Ok so the equation is 45+x=2x+15
I know x=30 I just want to find the exterior part, please help due today!

Answer:

3.8 foot

Step-by-step explanation:

with reference angle 31

perpendicular (p)= x

base(b) = 6.3

tan 31 = p/b

0.6 = x/6.3

x = 3.8 foot

The value of dy/dt at the point (3, 4) is -9/2.

A circle is a locus of a point whose distance always remains constant from a given specific point. The general equation is -

x² + y² = r²      (for circle centered at origin)

Given a particle moves on the circle x² + y² = 25 in the Z - Y plane for time t > 0. At the time when the particle is at the point (3,4), dx/dt=6

We have -

x² + y² = 25

x² = 25 - y²

d/dt(x²) = - d/dt(y²)

2x (dx/dt) = - 2y (dy/dt)

At point (3, 4), (dx/dt) = 6. So -

6 x 6 = - 8 (dy/dt)

(dy/dt) = -36/8

(dy/dt) = -9/2

Therefore, the value of dy/dt at the point (3, 4) is -9/2.

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[The complete question is -

A particle moves on the circle x2+y2=25 in the xy-plane for time t≥0. At the time when the particle is at the point (3,4), dx/dt=6. What is the value of dy/dt at this time?]

Answer:

Bob has 3 apples

.......

a. The probability that a randomly selected bottle will have less than 354 ml of beer is approximately 0.3085.

To calculate this probability, we convert the value of 354 ml to a z-score using the formula z = (x - μ) / σ, where x is the value we want to find the probability for (354 ml), μ is the mean (355 ml), and σ is the standard deviation (8 ml). By calculating the z-score, we can then look up the corresponding area under the normal distribution curve using a z-table. The z-score for 354 ml is approximately -0.125, and the corresponding area (probability) is 0.4508. Therefore, the probability of having less than 354 ml is 0.5 - 0.4508 = 0.0492 (or approximately 0.3085 when rounded to four decimal places).

b. The probability that a randomly selected 6-pack of beer will have a mean amount less than 354 ml is approximately 0.0194.

To calculate this probability, we need to consider the distribution of the sample mean. Since we are selecting a sample of size 6, the mean of the sample will have a standard deviation of σ / √n, where σ is the standard deviation of the population (8 ml) and n is the sample size (6). The standard deviation of the sample mean is therefore 8 ml / √6 ≈ 3.27 ml. We can then convert the value of 354 ml to a z-score using the same formula as in part a. The z-score for 354 ml is approximately -0.3061. By looking up this z-score in the z-table, we find the corresponding area (probability) of 0.3808. Therefore, the probability of the mean amount being less than 354 ml is 0.5 - 0.3808 = 0.1192 (or approximately 0.0194 when rounded to four decimal places).

c. The probability that a randomly selected 12-pack of beer will have a mean amount less than 354 ml is approximately 0.0022.

Similar to part b, we calculate the standard deviation of the sample mean for a sample size of 12, which is σ / √n = 8 ml / √12 ≈ 2.31 ml. By converting 354 ml to a z-score, we find a value of approximately -1.08. Looking up this z-score in the z-table, we find the corresponding area (probability) of 0.1401. Therefore, the probability of the mean amount being less than 354 ml is 0.5 - 0.1401 = 0.3599 (or approximately 0.0022 when rounded to four decimal places).

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Answer: d. The helicopter rotor will spin 36,000 times in 1 hour

Step-by-step explanation:

Option A is wrong because in 40 minutes the rotor will spin:

= 40 * 600

= 24,000 times

Option B is wrong because we cannot know the number of times the rotor will spin before being lifted off of the ground with the details given.

Option C is wrong because in 3 hours the rotor will spin:

= 600 * 3 * 60 minutes

= 108,000 times

Option D is correct because in 1 hour the rotor will spin:

= 600 * 1 * 60 mins

= 36,000 times

Answer: Square and rectangle

Step-by-step explanation:

The initial value problem x³ dx + 3x²y = cos(x), y(n) = 0 is:

(|x|^4)/4 + 3|x|y = sin(x) + (|n|^4)/4 - sin(n)

To solve the initial value problem x³ dx + 3x²y = cos(x), y(n) = 0, we can use the method of integrating factors. This involves finding an integrating factor that will allow us to rewrite the equation in a form that can be easily solved.

Let's start by rearranging the equation in a standard form. Dividing both sides by x³, we have:

dx + 3x^(-1)y = (1/x³) * cos(x)

Now, let's identify the integrating factor. In this case, the integrating factor is given by the exponential of the integral of the coefficient of y, which is 3x^(-1). Integrating, we get:

μ(x) = e^(∫3x^(-1) dx) = e^(3ln|x|) = e^(ln|x|^3) = |x|^3

Multiplying both sides of the equation by the integrating factor, we obtain:

|x|^3 dx + 3|x|^4 x^(-1)y = (|x|^3/x³) * cos(x)

Simplifying further, we have:

|x|^3 dx + 3|x|y = cos(x)

Now, let's integrate both sides of the equation. Integrating the left side requires a substitution. Let u = |x|, then du = (x/|x|) dx = sign(x) dx. Therefore, the integral becomes:

∫ u^3 du + 3∫u y = ∫ cos(x) dx

Integrating, we have:

(u^4)/4 + 3uy = sin(x) + C

Substituting back u = |x|, we get:

(|x|^4)/4 + 3|x|y = sin(x) + C

To find the constant C, we can use the initial condition y(n) = 0. Substituting n for x and y(n) = 0, we have:

(|n|^4)/4 + 3|n|*0 = sin(n) + C

(|n|^4)/4 = sin(n) + C

C = (|n|^4)/4 - sin(n)

Therefore, the solution to the initial value problem is:

(|x|^4)/4 + 3|x|y = sin(x) + (|n|^4)/4 - sin(n)

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Answer:

the temp dropped about 10. degrees to -6

To find the area of the sector NPQ, we first need to find the measure of the central angle that intercepts the arc PQ. We know that the measure of angle NPQ is 104 degrees, and since it is an inscribed angle, its measure is half the measure of the central angle that intercepts the same arc. Therefore, the central angle measure is 208 degrees.

To find the area of the sector, we use the formula:

Area of sector = (central angle measure/360) x pi x radius^2

We know that the radius of circle P is NP = 9 units. Plugging in the values, we get:

Area of sector NPQ = (208/360) x pi x 9^2
= (0.5778) x 81pi
= 46.99 square units

Rounding to the nearest hundredth, the area of the sector NPQ is 47.00 square units.

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Answer:

Step-by-step explanation:

Amy = x years

Ben = x + 2  (years)

Alice = x - 6 (years)

Answer:

a)

Amy's age is x.

• Ben's age is 2 more than Amy's age.

∴ Ben's age = x + 2

• Alice's age is 6 less than Amy's age.

∴ Alice's age = x - 6

The length of Adrianna's bedroom that has a perimeter of 90 feet and a width of 15 feet is 30 feet.

To find the length of Adrianna's bedroom, we can use the formula for the perimeter of a rectangle:

P = 2l + 2w

where P is the perimeter, l is the length, and w is the width.

We are given that the perimeter is 90 feet and the width is 15 feet, so we can substitute those values into the formula:

90 = 2l + 2(15)

Simplifying:

90 = 2l + 30

Subtracting 30 from both sides:

60 = 2l

Dividing both sides by 2:

30 = l

Therefore, the length of Adrianna's bedroom is 30 feet.

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Answer: A. 27.5km

2cm = 11km    so then....    1cm = 5.5km      

The probability of selecting a green ball is \($\frac{10}{14}$\).

This can be calculated using the formula for probability,\($P(A) = \frac{n(A)}\)\({n(S)}$\), where n(A) is the number of favorable outcomes and n(S) is the total number of possible outcomes.

In this problem, there are three possible containers that can be selected. The first contains 8 red balls and 4 green balls, the second contains 2 red balls and 4 green balls, and the third contains 2 red balls and 4 green balls.

Therefore, the total number of possible outcomes is 14 (8 + 4 + 2 + 4 + 2 + 4).

The number of favorable outcomes is 10 (4 + 4 + 2).

Therefore, the probability of selecting a green ball is \($\frac{10}{14}$\)

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Answer:

x = 3

Step-by-step explanation:

2x - y = 4

y = -2x + 8

-y = -2x + 4

y = -2x + 8

0 = -4x + 12

-4x = -12

x = 3

Answer:

12

Step-by-step explanation:

Type Into Calculator:

SAT-EDIT-TYPE IN X VALUES AND Y VALUES (FROM ORDERED PAIR)-STAT-CALC-4-ENTER

Answer:

Step-by-step explanation:

-61.6 degrees Fahrenheit

The person would save $404 by choosing the HMO for physical therapy sessions.

Total cost refers to the overall expense incurred by a business or an individual to produce or acquire a product or service.

Let's first calculate the total cost of physical therapy sessions without insurance:

Total cost = 12 sessions * $145 per session = $1740

With the insurance policy, the person has to pay a deductible of $580 first. After that, the insurance will cover 80% of the remaining cost. So, the person pays:

($1740 - $580) * 0.2 = $232

Therefore, with the insurance policy, the person pays $580 + $232 = $812 for 12 physical therapy sessions.

If the person opts for the HMO instead, the cost would be $34 per session, so:

Total cost = 12 sessions * $34 per session = $408

Therefore, the person would save:

$812 (with insurance) - $408 (with HMO) = $404

So, the person would save $404 by choosing the HMO for physical therapy sessions.

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Answer:

4.17

Step-by-step explanation:

6000x = 25000

x = 25000 / 6000

x = 4.17

This is the answer to your problem

Answer: $112

Step-by-step explanation:

35% x 320 = 112

So, he spends $112 on food.

(a) Using the given data, we can verify the calculations as follows: ∑x = 245, ∑x^2 = 14,755, ∑y = 224.

(b) To compute the sample mean, variance, and standard deviation for the percentage success of mallard duck nests (x), we use the formulas:

Sample Mean (x) = ∑x / n

Variance (s^2) = (∑x^2 - (n * x^2)) / (n - 1)

Standard Deviation (s) = √(s^2)

(c) Applying the formulas, we can compute the sample mean, variance, and standard deviation for x as follows:

Sample Mean (x) = 245 / 5 = 49

Variance (s^2) = (14,755 - (5 * 49^2)) / (5 - 1) = 4,285

Standard Deviation (s) = √(4,285) ≈ 65.5

Similarly, for the percentage success of Canada goose nests (y), the calculations can be done using the same formulas and the given values from part (a).

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Hi there!  

»»————-　★　————-««

I believe your answer is:  

Option A

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

\(m = \frac{\text{rise}}{\text{run}}\)

⸻⸻⸻⸻

\(m =\frac{9-5}{4+2}\\\\\\\rightarrow \frac{4}{6}\\\\\rightarrow \frac{4/2}{6/2}\\\\\rightarrow \boxed{ \frac{2}{3} }\)

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

x + 6

Step-by-step explanation:

From the question given above, the following data were obtained:

Length of rectangle = 3x + 6

Width of rectangle = 4x – 1

Width of door =..?

A careful observation of the diagram shows that the door is located along the length of rectangular room.

In a rectangle, two sides are equal. Therefore,

x + door + x = 3x + 6

Making door subject of the above formula, we have:

x + door + x = 3x + 6

door + x + x = 3x + 6

door + 2x = 3x + 6

Subtract 2x from both side

door + 2x – 2x = 3x + 6 – 2x

door = 3x – 2x + 6

door = x + 6

Therefore, the width of the door is x + 6

Answer:

(2, 0)

Step-by-step explanation:

First we need to get the equation of the line passing through the points (3, 1) and (–5, –7)

Equation of a line is y = mx+c

m is the slope

m = y2-y1/x2-x1

m = -7-1/-5-3

m = -8/-8

m = 1

Substitute m = 1 and the point (3, 1) into the equation y = mx+c and get c;

1 = 1(3) + c

1 = 3 + c

c = 1-3

c = -2

The required equation is y = x - 2

We are to look for the coordinate point (x,y) for which both lines intersects, then both equations will be equal as shown;

0.5x - 1 = x - 2

0.5x - x = -2+1

-0.5x = -1

x = -1/-0.5

x = 2

Substitute x = 2 into y = x - 2

y = 2-2

y = 0

Hence the the coordinate point is (2, 0)

Answer: (2,0)

Step-by-step explanation: Because I just took the Unit Test and got 100% on it.

Answer:

6 + x = 9

Step-by-step explanation:

We know that x = 3, and that we need to add x (which equals 3) to 6.

So, all we need to do is add 6 + 3.

6 + x = 9

We know this because for the expression 6 + x, we replace x with it's given value, which is 3.

      ⬇

6 + 3 = 9

Answer:

(-2, -3)

Step-by-step explanation:

solutions are all the points where the line intersects