Solve for x. 1+|2+x|=9

The results suggest that the new computer control system has a statistically significant impact on improving fuel efficiency, with the average increase in miles per gallon being less than 3.

Let's calculate the t-score:

t = (2.4 - 3) / (1.8 / √100)

t = -0.6 / (1.8 / 10)

t = -0.6 / 0.18

t ≈ -3.33

Since we're testing the hypothesis that the population mean is at least 3 (greater than 3), we're performing a one-tailed test. We need to find the p-value for the t-score of -3.33 in the right tail of the t-distribution.

The p-value can be found using statistical software or a t-table. Assuming an alpha level (significance level) of 0.05, the p-value is less than 0.001 (highly unlikely to occur by chance). This indicates strong evidence against the null hypothesis.

Since the p-value is less than the significance level (α = 0.05), we reject the null hypothesis. The results suggest that the new computer control system has a statistically significant impact on improving fuel efficiency, with the average increase in miles per gallon being less than 3.

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The approximate distance from the playground to the road along the other path is 1.3 miles.

The angle of the top vertex is 50 degrees. The length of the hypotenuse is 2 miles and the swing stands on the downside of the triangle.

Using trigonometric ratios, let's find the approximate distance from the playground to the road along the other path as follows:

cos 50 = adjacent / hypotenuse

cos 50° = x / 2

cross multiply

x = 2 cos 50°

x = 2 × 0.64278760968

x = 1.28557521937

x = 1.3 miles

Therefore,

distance from the playground to the road along the other path = 1.3 miles

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Answer:

average speed   = distance / time

60 =  distance /   (13.20 - 10.40)

13.20 - 10.40  =  2 hours 40 minutes  =  2 2/3  hours

60 = distance / 8/3  = 3 d / 8     (where d = distance)

3d = 480

d = 480/3  = 160 miles

The distance between the station in Boston and the one in Stamford is 160 miles.

Distance is calculated by the formula:

= Speed x Time

The Speed is 60 mph as given.

The time is:

= 1:00 pm  - 10:20AM

= 2 hrs 40 minutes

In decimals this is:

= 2 + 40/60 minutes

= 2 + 2/3

= 2.67 hours

The distance is therefore:

= Speed x Time

= 60 x 2.67

= 160 miles

In conclusion, the distance between the stations is 160 miles.

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60 pounds of effort is required to push the 180-pound ball up the 15-foot high platform using the 45-foot long ramp.

To determine the effort required to push the 180-pound ball up a 15-foot high platform using a 45-foot long ramp, we need to consider the forces involved and apply the principles of work and energy.

The work done to raise the ball to the platform is equal to the force applied multiplied by the distance over which the force is applied. In this case, the force applied is the effort required to push the ball up the ramp, and the distance is the length of the ramp.

First, we need to calculate the mechanical advantage of the ramp. The mechanical advantage is the ratio of the length of the ramp to the vertical height it lifts the object. In this case, the mechanical advantage is 45/15 = 3.

Next, we calculate the weight of the ball, which is 180 pounds.

The effort required can be determined using the formula:

Effort = (Weight of the ball) / (Mechanical advantage)

Effort = 180 pounds / 3 = 60 pounds

Therefore, approximately 60 pounds of effort is required to push the 180-pound ball up the 15-foot high platform using the 45-foot long ramp.

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Answer:

hi

Step-by-step explanation:

hello

Answer:

C

Step-by-step explanation:

Both students are correct; the slope should be –1, passing through (4, 2) with a y-intercept of 6.

Answer: Its c

Step-by-step explanation:

Both students are correct.

a. ln(7x) can be expanded as ln(7) + ln(x). b. ln(x + 3) remains as it is, since it cannot be simplified further. c. ln(x^8) can be expanded as 8ln(x). d. 15,000ln(xy^4) can be expanded as ln(x) + 4ln(y) + ln(15,000).

a. To expand the logarithmic expression ln(7x), we can use the property of the natural logarithm that states ln(ab) = ln(a) + ln(b).

Therefore, ln(7x) can be expanded as ln(7) + ln(x).

b. Similarly, the logarithmic expression ln(x + 3) can be expanded using the property ln(ab) = ln(a) + ln(b).

Hence, ln(x + 3) remains as it is since we cannot simplify it further.

c. Expanding the logarithmic expression ln(x^8) can be done using the property ln(a^b) = b * ln(a).

Thus, ln(x^8) becomes 8 * ln(x).

d. Expanding the logarithmic expression 15,000ln(xy^4) can be done by applying the property ln(ab) = ln(a) + ln(b).

Therefore, 15,000ln(xy^4) can be expanded as 15,000[ln(x) + ln(y^4)].

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Answer:

a^4+2ab^2+b^4+a^16+2ab^8+b^16

Step-by-step explanation:

(a^2+b^2)^2+(a^8+b^8)^2

(a^2+b^2)^2=(a^2+b^2)(a^2+b^2)

=a^2(a^2+b^2)+b^2(a^2+b^2)

=a^4+(ab)^2+(ba)^2+b^4

=a^4+2ab^2+b^4

(a^8+b^8)^2=(a^8+b^8)(a^8+b^8)

=a^8(a^8+b^8)+b^8(a^8+b^8)

=a^16+(ab)^8+(ba)^8+b^16

=a^16+2ab^8+b^16

(a^2+b^2)^2+(a^8+b^8)^2=(a^4+2ab^2+b^4)+(a^16+2ab^8+b^16)

the answer is a^4+2ab^2+b^4+a^16+2ab^8+b^16

i think it is simplified answer

Answer:

b=1.2×107mm

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

-93

..................................................................................................................................................

Answer:

i believe its 7 because -43+50 = 7

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

x + 11 = 15

x = 15 - 11

x = 4

square root of 4 = 2

proof: 2 × 2 = 4

Answer:

31.42

Step-by-step explanation:

you will need a calculator for this

you will need to do 2 x pi x r = C

2 x 3.14 x 5

2x5=10

3.14 x 10 = 31.42

you get 2 when you round to the nearest ten-thousandths

pi = 3.14159

Answer:

Step-by-step explanation:

Formula for circumference

Solving for the circle with radius of 5 in

Answer:The vowels in the left column are called "front vowels." Tongue body is in the front of the mouth. All vowels show a "gap" in frequency between F1 and F2. ... A traditional "vowel diagram" can be obtained by plotting the vowel formants in a graph where the horizontal axis is (F2-F1) and the vertical axis is inverse F1.

Step-by-step explanation:

Answer:

portable document format

Answer:

Portable document format

Based on the temperature at 2,000 meters and the rate of temperature change, the temperature at 6,000 meters is -16°C.

The difference between 2,000 meters and 6,000 meters is:

= 6,000 - 2,000

= 4,000 meters

For every 1,000 meters increase, the temperature will drop by 6.5 °C. At 4,000 meters:

= 6.5 x 4,000 / 1,000

= 26 °C

The temperature will reduce by 26°C to become:

= Temperature at 2,000 - Temperature change

= 10 - 26

= -16 °C

In conclusion, the temperature is -16 °C.

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Answer:

6561 / 128

Step-by-step explanation:

The nth term of a geometric sequence is:

a = a₁ (r)ⁿ⁻¹

The first term is 3, and the fourth term is 81/8.

81/8 = 3 (r)⁴⁻¹

27/8 = r³

r = 3/2

The eighth term is therefore:

a = 3 (3/2)⁸⁻¹

a = 6561 / 128

Answer:

Answer is 3^4/5*a^2*b*c^2

The total Distance between all points is 15. This is the shortest distance between all points, so it is the time needed to travel between them

In order to calculate the time needed, we need to consider the distances between each point.

This can be done using the Pythagorean Theorem, which states that the hypotenuse of a right triangle is equal to the square root of the sum of the squares of the other two sides.

For this problem, we can treat each segment as the hypotenuse of a right triangle, where the other two sides are the distances between each point.Using this method,

we can calculate the distances between each point:b1 to b2: distance = sqrt((b2 - b1)^2) = sqrt((8 - 10)^2) = 2b2 to b3: distance = sqrt((b3 - b2)^2) = sqrt((15 - 8)^2) = 7b3 to a: distance = sqrt((a - b3)^2) = sqrt((15 - 15)^2) = 0b3 to b: distance = sqrt((b - b3)^2) = sqrt((10 - 15)^2) = 5b4 to b: distance = sqrt((b - b4)^2) = sqrt((10 - 9)^2) = 1

Now that we have the distances,

we can add them up to get the total distance:2 + 7 + 0 + 5 + 1 = 15

Therefore, the total distance between all points is 15. This is the shortest distance between all points, so it is the time needed to travel between them.

So, the answer is we should take the shortest way, not the longest way.

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(i) The statement is true. The sum of a finite number of convex subsets of R^n is convex.

(ii) The statement is false. The collection of all convex subsets of R^2 is not a linear space.

(iii) The statement is false. The sum of two closed subsets of R^n is not necessarily closed.

(iv) The sentence in (iii) does not make sense if (X, d) is substituted for R^n.

(v) The statement is true. The projection onto any particular coordinate of a closed subset of a metric space R^n is closed.

(i) The statement is true. The sum of a finite number of convex subsets of R^n is convex.

Proof: Let A_1, A_2, ..., A_k be convex subsets of R^n. We want to show that the set B = A_1 + A_2 + ... + A_k (which is the set of all possible sums of elements from each A_i) is convex.

Let x, y ∈ B and let α ∈ [0, 1]. Since x and y are in B, there exist vectors a_1, a_2, ..., a_k and b_1, b_2, ..., b_k such that x = a_1 + a_2 + ... + a_k and y = b_1 + b_2 + ... + b_k, where a_i, b_i ∈ A_i for each i = 1 to k.

Now consider the point z = αx + (1 - α)y. We need to show that z is also in B.

z = αx + (1 - α)y

= α(a_1 + a_2 + ... + a_k) + (1 - α)(b_1 + b_2 + ... + b_k)

= (αa_1 + (1 - α)b_1) + (αa_2 + (1 - α)b_2) + ... + (αa_k + (1 - α)b_k)

Since each A_i is convex, we have αa_i + (1 - α)b_i ∈ A_i for all i = 1 to k. Therefore, z belongs to the set B = A_1 + A_2 + ... + A_k.

Hence, the sum of a finite number of convex subsets of R^n is convex.

(ii) The statement is false. The collection of all convex subsets of R^2 is not a linear space.

Counterexample: Consider two convex subsets of R^2, A = {(x, y) ∈ R^2 : x > 0} (the right half-plane excluding the y-axis) and B = {(x, y) ∈ R^2 : x < 0} (the left half-plane excluding the y-axis). Both A and B are convex subsets of R^2.

Now, let's consider their sum, A + B. For any point (x, y) in A + B, there exist points (a, b) from A and (c, d) from B such that (x, y) = (a, b) + (c, d). However, (a + c, b + d) must lie on both the right half-plane and the left half-plane simultaneously, which is not possible. Therefore, A + B is not a valid convex subset of R^2.

Hence, the collection of all convex subsets of R^2 is not a linear space.

(iii) The statement is false. The sum of two closed subsets of R^n is not necessarily closed.

Counterexample: Consider the closed subsets A = [0, 1] and B = [2, 3] of R. Both A and B are closed intervals in R.

The sum A + B = [0, 1] + [2, 3] = [2, 4]. However, [2, 4] is not closed since it does not contain its limit points, specifically the point 3.

Therefore, the sum of two closed subsets of R^n is not always closed.

(iv) The sentence in (iii) does not make sense if (X, d) is substituted for R^n.

The concept of "closed" subsets relies on the notion of limits and convergence, which is defined in the context of metric spaces. If (X, d) is a general metric space, the idea of closed subsets and their properties may vary depending on the specific metric and topology of the space. Therefore, it is not meaningful to discuss the closure of subsets in a general metric space without further specifying the properties of that particular space.

Hence, the claim is incoherent unless additional information about the specific metric space (X, d) is provided.

(v) The statement is true. The projection onto any particular coordinate of a closed subset of a metric space R^n is closed.

Proof: Let A be a closed subset of R^n, and consider its projection onto the i-th coordinate, proj_i(A) = {y_i ∈ R : (y_1, y_2, ..., y_n) ∈ A}.

We need to show that proj_i(A) is closed. To do this, we can show that its complement, proj_i(A)^c, is open.

Let x ∈ proj_i(A)^c. This means that x is not in proj_i(A), so there exists some (a_

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Answer: The answer should be -4

Step-by-step explanation:

1. The vector w = (-3, 2, -5) can be written as a linear combination of u and v.

2. The set {u, v} is linearly independent.

3. The vector w is not in the span of the set {u, v}.

1. To write w as a linear combination of u and v, we need to find scalars a and b such that w = au + bv. By solving the system of equations, we get:

-3 = a1 + b6,

2 = a2 + b4,

-5 = a*(-1) + b2.

Solving these equations, we find a = 2 and b = -1. Therefore, w = 2u - v.

2. The set {u, v} is linearly independent if the only solution to the equation au + bv = 0 is a = b = 0. We can write this equation as a system of equations:

a + 6b = 0,

2a + 4b = 0,

-a + 2b = 0.

Solving this system, we find that the only solution is a = b = 0. Therefore, the set {u, v} is linearly independent.

3. To determine if the vector w is in the span of {u, v}, we need to check if there exist scalars a and b such that w = au + bv. However, from the previous calculation, we found that w can be expressed as a linear combination of u and v with a = 2 and b = -1. Therefore, w is not in the span of {u, v}.

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Answer:

2

Step-by-step explanation:

slope=∆y/∆x

thus values of y and x at any point in the table can be used.

slope= (7-5)÷(2-1)

slope=2.

Answer:

y - 7 = - 1(x - 4)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 1 and (a, b) = (4, 7) , thus

y - 7 = - (x - 4)

The equation of line in the point-slope form is y = -1x + 11

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the point be P = P ( 4 , 7 )

Let the slope of the line be m = -1

So , the equation of line is given by the formula

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 7 = -1 ( x - 4 )

On simplifying the equation , we get

y - 7 = -1x + 4

Adding 7 on both sides of the equation , we get

y = -1x + 11

y = -x + 11

Therefore , the value of A is y = -x + 11

Hence , the equation of line is y = -x + 11

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Answer:

x = 83

Step-by-step explanation: