Which equations represents a proportional relationship.
please help

Answer:

you would have 3 white balls and 3 red balls

Step-by-step explanation:

Answer:

14.

Step-by-step explanation:

1) if the sides of the given triangle are 'a'=9, 'b'=x and 'c'=x+2, then its perimeter can be written as: P=a+b+c or P=9+x+x+2;

2) if according to the condition P=35, then 9+x+x+2=35;

2x=24; ⇒ x=12;

3) if x=12, then a=9; b=12 and 14;

4) finally, c=14 - the required longest side.

Answer:

yes it is rational, as it can be expressed in the form p/q where p=-2 and q=3

Step-by-step explanation:

Step-by-step explanation:

We know that the formula for slope is y=mx+b, with m equaling the slope itself and b equaling the y-intercept. Since the slope is -4, we can safely say that the equation starts off as y=-4x.

The y-intercept is (0,2). This means that the x-coordinate is 0 and the y-coordinate is 2, so the y-intercept is 2. Since 2 is being added, the equation is y=-4x+2

Answer:

y=-4x+2

The final answer is dy/dr = 2x^3 / (x^2 + y)

To find dy/dr, we first need to express y as a function of r. This can be done using the chain rule:
dy/dr = (dy/dx) * (dx/dr)
Since y = x^2, we have:
dy/dx = 2x
And since x = r cos(theta), we have:
dx/dr = cos(theta)
Putting it all together, we get:
dy/dr = 2x * cos(theta)
Now we can use this to find points with horizontal and vertical tangents:
(a) To find points with horizontal tangents, we need dy/dr = 0. This occurs when cos(theta) = 0, which means theta = pi/2 or 3pi/2. So the points with horizontal tangents are:
(r, theta) = (0, pi/2), (0, 3pi/2)
(b) To find points with vertical tangents, we need dx/dr = 0. This occurs when theta = pi/2 or 3pi/2, regardless of the value of r. So the points with vertical tangents are:
(r, theta) = (r, pi/2), (r, 3pi/2)
(c) To find the tangent at a given point, we just need to plug in the values of r and theta into our expression for dy/dr. For example, at the point (1, pi/4), we have:
dy/dr = 2(1) * cos(pi/4) = sqrt(2)
So the tangent at this point is given by y - x^2 = sqrt(2)(r - 1).
(d) To get parametric equations using y = x^2, we just need to eliminate r and theta from the equations x = r cos(theta) and y = x^2. We have:
x = r cos(theta)
y = x^2
Solving for r and theta, we get:
r = sqrt(x^2 + y)
theta = arctan(y/x)
So the parametric equations are:
x = r cos(theta) = sqrt(x^2 + y) cos(arctan(y/x))
y = x^2
(e) To express dy/dr in terms of x and y, we just need to substitute x = r cos(theta) and y = x^2 into our expression for dy/dr. We get:
dy/dr = 2x * cos(theta) = 2(r cos(theta)) cos(theta) = 2x cos^2(theta) = 2x (x^2 / (x^2 + y))
So dy/dr in terms of x and y is:
dy/dr = 2x^3 / (x^2 + y)

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Answer:

0.8 hours = 48 minutes per lawn

Step-by-step explanation:

10 lawns in 8 hours

hours per lawn 8/10 = 0.8 hours = 48 minutes

Answer:

4/5 hour per lawn

Step-by-step explanation:

We want to find Hunter's rate in hours per lawn.

Therefore, we must divide the number of hours by the number of lawns.

\(\frac{hours}{lawns}\)

He mowed 10 lawns in 8 hours.

\(\frac{8}{10}\)

This fraction can be simplified. Both the numerator and denominator can be divided by 2.

\(\frac{8/2}{10/2}\)

\(\frac{4}{5}\)

If we multiply by 60, we can find how many minutes this is. (60 minutes = 1 hour)

\(\frac{4}{5}*60=48\)

His rate is 4/5 hour per lawn or 48 minutes per lawn.

The simplified expression is \(21x^2 - 25x - 28\) in the given case.

An expression in mathematics is a combination of numbers, symbols, and operators (such as +, -, x, ÷) that represents a mathematical phrase or idea. Expressions can be simple or complex, and they can contain variables, constants, and functions.

"Expression" generally refers to a combination of numbers, symbols, and/or operations that represents a mathematical, logical, or linguistic relationship or concept. The meaning of an expression depends on the context in which it is used, as well as the specific definitions and rules that apply to the symbols and operations involved. For example, in the expression "2 + 3", the plus sign represents addition and the meaning of the expression is "the sum of 2 and 3", which is equal to 5.

To simplify the expression, first distribute the -3x and (3x + 4) terms:

\(-3x(4 - 5x) + (3x + 4)(2x - 7) = -12x + 15x^2 + (6x^2 - 21x + 8x - 28)\)

Next, combine like terms:

\(-12x + 15x^2 + (6x^2 - 21x + 8x - 28) = 21x^2 - 25x - 28\)

Therefore, the simplified expression is \(21x^2 - 25x - 28.\)

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The percent markup of a department, if they sell 300 shirts at a cost of $9 each is 50%

According to the question, we learn that a department store buys 300 shirts at a cost of $1,800 and sells them for $9 each. This means :

The selling price of 300 shirts = 300 × $9

The selling price of 300 shirts = $2700

Selling price > cost price i.e., 2700 > 1800

when selling price is greater than cost price it means department store made a profit.

Profit = selling price - cost price

Profit = 2700 - 1800 = $900

Profit percentage = profit/ cost price × 100

Profit % =\(\frac{900}{1800} \times 100\)

Profit % = 50%

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Point A can be described as a multiple of a power of ten as 0.1 or 10^-1.

Looking at the number line, we can see that Point A is located to the left of zero and to the right of -10. The distance between Point A and zero is 1 unit, which means that Point A has a value of 1.

To describe Point A as a multiple of a power of ten, we need to determine the power of ten that corresponds to the position of Point A on the number line. Since Point A is located to the left of zero, we know that its value is less than 1.

To determine the power of ten, we can use the fact that each unit on the number line represents a power of ten. For example, moving one unit to the right corresponds to multiplying by 10, and moving one unit to the left corresponds to dividing by 10.

Since Point A is located one unit to the left of zero, we can describe its value as 0.1, which is equivalent to 1 divided by 10. This means that Point A is a multiple of 10 to the power of -1.

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The probability of event A and event B is 6.

Given that, P(A)=6, P(B)=20 and P(A∩B)=6.

P(A/B) Formula is given as, P(A/B) = P(A∩B) / P(B), where, P(A) is probability of event A happening, P(B) is the probability of event B.

P(A/B) = P(A∩B) / P(B) = 6/20 = 3/10

We know that, P(A and B)=P(A/B)×P(B)

= 3/10 × 20

= 3×2

= 6

Therefore, the probability of event A and event B is 6.

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Answer:

24x+9+5y

Step-by-step explanation:

you just add all the like terms

Answer:

slope is -3

Step-by-step explanation:

Answer:

x = 4.25

Step-by-step explanation:

First, alter the equation until both exponents have the same base. We know that 9^3 is 27. Therefore, we can change 27^(x-3) into 9^3(x-3).

Now, the equation can be written as 9^(8-x) = 9^(3x-9)

Now that the bases are the same, we can cancel them out and just solve for the exponents. This will look like:

8-x = 3x-9.

8 = 4x - 9

17 = 4x

x = 4.25

To rewrite the integral ∫(2x)\(e^{4x^{2} }\)dx using integration by parts, we'll consider the function f(x) = (2x) and g'(x) = \(e^{4x^{2} }\).

Integration by parts states that ∫u dv = uv - ∫v du, where u and v are functions of x.

Let's assign:

u = (2x) => du = 2 dx

dv = \(e^{4x^{2} }\) dx => v = ∫\(e^{4x^{2} }\) dx

To evaluate the integral of v, we need to use a technique called the error function (erf). The integral cannot be expressed in terms of elementary functions. Hence, we'll express the integral as follows:

∫\(e^{4x^{2} }\) dx = √(π/4) × erf(2x)

Now, we can rewrite the integral using integration by parts:

∫(2x)\(e^{4x^{2} }\) dx = uv - ∫v du

= (2x) × (√(π/4) × erf(2x)) - ∫√(π/4) × erf(2x) × 2 dx

= (2x) × (√(π/4) × erf(2x)) - 2√(π/4) × ∫erf(2x) dx

The integral ∫erf(2x) dx can be further simplified using substitution. Let's assign z = 2x, which implies dz = 2 dx. Substituting these values, we get:

∫erf(2x) dx = ∫erf(z) (dz/2) = (1/2) ∫erf(z) dz

Therefore, the final expression becomes:

∫(2x)\(e^{4x^{2} }\) dx = (2x) × (√(π/4) × erf(2x)) - √(π/2) × ∫erf(z) dz

Please note that the integral involving the error function cannot be expressed in terms of elementary functions and requires numerical or tabulated methods for evaluation.

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a)  ⟨w', u⟩ = 0. Hence, w' is in W(orthogonal complement).Therefore, the statement is true.

b)  W⊥ = span(vk+1,...,vn). Therefore, the statement is true.

a) We need to prove that w' is in W(orthogonal complement).

Firstly, we know that w is an element of W. Since w and w' are orthogonal vectors, we have:⟨w, w'⟩ = 0... (1)

Given that v = w + w', we can express w' as follows:w' = v - w... (2)To prove that w' is in W(orthogonal complement), we must show that for all u in W, ⟨w', u⟩ = 0

We know that u is in W.

Thus, ⟨u, w⟩ = 0 because w is an element of W and w is orthogonal to every vector in W. Now, we need to find ⟨w', u⟩ and try to show that it is zero.⟨w', u⟩ = ⟨v - w, u⟩⟨w', u⟩ = ⟨v, u⟩ - ⟨w, u⟩⟨w', u⟩ = ⟨v, u⟩... (3)

We don't know whether ⟨v, u⟩ = 0. But we can observe that w' is the difference between v and w, both of which are elements of W.

Therefore, w' must also be an element of W. Since u is an element of W and W is a subspace, the linear combination w' + u must also be an element of W.

Thus, ⟨w', u⟩ = 0. Hence, w' is in W(orthogonal complement).

Therefore, the statement is true.

b) We need to prove that W(orthogonal complement) = span(vk+1,...,vn).

We know that v1, v2, ..., vn form an orthogonal basis for Rn.

Therefore, any vector v in Rn can be expressed as a linear combination of these vectors:v = c1v1 + c2v2 + ... + cnvn... (4)Let w be an element of W = span(v1, v2, ..., vk).

Then, w can be expressed as a linear combination of v1, v2, ..., vk:w = a1v1 + a2v2 + ... + akvk... (5)

The orthogonal complement of W is defined as W⊥ = {u in Rn : ⟨u, w⟩ = 0 for all w in W}

We need to prove that W⊥ = span(vk+1,...,vn).

Suppose that u is an element of W⊥. Then, ⟨u, vj⟩ = 0 for j = 1, 2, ..., k, because v1, v2, ..., vk are the basis vectors of W.

Substituting (4) and (5) into this equation, we obtain:⟨u, c1v1 + c2v2 + ... + cnvn⟩ = ⟨u, a1v1 + a2v2 + ... + akvk⟩ + ⟨u, c(k+1)vk + ... + cnvn⟩

We know that ⟨u, a1v1 + a2v2 + ... + akvk⟩ = 0 because u is orthogonal to every vector in W, including a1v1 + a2v2 + ... + akvk.

Therefore,⟨u, c1v1 + c2v2 + ... + cnvn⟩ = ⟨u, c(k+1)vk + ... + cnvn⟩

To complete the proof, we need to show that u can be expressed as a linear combination of vk+1, ..., vn.

Let's define u' = c(k+1)vk + ... + cnvn.

Then, we can express u as follows:u = (1/c1)u' - (c2/c1)v2 - ... - (ck/c1)vk - (c(k+1)/c1)v(k+1) - ... - (cn/c1)vn

Therefore, u is a linear combination of vk+1, ..., vn.

Hence, W⊥ = span(vk+1,...,vn).

Therefore, the statement is true.

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Answer:

162.3 in^2

Step-by-step explanation:

C=2πr=2·π·25.83≈162.29468in

7^4.3^-6.y is equivalent to 7.7.7.7.y/3.3.3.3.3.3 which is option (B).

b^10/b^4 is b^6 and (p^2+p-8)-(-4p^2-p+3) is 5p^2+2p-5.

Two expressions with equal sign in between is called as equation.

4. 7^4.3^-6.y

In the given expression, 7 has 4 exponent and 3 has -6 exponent.

This can be written as 7.7.7.7.y/3.3.3.3.3.3.

5. b^10/b^4 is b^10-4=b^6.

6. (p^2+p-8)-(-4p^2-p+3)

=p^2+p-8+4p^2+p-3

=5p^2+2p-5.

Therefore 7^4.3^-6.y is equivalent to 7.7.7.7.y/3.3.3.3.3.3 which is option (B), b^10/b^4 is b^6 and (p^2+p-8)-(-4p^2-p+3) is 5p^2+2p-5.

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Answer:

x=-1/2

Step-by-step explanation:

Answer:

Check out ironic p a n d u h on you tube

Step-by-step explanation:

the awnser is nowhere

By definition of a binomial random variable,  the probability that the machine will be working is 0.82045.

First of all, you should know that the Probability is the greater or lesser possibility that a certain event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

On the other hand, a random variable is a function that associates a real number, perfectly defined, to each sample point.

A random variable is discrete if the numbers it gives rise to are integers.

Finally, a binomial distribution is a discrete probability distribution that describes the number of successes in performing n independent experiments on a random variable.

The expression to calculate the binomial distribution is:

P(X=x)=(\(n\\ x\)) pˣ qⁿ⁻ˣ

Where:

Remember that:

(\(n\\ x\))=\(\frac{n!}{x!(n-x)!}\)

where the exclamation mark represents the factorial symbol, that is, the product of all positive integers from 1 to n.

A machine has 28 identical components which function independently. The probability that a component will fail is 0.19.

The following random variable is defined:

x= the number of components will stop working.

Being n the total number of pieces (in this case, 12 pieces) and p the probability of success (the piece fails, in this case 0.19), the expression to be used is expressed as:

P(X=x)=(\(12\\ x\)) 0.19ˣ (1-0.19)¹²⁻ˣ

P(X=x)=\(\frac{12!}{x!(12-x)!}\) 0.19ˣ (0.81)¹²⁻ˣ

Since the machine will stop working if more than three components fail, you need to know the probability that the machine will be working if 3 or less than 3 components fail. In other words, it may be that 0, 1, 2 or 3 pieces are broken and the machine continues to work:

P(X≤3)= P(X=0) + P(X=1) + P(X=2) + P(X=3)

Then:

P(X≤3)= \(\frac{12!}{0!(12-0)!}\) 0.19⁰ (0.81)¹²⁻⁰ + \(\frac{12!}{1!(12-1)!}\) 0.19¹ (0.81)¹²⁻¹ + \(\frac{12!}{2!(12-2)!}\) 0.19² (0.81)¹²⁻² + \(\frac{12!}{3!(12-3)!}\) 0.19³ (0.81)¹²⁻³

Solving:

P(X≤3)= \(\frac{12!}{0!12!}\) ×1×(0.81)¹² + \(\frac{12!}{1!11!}\) 0.19×(0.81)¹¹ + \(\frac{12!}{2!10!}\) 0.19²×(0.81)¹⁰ + \(\frac{12!}{3!9!}\) 0.19³×(0.81)⁹

P(X≤3)= 1×1×(0.81)¹² + 12×0.19×(0.81)¹¹ + 66×0.19²×(0.81)¹⁰ + 220×0.19³×(0.81)⁹

P(X≤3)= (0.81)¹² + 2.28×(0.81)¹¹ + 2.3826×(0.81)¹⁰ + 1.50898×(0.81)⁹

P(X≤3)= 0.82045

Finally, the probability that the machine will be working is 0.82045.

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If the total value of the coins is $15. The number of each type of coin is: 31 quarters, 72 dimes.

Let D = number of dimes

Let Q = the number of quarters

Equations

d + q = 103

0.10d + 0.25q = 15  

d = 103 -q

0.10(103 -q) + 0.25q = 15

10.3 - 0.10q + 0.25q = 15

0.15q = 4.7

q=4.7/0.15

q=31 quarters

Substitute q into second equation

D+31=103

D=72 dimes

Therefore the number of each type of coin is: 31 quarters, 72 dimes.

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Answer:

c is the answer

2 1/2 X 2 1/3 ( 1/2 and 1/3 is in power)

2 1/2+1/3

2 5/6

Answer:

x = g/cy

Step-by-step explanation:

To solve for x, we need to isolate it on one side of the equal sign algebraically. In this case, since  is being multiplied by  and  we can divide both sides by  and  to isolate 

The answer should be false

The number which best completes the sequence is 13, but since it's not in the given options, there might be an error in the question or the answer choices.

The pattern in this sequence is not immediately obvious, but we can try to identify some relationships between the numbers.

Starting with the first two numbers, we can see that the second number is obtained by multiplying the first number by 3 and adding 3:

2 x 3 + 3 = 9

Next, we can see that the third number is obtained by subtracting 4 from the second number:

9 - 4 = 5

The fourth number is obtained by adding 8 to the third number:

5 + 8 = 13

The fifth number is obtained by subtracting 3 from the fourth number:

13 - 3 = 10

The sixth number is obtained by adding 9 to the fifth number:

10 + 9 = 19

At this point, we can see that the pattern seems to be alternating between adding and subtracting some value. We can try to extend this pattern to find the missing number:

Starting with the sixth number, we subtract 2:

19 - 2 = 17

Next, we can add some value to get the next number. Based on the pattern we've seen so far, it seems likely that this value is 11:

17 + 11 = 28

However, 28 is not one of the options given. We can try to use the pattern to find another option. If we subtract 1 from the sixth number instead of 2, we get:

19 - 1 = 18

And if we add 8 instead of 11, we get:

18 + 8 = 26

26 is not one of the options given either, but it seems like a reasonable choice based on the pattern we've identified. Therefore, the number which best completes the sequence below is:

c) 25

To find the number that best completes the sequence, let's first identify the pattern. The sequence is as follows:

2 9 5 13 10 19 17 ?

Looking closely, we can see that there are two alternating patterns:

Pattern 1: Add 7 (2 to 9, 5 to 13, 10 to 17)
Pattern 2: Subtract 4 (9 to 5, 13 to 10, 19 to ?)

Now let's apply the pattern to find the next number in the sequence:

17 (the last number) - 4 (following Pattern 2) = 13

So, the number which best completes the sequence is 13, but since it's not in the given options, there might be an error in the question or the answer choices.

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Answer:32: altitude

Step-by-step explanation:it just is

the perimeter of the composite figure is 20cm and its area is 37cm².

what is perimeter  ?

Perimeter is the total length of the boundary of a two-dimensional shape or figure. In other words, it is the distance around the outside of a shape. To find the perimeter of a shape, you simply add up the lengths of all its sides.

In the given question,

To find the perimeter of the composite figure, we need to add up the lengths of all the sides.

Starting from the left side of the figure, we have a vertical line segment of length 6cm, followed by a horizontal line segment of length 5cm, then another vertical line segment of length 2cm, followed by a slanted line segment of length 3cm, then another horizontal line segment of length 2cm, and finally, a vertical line segment of length 2cm.

So the perimeter of the composite figure is:

Perimeter = 6cm + 5cm + 2cm + 3cm + 2cm + 2cm

Perimeter = 20cm

To find the area of the composite figure, we can break it down into simpler shapes and add up their areas.

The composite figure can be split into two rectangles, one with dimensions 6cm x 5cm and the other with dimensions 2cm x 2cm, and a right triangle with base 3cm and height 2cm.

The area of the first rectangle is:

Area = length x width

Area = 6cm x 5cm

Area = 30cm²

The area of the second rectangle is:

Area = length x width

Area = 2cm x 2cm

Area = 4cm²

The area of the right triangle is:

Area = (base x height) / 2

Area = (3cm x 2cm) / 2

Area = 3cm²

Therefore, the total area of the composite figure is:

Area = 30cm² + 4cm² + 3cm²

Area = 37cm²

So the perimeter of the composite figure is 20cm and its area is 37cm².

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Answer:

The average speed is 7.5 \(\frac{ m}{ s}\)

Step-by-step explanation:

Speed ​​is a physical quantity that expresses the relationship between the space traveled by an object and the time used for it.

Then, the average speed relates the change in position to the time taken to effect that change:

\(speed=\frac{change in position}{change in time}\)

The change in position is the difference between the final position and the initial position, while the change in time is the difference between the final and initial time.

In this case, the starting and ending positions are calculated by replacing the times in the function of the distance d (t):

d(5)= 0.5*5²= 12.5 m

d(10)= 0.5*10²= 50 m

So:

Replacing in the definition of speed:

\(speed=\frac{37.5 m}{5 s}\)

and solving you get:

speed= 7.5 \(\frac{ m}{ s}\)

The average speed is 7.5 \(\frac{ m}{ s}\)

Check the picture below, so let's check the equations below hmmm

\(\boxed{A}\\\\ y=\cfrac{16-3x}{4}\implies y=\cfrac{-3x+16}{4}\implies y = \cfrac{-3x}{4}+\cfrac{16}{4}\implies y=-\cfrac{3}{4}x\stackrel{\stackrel{b}{\downarrow }}{+4}~\hfill \bigotimes \\\\[-0.35em] ~\dotfill\)

\(\boxed{D}\\\\ y+4=2x\implies y=2x\underset{\stackrel{\uparrow }{b}}{-4}\qquad \textit{\Large \checkmark}\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)