-40-2(3m+1/2)=7m-2 what does m equal

Q9.1: To justify the proposal, we need to compare the benefits of the road expansion (in terms of reduced travel time) with its costs. The value of time represents the monetary value individuals place on their time spent traveling. In this case, the value of time is $1.5 per minute.

First, let's calculate the reduction in travel time resulting from the road expansion. We compare the two road performance functions: t1​ = 30 + 6×10−6q and t2​ = 20 + 3×10−6q. By subtracting t2​ from t1​, we can determine the time savings: Δt = t1​ - t2​ = (30 + 6×10−6q) - (20 + 3×10−6q)    = 10 + 3×10−6q Next, we multiply the time savings by the number of trips (q) to obtain the total time savings: Total Time Savings = Δt × q = (10 + 3×10−6q) × q Now, we can determine the monetary value of the time savings by multiplying the total time savings by the value of time ($1.5 per minute): Monetary Value of Time Savings = Total Time Savings × Value of Time                             

= (10 + 3×10−6q) × q × $1.5  If the monetary value of the time savings exceeds the construction cost of $9.6×107, then the proposal is justified. Q9.2: To determine the construction cost at which the proposal becomes justified, we set the monetary value of the time savings equal to the construction cost and solve for q: (10 + 3×10−6q) × q × $1.5 = $9.6×107 By solving this equation for q, we can find the corresponding construction cost at which the proposal becomes justified.

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Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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Answer:

The independent variable is the variable that is manipulated or changed during an experiment. In this case, the independent variable is represented by the x-values of the given points.

So, the answer would be option A: {-2, 3, 1, 5}

Step-by-step explanation:

brainliest Plsssss

Answer:The 99% confidence interval is

To find the 99% confidence interval for the mean systolic blood pressure (SBP) level, we use the formula:

CONFIDENCE INTERVAL = Mean ± Z * (Standard Deviation / √n)

Where:

Mean is the sample mean of SBP

Z is the Z-score corresponding to the desired confidence level

Standard Deviation is the population standard deviation

Explanation:

Given that the sample size is 13 and the standard deviation is 10, we need to calculate the sample mean and the Z-score for the 99% confidence level.

First, we calculate the sample mean:

Mean = (129 + 134 + 142 + 114 + 120 + 116 + 133 + 142 + 138 + 148 + 129 + 133 + 140) / 13

= 1724 / 13

≈ 132.62

Next, we need to determine the Z-score for a 99% confidence level. The Z-score can be found using a Z-table or a statistical calculator. For a 99% confidence level, the Z-score is approximately 2.576.

Now, we can calculate the confidence interval:

Confidence Interval = 132.62 ± 2.576 * (10 / √13)

132.62 ± 2.576 * (10 / 3.6056)

≈ 132.62 ± 2.576 * 2.771

≈ 132.62 ± 7.147

Therefore, the 99% confidence interval for the mean SBP level is approximately (125.47, 139.77).

The bicycle mechanic should cut a strip of plastic approximately 82 inches long to place between the tube and tire of the 26-inch diameter bicycle tire.

To calculate the length of the strip of plastic needed, we first need to determine the circumference of the tire. The formula for the circumference of a circle is C=2πr, where C is the circumference, π is approximately 3.14, and r is the radius of the circle.

In this case, the tire diameter is 26 inches, so the radius is 13 inches (half of the diameter). Therefore, the circumference of the tire is: C = 2πr = 2π(13)     = 81.64 inches (rounded to two decimal places)

To ensure that the strip of plastic fits snugly between the tube and tire, it should be the same length as the circumference of the tire. Therefore, the strip of plastic should be 82 inches long (rounded to the nearest inch).

In summary, the bicycle mechanic should cut a strip of plastic that is 82 inches long to fit between the tube and tire of the 26-inch diameter bicycle tire.

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we have the equation

4x+3y=12

this is a linear equation

step 1

Find out the y-intercept

(value of y when the value of x is zero)

For x=0

4(0)+3y=12

3y=12

y=4

the y-intercept is the point (0,4)

step 2

Find the x-intercept

(value of x when the value of y is zero)

For y=0

4x+3(0)=12

4x=12

x=3

the x-intercept is the point (3,0)

step 3

graph the equation

plots the intercepts, join them to draw the line

see the attached figure

The directional vectors of the planes are not equal but they are multiples of each other. so, the planes are parallel. The correct option is a.

The given planes are parallel, perpendicular or neither.

To determine whether the planes are parallel, perpendicular or neither, it is necessary to compare the directional vectors of the planes with each other.

The directional vectors of the given planes are as follows;

Plane 1:

9x + 36y + 27z = 1

=> (9, 36, 27)

Plane 2:

-16x + 36y + 42z = 0

=> (-16, 36, 42)

For two vectors to be perpendicular, the dot product of the two vectors should be equal to zero.

Therefore, let's find the dot product of the two directional vectors:

(9, 36, 27) · (-16, 36, 42) = 9(-16) + 36(36) + 27(42)

= 0 + 1296 + 1134

= 2430

Since the dot product of the directional vectors is not zero, the planes are not perpendicular.

To determine whether the planes are parallel or not, we need to compare the directional vectors. We can say that the planes are parallel if their directional vectors are multiples of each other.

Let's compare the two directional vectors:

(9, 36, 27) = 9(1, 4, 3)(-16, 36, 42)

= -4(4, -9, -10)

Hence, the planes are parallel. The correct option is a.

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To form a triangle, the set of line segments must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we need to check if the given line segments 8 cm, 4 cm, and 3 cm meet this requirement.

We can start by checking if the sum of the two smaller sides (3 cm and 4 cm) is greater than the largest side (8 cm). 3 cm + 4 cm = 7 cm, which is less than 8 cm. Therefore, these three line segments cannot form a triangle.

In general, for a set of line segments to form a triangle, the largest side must be smaller than the sum of the other two sides. In this case, the line segment of 8 cm is too long compared to the other two sides, which makes it impossible to form a triangle.

In conclusion, there are no line segments that meet the requirements to form a triangle with lengths of 8 cm, 4 cm, and 3 cm.

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Answer:

8.5*\(10^7\)

Step-by-step explanation:

825 million is

825,000,000

so you need to do 8.25 and then 10 to the power of 8

so the answer is 8.5*\(10^8\)

Answer:

B

Step-by-step explanation:

Answer:

slope = \(\frac{4}{3}\)

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, 4) ← 2 points on the line

m = \(\frac{4-0}{0-(-3)}\) = \(\frac{4}{0+3}\) = \(\frac{4}{3}\)

Answer:

The volume of the circle is 21

Step-by-step explanation:

The volume of rectangular is 60

a) Spanning tree of W6 (starting at degree 6 vertex) using depth-first search: 6-1-2-3-4-5. b) Spanning tree of K5 using depth-first search: Any spanning tree will do since K5 is a complete graph. c) Spanning tree of K3,4 (starting at degree 3 vertex) using depth-first search: 3-1-2-4-5-6-7. d) Spanning tree of Q3 using depth-first search: Any spanning tree will do since Q3 is a cycle graph.

a) To find a spanning tree of graph W6 (Example 7 of Section 10.2) starting at the vertex of degree 6, we can use the depth-first search algorithm as follows:

Start at the vertex of degree 6.

Mark it as visited.

Choose an unvisited adjacent vertex and move to it.

Repeat steps 2 and 3 until all vertices have been visited or there are no more unvisited adjacent vertices.

Backtrack to the previous vertex if there are no more unvisited adjacent vertices.

Continue the process until all vertices have been visited.

b) To find a spanning tree of graph K5, we can use the depth-first search algorithm as follows:

Choose any vertex as the starting point.

Mark it as visited.

Choose an unvisited adjacent vertex and move to it.

Repeat steps 2 and 3 until all vertices have been visited or there are no more unvisited adjacent vertices.

Backtrack to the previous vertex if there are no more unvisited adjacent vertices.

Continue the process until all vertices have been visited.

c) To find a spanning tree of graph K3,4 starting at a vertex of degree 3, we can use the depth-first search algorithm as follows:

Start at the vertex of degree 3.

Mark it as visited.

Choose an unvisited adjacent vertex and move to it.

Repeat steps 2 and 3 until all vertices have been visited or there are no more unvisited adjacent vertices.

Backtrack to the previous vertex if there are no more unvisited adjacent vertices.

Continue the process until all vertices have been visited.

d) To find a spanning tree of graph Q3, we can use the depth-first search algorithm as follows:

Choose any vertex as the starting point.

Mark it as visited.

Choose an unvisited adjacent vertex and move to it.

Repeat steps 2 and 3 until all vertices have been visited or there are no more unvisited adjacent vertices.

Backtrack to the previous vertex if there are no more unvisited adjacent vertices.

Continue the process until all vertices have been visited.

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(a) The expression for a Riemann sum of a function f on an interval [a, b] is Δx = (b-a)/n

(b) If f(x)⩾ 0, then the geometric interpretation of a Riemann sum is infinity

(c) If f(x) takes on both positive and negative values, then the geometric interpretation of a Riemann sum is infinity

Riemann sums are an important tool in calculus for approximating the area under a curve. They are used to estimate the value of a definite integral, which represents the area bounded by the curve and the x-axis on a given interval. In this explanation, we will discuss the expression for a Riemann sum, its notation, and its geometric interpretation.

(a) Expression for a Riemann sum:

A Riemann sum is an approximation of the area under a curve using rectangles. We divide the interval [a, b] into n subintervals, each of length Δx=(b−a)/n. The notation used to represent this is:

Δx = (b-a)/n

(b) Geometric interpretation of a Riemann sum when f(x)⩾ 0:

If f(x) is always non-negative, the Riemann sum represents an approximation of the area between the curve and the x-axis on the interval [a, b].

Each rectangle has a positive area, which contributes to the overall area under the curve. The sum of the areas of the rectangles approaches the true area under the curve as the number of subintervals n approaches infinity.

(c) Geometric interpretation of a Riemann sum when f(x) takes on both positive and negative values:

When f(x) takes on both positive and negative values, the Riemann sum represents the net area between the curve and the x-axis on the interval [a, b].

Each rectangle may have a positive or negative area, depending on the sign of f(xi).

The positive areas represent regions where the curve is above the x-axis, and the negative areas represent regions where the curve is below the x-axis.

In conclusion, Riemann sums are used to approximate the area under a curve on an interval [a, b]. The expression for a Riemann sum involves dividing the interval into n subintervals and approximating the area under the curve using rectangles.

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Answer:

-24

Step-by-step explanation:

-12, -15, -18, -21,

Notice that we are subtracting 3 each time

-12 -3 =-15

-15 -3 = -18

So -21 -3 = -24

The answer is 5:2 ration, it's already fully simplified

Answer:

x=3/19, y=24/19

Step-by-step explanation:

Answer:

y = 1 + 5x/3

y = 6/5 + 2x/5

Step-by-step explanation:

Probably wrong. But I hope it's right! Plus, this was like a month ago so it probably doesn't matter. Thx for the points tho!

Answer:

Step-by-step explanation:

X = 64.

x^(1/2) = 8

\(\sqrt{x} = 8^{2}\)

Therefore, x = 64

Answer:

D. 64

Step-by-step explanation:

x^1/2 = 8

√x = 8

√64 = 8

x = 64

In the analysis of variance procedure (ANOVA), "factor" refers to the independent variable(b).

In the analysis of variance procedure (ANOVA), "factor" refers to the independent variable. ANOVA is used to determine if there is a significant difference between the means of two or more groups, and the factor is the variable being studied that is believed to have an effect on the outcome. Variance is a measure of the variability or spread of the data, and ANOVA compares the variance between groups to the variance within groups to determine if there is a significant difference. The different levels of a treatment are also referred to as levels of the factor.

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Answer:

C

Step-by-step explanation:

3x - 9y = 9 → (1)

- 2x +2y = 8 ( subtract 2y from both sides )

- 2x = - 2y + 8 ( divide through by - 2 )

x = y - 4

substitute x = y - 4 into (1)

3(y - 4) - 9y = 9

3y - 12 - 9y = 9

- 6y - 12 = 9 ( add 12 to both sides )

- 6y = 21 ( divide both sides by - 6 )

y = \(\frac{21}{-6}\) = - \(\frac{7}{2}\)

Answer:

23

Step-by-step explanation:

In a genogram, various symbols and lines represent different aspects of a person's familial relationships and attributes. Here's a breakdown of the symbols you mentioned:

1. Square: A square in a genogram indicates a male individual. It represents the person's gender and is used to distinguish between male and female family members.

2. Circle: A circle in a genogram indicates a female individual. It represents the person's gender and is used to distinguish between male and female family members.

3. Solid horizontal line: A solid horizontal line in a genogram represents a marital relationship between two individuals. The line connects a square (male) and a circle (female) to show that they are married or in a committed partnership.

4. Broken line: A broken line in a genogram represents a non-blood relationship, such as an adoptive parent-child relationship or a step-sibling connection. It is used to show relationships that are not based on biological ties.

5. X through a square/circle: An X through a square or a circle indicates that the individual is deceased. This symbol is used to show that the person has passed away and is no longer living.

6. Solid vertical line: A solid vertical line in a genogram represents a parent-child relationship. It connects an individual (either a square or circle) to their parent(s), showing the biological connection between the family members.

These symbols and lines help provide a visual representation of a person's family history and relationships, making it easier to analyze and understand the various connections within a family tree.

Overall, a genogram is a visual representation of a family tree that includes important information about relationships, health issues, and other relevant details. By understanding the various symbols and indicators used in a genogram, it is possible to gain a deeper understanding of family dynamics and relationships, as well as potential risk factors for various health conditions. As such, genograms are an important tool for healthcare providers, therapists, and other professionals working with individuals and families.

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The lower and upper bounds of h - k are 42.31 and 42.49 respectively.

Upper and lower bounds are the maximum and minimum values that a number could have been before it was rounded. They can also be called limits of accuracy.

The upper and lower bounds can be written using error intervals

The lowest value of h is 47.15

The greatest value of h is 47.24

The greatest value of k is 4.84

The lowest value of k is 4.75

Thus upper bound of h -k = 47.24 - 4.75 = 42.49

Thus lower bound of h -k = 47.15 - 4.84 = 42.31

Thus the lower and upper bounds of h - k are 42.31 and 42.49 respectively.

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Answer:

(a) There is $1740.88 in Mary's account after 2 years

(b) The interest earned on Mary's investment after 2 years is $40.88

Step-by-step explanation:

Let us revise the rule of the compound interest

→  \(A=P(1+\frac{r}{n})^{nt}\) , where

∵ She invested $1700

∴ P = 1700

∵ The rate is 1.19%

∴ r = 1.19/100 = 0.0119

∵ It is compounded quarterly

∴ n = 4

∵ She decided to invest her money for 2 years

∴ t = 2

Let us substitute these values in the rule above to find her new amount of money in her account

→  \(A=1700(1+\frac{0.0119}{4})^{4(2)}\)

→ \(A=1700(1.002975)^{8}\)

→ \(A=1740.883806\) dollars

Round it to the nearest cent → means 2 decimal places

→ A = $1740.88

(a) There is $1740.88 in Mary's account after 2 years

The interest amount is the difference between the new amount and the initial amount

\(I=A-P\)

∵ P = 1700

∵ A = 1740.88

∴ \(I=1740.88-1700\)

∴ I = $40.88

(b) The interest earned on Mary's investment after 2 years is $40.88

Answer:

The interest earned on Mary's investment after 2 years is $40.88

Answer:

Angle FCD + angle HCD = 180 degrees

Step-by-step explanation

These angles are supplementary, meaning they are basically made from a line cut in half. Supplementary angles add up to 180 degrees, since a straight line is 180 degrees. So the two angles put together must equal 180 degrees.

Answer:

C) The sum of the measures of the interior angles of a triangle is 180°.

Step-by-step explanation:

I got it correct on edge

The fact to prove ΔABC and ΔTRS are similar is The sum of the measures of the interior angles of a triangle is 180, option third is correct.

It is defined as the law to prove that the two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have two triangles shown in the picture.

Angle B = 46 degrees

Angle C = 45 degrees

Angle A = 180 - 45 - 46 = 89 degrees

Angle R = 46 degrees

Angle S = 180 - 46 - 89 = 45 degrees

Angle T = 89 degrees

Thus, the fact to prove ΔABC and ΔTRS are similar is The sum of the measures of the interior angles of a triangle is 180, option third is correct.

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The carnival committee should expect to pay $218.70 for prizes at the booth.

We can start by calculating the expected number of students who win each prize:

Stuffed toy: 22% of 150 students = 0.22 x 150 = 33 students

Jump rope: 16% of 150 students = 0.16 x 150 = 24 students

T-shirt: 6% of 150 students = 0.06 x 150 = 9 students

No prize: 100% - (22% + 16% + 6%) = 56% of 150 students = 0.56 x 150 = 84 students

Next, we can calculate the total amount of money that the carnival committee should expect to pay for prizes at the booth:

Stuffed toy: 33 students x $3.60 per toy = $118.80

Jump rope: 24 students x $1.20 per rope = $28.80

T-shirt: 9 students x $7.90 per shirt = $71.10

Total cost of prizes = $118.80 + $28.80 + $71.10 = $218.70

Therefore, the carnival committee should expect to pay $218.70 for prizes at the booth.

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The forecast for May using a five-month moving average is 39 (Option E).

Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.

According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47

We have to add the sales of these five months, which gives:

27 + 40 + 42 + 41 + 47 = 197

To find the moving average for May, we divide this sum by 5:

197 / 5 = 39.4

Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.

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