The instructions for a model airplane show a scale of 1 in:
36 ft. What is the length of the drawing if the actual length
of an airplane is 144 ft?

Answer:

Y= x+2

Step-by-step explanation:

The x value is always adding 2 to get the y value

1+2=3

2+2=4

3+2=5

4+2=6

5+2=7

Therefore your answer is y = x + 2

Hope this helps!

Answer:

2

Step-by-step explanation:

y = x + c

Put x as 1, and y as 3 and solve for c.

3 = 1 + c

3 - 1 = c

2 = c

The equation of the loci of the points are presented as follows;

The locus of a point is the shape or curve formed by points that satisfy a specified equation.

1. The equation of the locus of a point P(x, y) that moves such that the distance from a point is constant is of the form; (x - h)² + (y - k)² = r², which is the equation of a circle.

Where;

(h, k) is the point from which the point P(x, y) is equidistant from = The center of the circle

r = The distance from the point = The radius of the circle

Therefore;

(h, k) = (-1, -1)

r = 9

(x - h)² + (y - k)² = r² is therefore;

(x - (-1))² + (y - (-1))² + 9²

The equation of the locus of the point P(x, y) is therefore;

2. The locus of a point that moves equidistant from two points is the perpendicular bisector of the line joining the points.

The perpendicular bisector of the line joining the points (-4, 6) and (2, -7) can be found as follows;

The slope, m, of the line that has the above points; (-7 - 6)/(2 - (-4)) = -13/6

The equation of the line is therefore;

y - 6 = (-13/6) × (x - (-4))

y = (-13/6) × (x - (-4)) + 6

The midpoint of the line is; (-4 + (2 - (-4))/2, 6 + (-7 - 6)/2) = (-1, -0.5)

The slope of the perpendicular line is therefore; -1/(-13/6) = 6/13

The equation of the perpendicular bisector is therefore;

y - (-0.5) = (6/13)×(x - (-1))

y = (6/13)×(x - (-1)) - 0.5 = (6/13)·x - 1/26

y = (6/13)·x - 1/26

3. The locus of a point that moves equidistant from a point and a line is a parabola.

The line y = 3 is the directrix of the parabola

The point (-5, 1) is the focal point of the parabola

The general equation for the directrix is; y = k - p

The coordinates of the focus is (h, k + p)

By comparison;

h = -5

k - p = 3...(1)

k + p = 1...(2)

Adding equation (1) to equation (2), we get;

k - p + k + p = 2·k = 3 + 1 = 4

2·k = 4

k = 4 ÷ 2 = 2

k = 2

k - p = 3

2 - p = 3

p = 2 - 3 = -1

p = -1

The vertex, (h, k) = (-5, 2)

The equation of a parabola, (x - h)² = 4·p·(y - k),  is therefore;

(x - (-5))² = 4 × (-1) × (y - 2) = -4·y + 8

x² + 10·x + 25  = -4·y + 8

-4·y + 8 = x² + 10·x + 25

-4·y = x² + 10·x + 25 - 8 = x² + 10·x + 17

The equation of the line is therefore;

y = -0.25·x² - 2.5·x - 4.25

4. The locus of the point, P(x, y) that moves such that it is equidistant from the points (3, 2) and (-1, 5), is the perpendicular bisector to the line joining the points.

The midpoint of the line is; (3 + (-1 - 3)/2, 2 + (5 - 2)/2) = (1, 3.5)

The slope of the line is; (5 - 2)/(-1 - 3) = -0.75

The slope of the perpendicular bisector is therefore;

-1/(-0.75) = 4/3

The equation of the line is therefore;

y - 3.5 = (4/3)×(x - 1)

y = (4/3)×(x - 1) + 3.5 = (4/3)·x + 13/6

The equation of the line is therefore;

y = (4/3)·x + 13/6

5. The equation of the locus of the point that moves so that it is equidistant from the point (2, -3) and the line y = 7 is a parabola.

The directrix is; y = 7

The focus is; (2, -3)

Therefore;

(h, k + p) = (2, -3)

h = 2

k + p = -3

k - p = 7

Which indicates; 2·k = -3 + 7 = 4

k = 4 ÷ 2 = 2

k = 2

The vertex, (h, k) = (2, 2)

k - p = 7

2 - p = 7

p = 2 - 7 = -5

p = -5

The equation of the line, (x - h)² = 4·p·(y - k), is therefore;

(x - h)² = 4·p·(y - k) = (x - 2)² = 4×(-5)×(y - 2)

(x - 2)² = 4×(-5)×(y - 2) = -20·(y - 2) = -20·y + 40

x² - 4·x + 4 = -20·y + 40

20·y - 40 = -x² + 4·x - 4

20·y = -x² + 4·x - 4 + 40 = -x² + 4·x + 36

y = (-x² + 4·x + 36)/20 = -x²/20 + x/5 + 1.8

y = -x²/20 + x/5 + 1.8

The equation of the locus of the point is therefore;

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Answer:

139

Step-by-step explanation:

Supplementary angles add to 180 degrees

BOC + 41 = 180

BOC = 180-41

BOC = 139

Answer:

315,000

Step-by-step explanation:

(50,000+20,000)+(35,000+20,000)+(40,000+20,000)=185,000

500,000-185,000=315,000

The population of an island in 1950 was 2 million. The population grew exponentially for 63 years and reached 6.5 million in 2013. The carrying capacity of the island is estimated to be 10 million.

If the population growth rate in the future is similar to the last 50 years, what will the population be in 2050

The population is given to be increasing exponentially, which means it will follow the equation:

\($P(t) = P_0 e^{rt}$\)Here,\($P(t)$\) is the population after a period of time \($t$, $P_0$\) is the initial population, $r$ is the annual growth rate (which we are given is the same as the growth rate of the last 50 years), and \($t$\) is the time.

We can find the annual growth rate $r$ using the formula:\($$r = \frac{\ln{\frac{P(t)}{P_0}}}{t}$$\)
We know\($P_0 = 2$ million, $P(t) = 6.5$ million, and $t = 63$\) years. Substituting these values, we get:

\($r = \frac{\ln{\frac{6.5}{2}}}{63} = 0.032$\) (rounded to 3 decimal places)

Since the carrying capacity of the island is 10 million, we know that the population will not exceed this limit.

Therefore, we can use the logistic model to find the population growth over time. The logistic growth model is:

\($$\frac{dP}{dt} = r P \left(1 - \frac{P}{K}\right)$$\)

where $K$ is the carrying capacity of the environment. This can be solved to give:\($P(t) = \frac{K}{1 + A e^{-rt}}$\)

where \($A = \frac{K-P_0}{P_0}$. We know $K = 10$ million, $P_0 = 2$ million, and $r = 0.032$\). Substituting these values, we get:\($A = \frac{10-2}{2} = 4$\)

Therefore, the equation for the population of the island is:\($P(t) = \frac{10}{1 + 4 e^{-0.032t}}$\)

To find the population in 2050, we substitute\($t = 100$\) (since 63 years have already passed and we want to find the population in 2050, which is 100 years after 1950):

\($P(100) = \frac{10}{1 + 4 e^{-0.032 \times 100}} \approx \boxed{8.76}$ million\)
Therefore, the estimated population of the island in 2050, assuming constant carrying capacity and consumption per capita, is approximately 8.76 million.

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The series converges on the interval from 7 inclusive to 9 exclusive.

To find the radius of convergence, we use the ratio test:

So the series converges absolutely if |x - 8| < 1, and diverges if |x - 8| > 1. Therefore, the radius of convergence is R = 1.

To find the interval of convergence, we need to test the endpoints x = 7 and x = 9:

When x = 7, the series becomes:

[infinity] (-1)ⁿ (n+9) / (n+1)

n = 0

which is an alternating series that satisfies the conditions of the alternating series test. Therefore, it converges.

When x = 9, the series becomes:

[infinity] 1 / (n+1)

n = 0

which is a p-series with p = 1, which diverges.

Therefore, the interval of convergence is [7, 9).

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The answer to questions are as follows- a)720 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used once. b)240 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used once, containing the block cd. c)120 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used once, that start with the letter f.d)4 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used once, that contain the blocks abc and ef.

a) To find the number of strings that can be formed using the letters a, b, c, d, e, f with each letter used formerly, we need to find the number of permutations of the letters. This can be set up using the formula for permutations of n objects taken r at a time, which is n!/( n- r)!.

In this case, we've 6 objects and we want to take all 6, so we have

6!/( 6- 6)! = 6! = 720

thus, there are 720 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly.

b) To find the number of strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly, that contain the block cd, we can treat the block cd as a single object and find the number of permutations of the performing 5 objects( alphabet, e, f, and the block cd). We also multiply this by the number of ways that cd can be arranged within the string( which is 2 since cd can be arranged as cd or dc).

So we have

5! * 2 = 240

thus, there are 240 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly, containing the block cd.

c) To find the number of strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly, that starts with the letter f, we can fix f as the first letter and also find the number of permutations of the remaining 5 objects. This can be set up using the formula for permutations of n objects taken r at a time, which is n!/( n- r)!.

In this case, we've 5 objects and we want to take all 5, so we have

5!/( 5- 5)! = 5! = 120

thus, there are 120 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly, that start with the letter f.

d) To find the number of strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly, that contain the blocks alphabet and ef, we can fix alphabet and ef as blocks and find the number of permutations of the remaining 2 objects( d and f). We also multiply this by the number of ways that the blocks can be arranged within the string( which is 2 since alphabet can be before ef or ef can be before the alphabet).

So we have

2 * 2! = 4

thus, there are 4 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly, that contain the blocks alphabet and ef.

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The correct questions are given below-

a)how many strings can be formed using the letters a, b, c, d, e, f, with each letter used once?

b) how many strings can be formed using the letters a, b, c, d, e, f, with each letter used once, that contain the block cd?

c)how many strings can be formed using the letters a, b, c, d, e, f, with each letter used once, that start with the letter f?

d)how many strings can be formed using the letters a, b, c, d, e, f, with each letter used once, that contain the blocks abc and ef?

The quotient of 4 and \(\frac{1}{3}\) is equal to 12.

In Mathematics, quotient is a mathematical expression that is simply used to represent division i.e the division of a number by another number.

Translating the word problem into an equation, we have:

The quotient of 4 and \(\frac{1}{3}\) ;

\(\frac{4}{\frac{1}{3} }\)

Simplifying further, we have:

\(4 \times \frac{3}{1} = 12\)

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The confidence interval for the given numbers, with a sample proportion of 0.88 and a confidence level of 0.94, is approximately (0.798, 0.962) when rounded to two decimal places.

To calculate the confidence interval for a random sample with a sample proportion of 0.88 and a confidence level of 0.94, we can use the formula:

\[ \text{Confidence Interval} = \text{Sample Proportion} \pm \text{Margin of Error} \]

The margin of error can be calculated using the formula:

\[ \text{Margin of Error} = \text{Critical Value} \times \text{Standard Error} \]

The critical value can be obtained from the Z-table or calculated using the inverse cumulative distribution function for the standard normal distribution.

Since the level of difficulty is set to 2, we can assume a two-tailed test. The critical value for a 94% confidence level with a two-tailed test is approximately 1.99.

The standard error can be calculated using the formula:

\[ \text{Standard Error} = \sqrt{\frac{\text{Sample Proportion} \times (1 - \text{Sample Proportion})}{\text{Sample Size}}} \]

Plugging in the values:

Sample Proportion (\( p \)): 0.88

Sample Size (\( n \)): 53

Confidence Level: 0.94

Critical Value (\( z \)): 1.99

We can calculate the standard error:

\[ \text{Standard Error} = \sqrt{\frac{0.88 \times (1 - 0.88)}{53}} \]

Now, we can calculate the margin of error:

\[ \text{Margin of Error} = 1.99 \times \text{Standard Error} \]

Finally, we can calculate the confidence interval:

\[ \text{Confidence Interval} = 0.88 \pm \text{Margin of Error} \]

Calculating the values:

Standard Error ≈ 0.041

Margin of Error ≈ 0.082

Confidence Interval ≈ (0.798, 0.962)

Therefore, the confidence interval for the given numbers, with a sample proportion of 0.88 and a confidence level of 0.94, is approximately (0.798, 0.962) when rounded to two decimal places.

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Answer:

Step-by-step explanation:

hello

Step-by-step explanation:

1)8x-2x=35-17

6x=18

x=18/6

x=3

2)7k-2k=-37-8

5k=-45

k=-45/5

k=-9

3)m-9m=-13-3

-8m=-16

8m=16

m=16/8

m=2

4)-4y+3y=12-6

-y=6

y=-6

5)6a-2a=-40

4a=-40

a=-40/4

a=-10

6)5w+2w=55+29

7w=84

w=84/7

w=12

7)5p-13p=-43+11

-8p=-32

8p=32

p=32/8

p=4

8)-c-5c=-2+50

-6c=48

c=-48/6

c=-8

The option that is not a factor of capacity planning is the option d

d) Proximity to suppliers

The process of ascertaining the production capacity an organization needs in order to meet changing demand for the products and services of the organization is known as capacity planning.

The factors considered in capacity planning are factors which include the capacity measurement approach, the economies of scale, preparedness to deal with the capacity in chunks, and activities towards identifying the best operating level.

Therefore, from the listed options, the option that is not a factor in capacity planning is the option (d) proximity to suppliers

Other aspects of the operations of an organization, such as supply chain management and logistics can be affected by the proximity of suppliers, but the proximity of suppliers is not directly linked to the determination process for the production capacity needed to meet the market demand.

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Answer:

Hiii the answer would be a= -4b+8/3

Answer:

square root of 4761 = 69

Step-by-step explanation:

Answer:

y=2x-1

Step-by-step explanation:

y-y sub 1=m(x- xsub1)

y-(-1)=2(x-0)

y+1=2(x-0)

y+1=2x-0

y=2x-1

Answer:

142,600,000

Step-by-step explanation:

The current population is 115,000,000

1 year = 2.4%

10 years = 24%

24% = 0.24

115, 000, 000 times 0.24 = 27,600,000

27,600,000 is the increase rate 24% after 10 years

Then we add both numbers to find the population after 10 years

115,000,000 + 27,600,000 = 142,600,000

So, the population after 10 years is 142,600,000

the integrals.

1.6 (7) dx x+1 R 2. cos3x cos cos3x cos4x dx 3. f- 4xvx²-16 ,The value of the integral is 43/2.2.

to evaluate the given integrals, let's go through each one step by step:

1. ∫[6,7] (x+1) dx   applying the power rule of integration, we have:

  ∫[6,7] (x+1) dx = [(x²)/2 + x] |[6,7]   evaluating the integral at the limits:

  = [(7²)/2 + 7] - [(6²)/2 + 6]   = (49/2 + 7) - (36/2 + 6)

  = 67/2 - 24/2   = 43/2 ∫ cos³(x) * cos(cos³(x)) * cos(4x) dx   unfortunately, this integral does not have a simple closed-form solution. it involves the composition of trigonometric functions, which makes it challenging to evaluate analytically. numerical integration methods, such as numerical approximation techniques or computer algorithms, can be used to estimate the value of this integral.

3. ∫(f⁻¹(4x)) * (v(x²-16)) dx

  it seems that there is some missing information or clarification needed regarding this integral. the notation f- likely indicates the inverse of a function f, but without knowing the specific function or the context of the problem, it is not possible to evaluate this integral. if you can provide more information or clarify the expression, i would be happy to assist you further.

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Answer:

Answer: 6 3/4

Step-by-step explanation:

You have to mulitply 2 x 4 + 1 = 9 and 4 is going to be the denomiator and how much can 3 can go into 9 only 3 times and that going to be on top of the denomiator  and 2 x 3 = 6

Answer:

4/9

Step-by-step explanation:

Answer:

4 9/10 or 49/10

Step-by-step explanation:

49 over 10

49

10

=4 and 9 over 104

9

10

=4.9

Answer:

x = 1, 3

Step-by-step explanation:

f(x) = y

Where does y = -4?

When x = 1 and x=3

Answer:

The slope is -2. The equation is y= -2x+8.

Answer:

-2

Step-by-step explanation:

slope = m

m=\(\frac{ y2-y1}{x2-x1}\)

points:

(0, 8)aka x1, y1

(4, 0)aka x2, y2

plug in the points

m= \(\frac{0-8}{4-0} = \frac{-8}{4} = -2\)

Answer:

1. 24/40, 32/40, 24/32 (This is in order from top to bottom)

2. 21.1

3. 4.1

Step-by-step explanation:

1. Here, we only have to focus on Angle X.

Let's label in the sides:

Opposite = YZ = 24

Adjacent = XY = 32

Hypotenuse = XZ = 40

SOHCAHTOA simply means:  You can memorise this through the acrostic poem of - Slap On Head Causes A Headache Take One Aspirin, but I remember it by Suck A Toe because that's what it sounds like.

Sin(x) = Opposite/Hypotenuse

Cos(x) = Adjacent/Hypotenuse

Tan(x) = Opposite/Adjacent

Sin(X) = 24/40

Cos(X) = 32/40

Tan(X) = 24/32

The question only asks to give the ratios by using / for a fraction, so we don't simplify it.

2. We are given the angle of 64°, the opposite length 19 and we have to work out x, which is the hypotenuse. We can use the sin function as we have our opposite length and we have to work out the hypotenuse.

Sin(64) = 19/x

xSin(64) = 19

x = 19/Sin(64)

x = 21.13943687

x = 21.1

3. We are given the angle of 70°, the hypotenuse 12 and we have to work out x, which is the adjacent side. We can use the cos function as we have to work out the adjacent side and we have our hypotenuse given to us.

Cos(70) = x/12

12Cos(70) = x  All we have to do here is multiply by 12!

x = 4.10424172

x = 4.1

There are eleven proper subsets in the power set P(ABCD).So, the total number of proper subsets in the P(ABCD) set is 11.

The members of the set P(ABCD) that are proper subsets of ABCD are explained below:Definition: A subset is known as a proper subset if it contains fewer elements than the set it is drawn from.Explanation:In the set of ABCD, there are four elements, A, B, C, and D. The collection of subsets, or the power set, of ABCD is referred to as P(ABCD).In the power set of ABCD, the following members are proper subsets: {}, {A}, {B}, {C}, {D}, {A, B}, {A, C}, {A, D}, {B, C}, {B, D}, and {C, D}.Explanation:A proper subset of a set is a subset that does not include all of the elements of the original set. It contains at least one element from the original set, but it does not contain all of them. In the case of ABCD, all of its proper subsets are simply subsets that exclude one or more of the elements A, B, C, and D. So, each of the single-element subsets, as well as the subsets containing two or three elements, are proper subsets. Hence, there are eleven proper subsets in the power set P(ABCD).So, the total number of proper subsets in the P(ABCD) set is 11.

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Answer:

see explanation

Step-by-step explanation:

The first multiplier is the number of terms being added.

The second multiplier is one more than the first multiplier, that is

2 + 4 + 6 + 8 + 10 ← has 5 terms being added and 6 is one more than 5, thus

2 + 4 + 6 + 8 + 10 = 5 × 6

Answer:

The first multiplier is the number of terms being added.

The second multiplier is one more than the first multiplier, that is

2 + 4 + 6 + 8 + 10 ← has 5 terms being added and 6 is one more than 5, thus

2 + 4 + 6 + 8 + 10 = 5 × 6

The results from the given data,

Mean = 0

Median = 0

Mode = 0

To find the mean, median, and mode of the given data set {-4, -3, -2, -1, 0, 0, 1, 2, 3, 4},

we'll calculate each of these measures step by step:

Mean, To find the mean, we sum up all the values in the data set and divide by the total number of values:

Mean = (-4 + -3 + -2 + -1 + 0 + 0 + 1 + 2 + 3 + 4) / 10

Mean = 0 / 10

Mean = 0

Median, The median is the middle value when the data set is arranged in ascending order.

Since we have 10 values, the median will be the average of the fifth and sixth values:

Arranged data set: -4, -3, -2, -1, 0, 0, 1, 2, 3, 4

Median = (0 + 0) / 2

Median = 0

Mode, The mode is the value(s) that appear(s) most frequently in the data set. In this case, the mode is 0 since it appears twice, more than any other value in the data set.

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Displacement is the length of the straight line drawn from an object’s initial position to the object’s final position

The term "displacement" refers to a change in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial position to the ending position. For instance, if an object shifts from position A to position B, its position changes.

If an object moves with respect to a reference frame, such as when a passenger moves to the back of an airplane or a professor moves to the right with respect to a whiteboard, the object's position changes. This change in location is described as displacement.

The displacement is the shortest distance between an object's initial and final positions. Displacement is a vector. It is visualized as an arrow that points from the initial position to the final position, indicating that it has both a direction and a magnitude.

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It is important to consider the scale of measurement and the specific characteristics of the variables when selecting an appropriate statistical test.The tests can be classified as follows:

1. A researcher measures the proportion of schizophrenic patients born in each season.

This test is nonparametric. The scale of measurement is categorical, as the seasons (spring, summer, fall, winter) represent distinct categories rather than continuous numerical values. Therefore, parametric assumptions, such as normality and equal variances, do not apply to this measurement.

2. A researcher measures the average age that schizophrenia is diagnosed among male and female patients.

This test is parametric. The scale of measurement is continuous and numerical (age in years). Parametric tests, such as t-tests or ANOVA, can be applied when working with continuous data, assuming the data meet the required assumptions (e.g., normality, independence, and equal variances).

3. A researcher tests whether frequency of Internet use and social interaction are independent.

This test can be both parametric or nonparametric, depending on the measurement scale and the specific statistical test used. If the variables are measured on a nominal or ordinal scale, nonparametric tests, such as the chi-square test, would be appropriate. If the variables are measured on a continuous scale, parametric tests, such as logistic regression, could be employed.

4. A researcher measures the amount of time (in seconds) that a group of teenagers uses the Internet for school-related and non-school-related purposes.

This test is parametric. The scale of measurement is continuous (time in seconds), and parametric tests, such as t-tests or ANOVA, can be utilized to compare means or variances, assuming the required assumptions are met.

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