Simplify: 1/6x + 42 + 2/5x - 8/3 -19

A: 97/30x + 23
B: 21/10x - 23
C: -21/10x + 23
D: 97/30x - 23

The sample in this example is D) the small group of college students who are observed. The correct option is D.

The researcher has identified college students as her group of interest, but it is not feasible or practical to observe or study all college students. Therefore, she needs to select a subset of college students, which is known as a sample. In this case, she has chosen to observe a small group of local college students, which is the sample. It is important to note that the sample needs to be representative of the larger population of interest, in this case, all college students, in order for the results to be applicable to the larger group.

While the sample in this example is only a small group of local college students, the researcher would need to ensure that they are representative of all college students in order for the results to be generalizable.

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The length of the hypotenuse of the isosceles triangle is 7.1 units.

We can use the distance formula to find the length of ST (base) and TU(perpendicular). Further, using these lengths, we can find the hypotenuse of the isosceles triangle.

The distance formula is given as follows,

d = √(x₂ - x₁)² + (y₂ - y₁)²

Here, d is the distance between the two points (x₁, y₁) and (x₂, y₂)

As shown in the drawn isosceles triangle STU,

The length of the base ST is given as,

ST = √(x₂ - x₁)² + (y₂ - y₁)²

Here,

x₁ = 1 and y₁ = 1

x₂ = 6 and y₂ = 1

∴ ST = √(6-1)² + (1-1)²

ST = √5²

ST = 5 units

Similarly, for TU as the other leg passes through the point(6,2) and is of length 5 units ( STU being isosceles triangle), we have,

x₁ = 6 and y₁ = 1

x₂ = 6 and y₂ = 6

Also, TU = 5 units

Now, using Pythagoras Theorem,

(hypotenuse)² = (base)² + (perpendicular)²

(SU)² = (ST)² + (TU)²

(SU)² = (5)² + (5)²

(SU)² = 50

SU = √50

SU = 7.071 units

SU ≈ 7.1 units (after rounding of to the nearest tenth)

hence, the hypotenuse of the isosceles triangle is of 7.1 units.

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The optimal point (x, y) can be found by solving the simultaneous equations. The slack for constraint (1) is the difference between the right-hand side and the left-hand side of the inequality, representing the unused capacity in the constraint.

The optimal point (x, y) can be found using the simultaneous equations method. From the given constraints:

2X + 3Y ≤ 240 ...(1)

2X + Y ≤ 120 ...(2)

X, Y ≥ 0

To find the optimal point, we need to solve these two equations simultaneously. By solving equations (1) and (2), we can find the values of X and Y that satisfy both constraints. Once we have the values of X and Y, we can substitute them into the objective function (profit function) to determine the maximum profit.

To find the slack for constraint (1), we need to evaluate the difference between the left-hand side (LHS) and the right-hand side (RHS) of the inequality. In this case, the slack for constraint (1) is calculated as:

Slack for constraint (1) = RHS - LHS = 240 - (2X + 3Y)

The slack represents the amount of unused resources or capacity in the constraint. It tells us how much "slack" or leeway we have in the constraint before it becomes binding. If the slack is positive, it means that the constraint is not fully utilized and there is room for improvement. If the slack is zero, it indicates that the constraint is exactly satisfied. If the slack is negative, it implies that the constraint is violated and adjustments need to be made.

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Using the central limit theorem, for different sample sizes, we find the probabilities Pr(Y < 68) ≈ 0.9439, Pr(68 < Y < 69) ≈ 0.0590, and Pr(Y > 66) ≈ 0.0228.

a) In a random sample of size n = 69, we can approximate the distribution of the sample mean using a normal distribution. The mean of the sample mean will be equal to the population mean μY = 65, and the variance of the sample mean will be σY^2 / n = 49 / 69 ≈ 0.7101. To find Pr(Y < 68), we calculate the z-score using the formula z = (x - μ) / σ, where x is the value we want to find the probability for.

z = (68 - 65) / √(0.7101) ≈ 1.5953

Using a standard normal distribution table or a calculator, we find the probability associated with z = 1.5953 to be approximately 0.9439. Therefore, Pr(Y < 68) ≈ 0.9439.

b) In a random sample of size n = 124, we can again approximate the distribution of the sample mean using a normal distribution. The mean of the sample mean will still be equal to the population mean μY = 65, and the variance of the sample mean will be σY^2 / n = 49 / 124 ≈ 0.3952. To find Pr(68 < Y < 69), we calculate the z-scores for the lower and upper limits.

Lower z-score: z1 = (68 - 65) / √(0.3952) ≈ 1.5225

Upper z-score: z2 = (69 - 65) / √(0.3952) ≈ 2.5346

Using the standard normal distribution table or a calculator, we find the probability associated with z1 = 1.5225 to be approximately 0.9357 and the probability associated with z2 = 2.5346 to be approximately 0.9947. Therefore, Pr(68 < Y < 69) ≈ 0.9947 - 0.9357 ≈ 0.0590.

c) In a random sample of size n = 196, we can once again approximate the distribution of the sample mean using a normal distribution. The mean of the sample mean will still be equal to the population mean μY = 65, and the variance of the sample mean will be σY^2 / n = 49 / 196 ≈ 0.2500. To find Pr(Y > 66), we calculate the z-score.

z = (66 - 65) / √(0.2500) = 2

Using the standard normal distribution table or a calculator, we find the probability associated with z = 2 to be approximately 0.9772. Therefore, Pr(Y > 66) ≈ 1 - 0.9772 ≈ 0.0228.

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Answer:

B(2, - 1 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( \(\frac{x_{1}+x_{2} }{2}\), \(\frac{y_{1}+y_{2} }{2}\) )

let the coordinates of B = (x, y )

Then using the midpoint formula, equate to each coordinate of the given midpoint, that is

(x₁, y₁ ) = A(4, 3) and (x₂, y₂ ) = B(x, y) , then

\(\frac{4+x}{2}\) = 3 ( multiply both sides by 2 )

4 + x = 6 ( subtract 4 from both sides )\

x = 2

\(\frac{3+y}{2}\) = 1 ( multiply both sides by 2 )

3 + x = 2 ( subtract 3 from both sides )

x = - 1

Coordinates of B = (2, - 1 )

The volume of the rectangular pyramid with a height of 6in, width of 2in and length of 4in is 16 cubic inches.

A rectangular pyramid is a three-dimentional object with a rectangular shaped base and triangular shaped faces that correspond to each side of the base.

The volume of rectangular pyramid is expressed as;

V = (1/3) × l × w × h

From the image:

Length l = 4 in

Width w = 2 in

Height h = 6 in

Volume V = ?

Plug the given values into the above formula and solve for the volume.

V = (1/3) × l × w × h

V = (1/3) × 4 × 2 × 6

V = (1/3) × 48

V = 16 in³

Therefore, the volume is 16 cubic inches.

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The volume of the newly formed prism is:  29160 cubic units

The formula for the volume of a prism is:

V = Base area * height

Now, we are told that the dimensions are dilated by a scale factor of 3 and this means the new dimensions will be gotten by multiplying the original dimensions by the scale factor of 3.

Thus, the new dimensions are:

Base length = 5 * 3 = 15

Base width = 18 * 3 = 54

New height = 12 * 3 = 36

Thus:

Volume of prism = 15 * 54 * 36

Volume of prism = 29160 cubic units

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Answer:

D

Step-by-step explanation:

Number of chickens (c) is = 4 times number of horses (4h). c = 4h

The way that the sample size would have to change to decrease the length of the confidence interval is to increase from 400 to 1600.

The confidence interval's length is directly proportional to the sample size. The specific relationship between these two factors follows an inverse proportion that correlates to the square root of the sample size.

One could represent this correlation through a proportionality statement: the larger the sample size, the smaller the confidence interval's length becomes.

Given that L1 = 0. 06 and n1 = 400, we want to find n2 such that L 2 = 0. 03:

L1 / L2 = √(n 2 / n 1)

The values would then be:

L1 / L2 = √ ( n2 / n1 )

0.06 / 0.03 = √ ( n2 / 400)

2 = √ (n2 / 400)

2² = ( √ (n2 / 400))²

4 = n2 / 400

n2 = 4 x 400

n2 = 1600

In conclusion, the sample size needs to increase to 1, 600.

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Answer:

Lines 1 and 4 are parallel

Step-by-step explanation:

The image below shows the four lines graphed, and proves that lines 1 and 4 are parallel.

Hope this helps! :)

The value of g of (-12)​ is -7

What is Function?

A relation between a collection of inputs and outputs is known as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

g(x) = x +5

substitute x= -12

g(-12) = -12 +5 = -7

The value of g of (-12)​ is -7

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The proportions of parts produced within specifications by the two shifts at a 4% significance level with the help of an equation.

A formula exists in every equation. Some equations do not have formulae. Equations are designed to be solved for a variable.

(a) To estimate the difference in proportions of parts produced within specifications by the two shifts, we need to calculate the confidence interval.

First, we can calculate the sample proportions of parts produced within specifications for each shift:

For the day shift, the sample proportion is:

p1 = 188/200 = 0.94

p2 = 180/200 = 0.90

p1 - p2 = 0.94 - 0.90 = 0.04

To calculate the confidence interval, we can use the following formula:

(point estimate) ± (critical value) x (standard error)

We will use a 96% confidence level, so our critical value is z* = 2.05 (from the z-table).

The standard error can be calculated as follows:

SE = sqrt((p1*(1-p1)/n1) + (p2*(1-p2)/n2))

where n1 and n2 are the sample sizes.

Substituting in our values, we get:

SE = sqrt((0.94*(1-0.94)/200) + (0.90*(1-0.90)/200))

SE = 0.040

Now we can calculate the confidence interval:

0.04 ± 2.05(0.040)

The confidence interval is (0.003, 0.077).

Therefore, we are 96% confident that the true difference in proportions of parts produced within specifications by the two shifts is between 0.003 and 0.077.

(b) To determine whether the difference in proportions of parts produced within specifications by the two shifts is significantly different from 0, we need to check if 0 is within the confidence interval we calculated.

Since the confidence interval does not include 0, we can conclude that the difference in proportions of parts produced within specifications by the two shifts is significantly different from 0 at a 96% confidence level.

(c) The hypotheses of interest for the significance test are:

H0: p1 - p2 = 0 (There is no difference in proportions of parts produced within specifications by the two shifts)

Ha: p1 - p2 ≠ 0 (There is a difference in proportions of parts produced within specifications by the two shifts)

We will use a significance level of α = 0.04.

To perform the significance test, we need to calculate the test statistic:

z = (p1 - p2 - 0) / SE

where p1, p2, and SE are the same as calculated in part (a).

Substituting in our values, we get:

z = (0.94 - 0.90 - 0) / 0.040

z = 1.00

Using a z-table, we find that the p-value for a two-tailed test with z = 1.00 is approximately 0.317.

Since the p-value is greater than our significance level of 0.04, we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to conclude that there is a difference in proportions of parts produced within specifications by the two shifts at a 4% significance level.

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The equation of the absolute value function is y = -|x - 3| + 6

The given parameters are

Vertex = (3, 6)

Crosses the x-axis at (-3,0) and (9,0)

An absolute value equation is represented as

y = a|x - h| + k

Where

Vertex = (h, k)

So, we have

y = a|x - 3| + 6

At (-3, 0), we have

0 = a|-3 - 3| + 6

This gives

0 = a|-6| + 6

So, we have

0 = 6a + 6

Solve for a

a = -1

Substitute a = -1 in y = a|x - 3| + 6

y = -|x - 3| + 6

Hence, the equation of the absolute value function is y = -|x - 3| + 6

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The correct statement is :David started at 0 instead of 2

A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, plotting a point.

Given here: In a number line the interval (-5,5) is marked and 2 to 5 is 3

The right steps are

Add 3 to 2 to obtain the required number as there are 3 spaces between 2 and 5

Thus 2+3=5 which is the required answer

but David addes 2-3=-1 which is incorrect.

Hence, David started at 0 instead of 2

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Answer:

70

Step-by-step explanation:

\(56(5/4)=70\)

To find a plane containing the point (-5, 6, -6) and the line defined by parametric equations x(t) = 7 - 5t, y(t) = 3 - 6t, and z(t) = -6 - 6t, we can use the point-normal form of the equation of a plane.

The equation of a plane in point-normal form is given by Ax + By + Cz + D = 0, where (A, B, C) is the normal vector to the plane, and (x, y, z) are the coordinates of a point on the plane. We can determine the normal vector by taking the cross product of two direction vectors in the plane.

The direction vector of the line can be obtained by taking the coefficients of t in the parametric equations, which gives us (-5, -6, -6). We can choose any two non-parallel direction vectors in the plane, for example, (1, 0, 0) and (0, 1, 0). Taking the cross product of these two vectors, we get the normal vector (0, 0, -1).

Now, we can substitute the values of the point (-5, 6, -6) and the normal vector (0, 0, -1) into the point-normal form equation. This gives us 0*(-5) + 0*6 + (-1)*(-6) + D = 0, which simplifies to D = -6. Thus, the equation of the plane containing the point (-5, 6, -6) and the given line is 0*x + 0*y - z - 6 = 0, or simply -z - 6 = 0.

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The maximum number of mail swaps that Bagelbot can perform between officials from A and officials from B can be 150 .

It can be determined by calculating the maximum number of edges possible for a bipartite graph between A and B. A bipartite graph is a graph in which the vertices can be divided into two disjoint sets such that every edge connects a vertex in one set to a vertex in the other set.

In this case, the officials from A and officials from B represent the two disjoint sets.

The maximum number of edges in a bipartite graph between A and B can be calculated as the product of the number of officials in A and the number of officials in B. Therefore, if there are n officials in A and m officials in B, the maximum number of mail swaps that Bagelbot can perform is n x m.

For example, if there are 10 officials in A and 15 officials in B, the maximum number of mail swaps that Bagelbot can perform is 10 x 15 = 150.

This means that Bagelbot can potentially redirect up to 150 pieces of mail between officials from A and officials from B.

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Answer:

Step-by-step explanation:

Only option B is true.

y=5 is a asymptote horizontal f(x) -> 5 as x -> +oo

The asymptote of the given graph is y = 5 because as x tends to the infinite value of graph approach to 5 so option (B) will be correct.

A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.

In order to plot the graph, we need to find out y's values corresponding to x's value

After that, we need to substitute the values of x's and y's into the coordinate geometry.

Asymptote is an imaginary straight line that represents the overall graph nearest to that.

It means the distance from the line to the curve tends to be zero.

Given the curve,

If we look at the graph then it is going near to five horizontal.

As x → ∞ the graph is approaching the value of approx 5.

Hence "The asymptote of the given graph is y = 5 because as x tends to the infinite value of graph approach to 5".

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Answer:

C

Step-by-step explanation:

sinx=9/19

sinx=0.47

opposite function on calculator

x= ~28

Answer:

28˚

Step-by-step explanation:

Answer:

whats question ?

Step-by-step explanation:

When the weight moves from x = -8 cm to x = 8 cm, the spring moves from its maximum stretched position to its maximum compressed position.Hence, the spring oscillates between its maximum stretched and compressed positions when the weight is set in motion. Therefore, the spring is a simple harmonic oscillator.

Given: Displacement x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0. To find: What is the spring?Explanation:We know that displacement is given by x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0.Comparing this with the standard equation, x

= Acos(ωt+ φ)A

= amplitude

= 8 cmω

= angular frequencyφ

= phase angleWhen the spring is at equilibrium position, the weight attached to the spring does not move. Hence, no force is acting on the weight at the equilibrium position. Therefore, the spring is neither stretched nor compressed at the equilibrium position.Now, the spring is set in motion resulting in a displacement of x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0. The maximum displacement of the spring is 8 cm in the positive x direction. When the weight is at x

= 8 cm, the restoring force of the spring is maximum in the negative x direction and it pulls the weight towards the equilibrium position. At the equilibrium position, the weight momentarily stops. When the weight moves from x

= 8 cm to x

= -8 cm, the spring moves from its natural length to its maximum stretched position. At x

= -8 cm, the weight momentarily stops. When the weight moves from x

= -8 cm to x

= 8 cm, the spring moves from its maximum stretched position to its maximum compressed position.Hence, the spring oscillates between its maximum stretched and compressed positions when the weight is set in motion. Therefore, the spring is a simple harmonic oscillator.

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The displacement of the weight attached to the spring is given by the equation x = 8 cos t. The amplitude of the motion is 8 centimeters and the period is 2π seconds.

The equation x = 8 cos t represents the displacement of a weight attached to a spring in simple harmonic motion. In this equation, x is measured in centimeters and t is measured in seconds.

The amplitude of the motion is 8 centimeters, which means that the weight oscillates between x = 8 and x = -8.

The period of the motion can be determined from the equation T = 2π/ω, where ω is the angular frequency. In this case, ω = 1, so the period T is 2π seconds.

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The equation that can be written from the given sequence is: an = 17n - 67

This equation represents a linear relationship between the index 'n' and the corresponding term 'an' in the sequence. Each term can be obtained by multiplying the index 'n' by 17 and subtracting 67 from it. By substituting different values of 'n' into the equation, we can generate the sequence. The initial term in the sequence is -50, and each subsequent term increases by 17, following the pattern described by the equation.

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Answer:

9xx2401x=21609x

Step-by-step explanation: 3x3=9. 40x40=1600, 40x9=360x2 because there are 2 of the same problem because the number is the same. 9x9=81.

Now we add them up. 1600+720+81=2401. 2401x9=21609

But don't forget to add the x at the end or the answer is wrong!!!

The displacement of the object between t=0 and t=1 second is 5.66 m.

The displacement of the object between t=0 and t=1 second is calculated as follows;

The given equation of the object's motion;

x = 4 cos (πt  +  π/4)

where;

at a time, t = 0 second, the displacement of the object is calculated as;

x = 4 cos (πt  +  π/4)

x = 4 cos (0 + π/4)

x = 4 cos (π/4)

x = 2.83 m

at time t = 1 second, the displacement of the object is calculated as;

x = 4 cos (π  + π/4)

x = 4 cos (5π/4)

x = -2.83 m

The displacement of the object between the time given;

x = 2.83 m - ( - 2.83 m )

x = 5.66 m

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Option C, Student 3 has it right. The Triangle Inequality Theorem states that any two sides of a triangle must add up to a length larger than the third side.

Applying the Triangle Inequality Theorem, which asserts that the length of the third side must be bigger than the sum of any two other sides of a triangle.

We must thus evaluate if the total of any two sides is more than the length of the third side in order to ascertain how many triangles may be formed using the three pieces of wood.

Let's look at each student's response:

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The question is -

A teacher has three pieces of wood that measure 2 ft, 3 ft, and 6 ft, respectively. The teacher asks four students to explain how many triangles they can make with the pieces of wood. The table shows the students.

1. The three pieces of wood will make no triangles because 2+3= 5, and 5 < 6.

2. The three pieces of wood will make one triangle because 2+35, and <6. The three pieces of wood will make many triangles because

3. 2+3=5, and 5> 6.

4. The three pieces of wood will make one triangle because 2+3=5, and 5 > 6.

Which student is correct?

A. Student 1

B. Student 2

C. Student 3

D. Student 4

Answer

\(18\pi\)

Step-by-step explanation:

\(\pi \times diameter \\ = \pi \times 18\)

Answer: 56.52

Step-by-step explanation: Circumference is found by using 2πr. Since diameter is twice of radius, this formula can also be used as C = πd. So the circumference will be 18 * 3.14 (which is approximate for π). This gives us the answer of 56.52.

Would appreciate a brainly <3

Answer:

The answer is 5.2. Your welcome :)

Step-by-step explanation: