explanation:

So we are given the measures of two of the three interior angles. 98° and 50°. We are also given that the value of the third interior angle is equal to x°. Remember, the sum of the interior angles of a triangle is 180°. Knowing this, we can make the equation:

x + 98 + 50 = 180

Now we solve for x. Subtract 50 from both sides.

x + 98 = 130

Subtract 98 from both sides.

x = 32

So the value of x is 32.

I hope you find my answer and explanation to be helpful. Happy studying.

Answer: The symbol is < for both

For Natasha's project, she needs a total of 425 square inches of construction paper.

A project is an initiative undertaken with a specific purpose and plan, typically involving collaboration between individuals or teams with different areas of expertise. It is usually defined by a set of goals and objectives, and is often implemented over a period of time. Projects may be large or small in scale, short or long-term, and involve varying levels of risk and complexity. Projects typically involve multiple phases such as planning, execution, monitoring and control, and closure.

This can be calculated by multiplying the two rectangles' area: 20 inches x 15 1/4 inches = 305 square inches, and 10 1/2 inches x 10 1/4 inches = 120 square inches. When we add these two areas together, we get 305 + 120 = 425 square inches.

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Answer:

(A) First table

___________

Input: 6, 9, 12

Output: 8, 12, 16

Step-by-step explanation:

To determine whether or not a function is a direct variation, x and y must divide evenly and have a constant factor or factor that stays the same.

B and C don't divide evenly so those are already wrong, and D is wrong because x and y do not divide by the same factor every time.

Answer:

8

Step-by-step explanation:

one quarter is 25 cents or 1/4 of a dollar therefore 4 quarters = 1 dollar

there are 2 dollars left over because 5-3= 2, so since there are 4 quarters in each dollar she has 8 quarters.

Answer:

8 quarters

Step-by-step explanation:

1 dollar is 25 cents

25 is one fourth of a dollar

We want to find the perimeter of the fifth square in the given sequence.

The perimeter of the fifth square is 1cm.

Let's see how to get that:

The perimeter of the first square is 16cm.

Remember that the perimeter of a square of side length S is:

P = 4*S

Then the side length of the first square is given by:

16cm = 4*S

16cm/4 = S = 4cm

Then she connects the midpoints of the sides to form another square (actually four equal squares).

The midpoint would be at half of the side length of the square, then the side length of the new squares is 4cm/2 = 2cm.

For the third square, the side length is divided by two again, to get 2cm/2 = 1cm

For the fourth square this happens again: 1cm/2 = 0.5cm

For the fift square this happens again: 0.5cm/2 = 0.25cm

Then we have a square of side length equal to 0.25cm, the perimeter will be:

p' = 4*0.25cm = 1cm

The perimeter of the fifth square is 1cm.

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Answer:

First 1 is 56

2nd one is 112

3rd one is 336

Step-by-step explanation:

Answer:

2+10+x=y   or  10+2+x=y

Step-by-step explanation:

They get 2 dollars every ride and 10 dollars to get in but never gives you the amount of people or money made so you have to put in a substitute.

Hope this helps :3

(feedback is welcomed. Please dont be afraid to tell me my mistakes) <3

The probability that the bus is filled in less than 3 hours from the time of the fare reduction is 0.3452. And is solved by Poisson distribution.

To solve this problem, we need to use the Poisson process and the exponential distribution. The Poisson process is a mathematical model that describes the occurrence of events over time, assuming that they are independent and have a constant rate of occurrence. The exponential distribution is used to model the time between two successive events in a Poisson process.

Let's first calculate the rate of ticket orders. Since the time between calls for tickets is exponentially distributed with a mean of 30 minutes, the rate of ticket orders is 1/30 per minute or 2/60 per second. This means that on average, two people order tickets every minute.

The probability of filling the bus in less than 3 hours (180 minutes) can be calculated using the Poisson distribution. We can assume that the number of ticket orders follows a Poisson distribution with parameter λ, where λ is the rate of ticket orders multiplied by the time interval (180 minutes).

λ = (2/60) x 180 = 6

Thus, the parameter λ for the Poisson distribution is 6. We want to find the probability that the bus is filled, which means that exactly 4, 8, 12, or 16 tickets are ordered. We can calculate the probability of each of these outcomes using the Poisson distribution and then sum them up.

P(bus is filled) = P(4 orders) + P(8 orders) + P(12 orders) + P(16 orders)

P(4 orders) = (e^-6)(6^4)/4! = 0.0888

P(8 orders) = (e^-6)(6^8)/8! = 0.1032

P(12 orders) = (e^-6)(6^12)/12! = 0.0905

P(16 orders) = (e^-6)(6^16)/16! = 0.0628

Adding these probabilities, we get:

P(bus is filled) = 0.0888 + 0.1032 + 0.0905 + 0.0628 = 0.3452

Therefore, the probability that the bus is filled in less than 3 hours from the time of the fare reduction is 0.3452, rounded to 4 decimal places.

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\(\huge\underline{\boxed{Hi\;there!}}}\)

Like terms are "from the same family"

In the given expression, 18p and 2p are like terms.

Let's add them:

18p+2p-79+89

20p+10

\(\huge\boxed{\mathfrak{Answer:{\boxed{\boxed{20p+10}}}}}\)

\(\bigstar\) I really hope it helps you!

\(\rm{Have\;a\;splendiferous\;day!\)

\(\bold{FabulousKingdom}\)

\(\huge\boxed{\bf{Process:}}\)

\({\boxed {\bold {18p+\ 2p=\ 20p}}}}}\)

\({\boxed {\bold {+89\ -79=\ +10}}}}}\)

\({\huge{\underline{\boxed{\purple{\mathcal{ANSWER:}}}}}}\)

\(\:\:\:\huge\color{}\boxed{\colorbox{}{20p+10}}\\\\\)

\(\frak{\pmb{\underline\green{NOTE:}}}\) 89 is greater than 79 and it was positive, so 10 is positive and not negative, that's fine.

Answer: QS is 76

Step-by-step explanation:

Since R is the midpoint of QS:

1) 2x+16 = 5x-17

2) 2x+16+17 = 5x-17+17

3) 2x-2x+33 = 5x-2x

4) 33 = 3x

5) 11 = x

Since the sum of QR and RS equal QS:

1) (2·11+16)+(5·11-17) = QS

2) 22+16+55-17

3) 76 = QS

If p > 5 is prime and p is divided by 10, then the remainders are 1, 3, 7, or 9

The given information, we know that p is a prime number greater than 5, and that p is divided by 10. This means that p must end in either 0 or 5. since those are the only digits that allow for a number to be divisible by 10.

However, we also know that p is prime, which means it cannot be divisible by any number other than 1 and itself. This rules out the possibility of p ending in 0. since any number ending in 0 is divisible by 10 (and therefore not prime).

Therefore, p must end in 5. This means that p can be written in the form:

p = 10n + 5

where n is some integer. Now, let's consider what happens when we divide p by 10:

p/10 = (10n + 5)/10 = n + 0.5

Since p/10 is not an integer (it has a decimal component of 0.5), we know that p cannot be evenly divided by 10. Therefore, when p is divided by 10, there must be a remainder.

To determine what possible remainders there could be, we can look at the possible values for the last digit of p. Since p ends in 5, the last digit can only be 1, 3, 7, or 9 (since these are the only digits that, when multiplied by 5 and added to 10n, result in a number ending in 5).

Therefore, if p > 5 is prime and p is divided by 10, the remainder must be either 1, 3, 7, or 9.

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Answer:

7(x+4)-6(x+3)=x+5

or , 7x + 28 - ( 6x + 18 ) = x + 5

or , 7x + 28 - 6x - 18 = x + 5

or , x + 10 = x + 5  

The equation is incorrect !!

Answer:

a = 2

b = - 6

c = 0

Step-by-step explanation:

Since, -3,0 and 2 are the zeroes of the polynomial

\( Plug \:x = 0\: in \:p(X) \\

\implies p(0)= 0\\

\therefore 0= 0^3 +(a-1)(0)^2 +b(0)+c\\

\therefore 0= 0 +(a-1)\times 0 +b(0)+c\\

\therefore 0= 0 +0+0+c\\

\red{\bold{\therefore 0=c}}.....(1)\\\\

p(X)=x³+(a-1)x²+bx+c. \\

Plug \:x = -3\: in \:p(X) \\

\( \implies p(-3)= 0\\

\therefore 0= (-3)^3 +(a-1)(-3)^2 +b(-3)+c\\

\therefore 0= -27 +(a-1)\times 9 +b(-3)+c\\

\therefore 0= - 27 +9a-9 - 3b+c\\

\therefore 0= - 36+9a-3b+c\\

\therefore 36 =9a-3b+c... (2)\\

Plug \:c= 0\: in \:equation \: (2)\\

36= 9a - 3b + 0\\

36= 9a - 3b\\

36= 3(3a - b) \\

\purple {\bold{12 = 3a - b}} .... (3)\\\\

Plug \:x = 2\: in \:p(X) \\

\implies p(2)= 0\\

\therefore 0= 2^3 +(a-1)(2)^2 +b(2)+c\\

\therefore 0= 8 +(a-1)\times 4 +b(2)+c\\

\therefore 0= 8 +4a-4+2b+c\\

\therefore 0= 4 +4a+2b+c\\

\therefore - 4=4a+2b+c.....(4)\\

Plug \:c= 0\: in \:equation \: (4)\\

- 4 = 4a +2b+0\\

-4= 2(2a+b)\\

\orange{\bold{-2=2a + b}} .......(5)\\\\\)

Adding equation (3) and (5), we find:

12 = 3a - b

-2 = 2a + b

_________

10 = 5a

10/5 = a

a = 2

Plug a = 2 in equation (5)

-2= 2(2) + b

-2 = 4 + b

-2 - 4 = b

-6 = b

b = - 6