When x is decreased by 129 and then that number is multiplied by 129 , the result is 129. What is the value of x?

Answer:

(-1, 0) and (5, 0)

Step-by-step explanation:

Just know that zeros is another term for x-intercepts. That's the point on the graph where the y coordinate equals 0.

We have two points here. (-1, 0) and (5,0) because those two points cross the line x=0

Answer:

The slope of the line, m=-80 and

The equation of the line is, \(y=-80+440\)

Step-by-step explanation:

Given that initially the hot tub is filled with 440 gallons of water.

So, at time t=0, the amount of water = 440 gallons.

Further, after 1.5 hours, the amount of water had  decreased to 320 gallons.

So, at time t=1.5 hours, the amount of water = 320 gallons.

The point (0,440) and (1.5, 320) are on the line.

So, the slope, m, of the line is

\(m=\frac{440-320}{0-1.5}=-\frac{120}{1.5}=-80\)

The equation of the line is

\(y-440=-80(x-0) \\\\\Rightarrow y-440=-80x \\\\\Rightarrow y=-80x+440\)

Hence, the slope of the line, m=-80 and the equation of the line is, \(y=-80+440\).

Answer:

infinite solutions

Step-by-step explanation:

y=3x-1

6x-2y=-2  ==> solve for y

6x-2y+2y=-2+2y  ==> remove -y in equation

6x=-2+2y

6x-2=2y

2y=6x-2

(y=3x-1)*2  ==> multiply the equation by 2 so the equation equals 2y

2y=6x-2

Since (y=3x-1) = (2y=6x-2)  and  (6x-2y=-2) = (2y=6x-2),

(y=3x-1) = (6x-2y=-2) ==> hence, there are infinite solutions

Answer: a₁₄=90x-31

Step-by-step explanation:

-x-5,  6x-7,  13x-9 ...

Hence,

a₁=-x-5

a₂=6x-7

a₃=13x-9

d=a₂-a₁

d=6x-7-(-x-5)

d=6x-7+x+5

d=7x-2

aₙ=a₁+d(n-1)

a₁₄=-x-5+(7x-2)(14-1)

a₁₄=-x-5+13(7x-2)

a₁₄=-x-5+91x-26

a₁₄=90x-31

The total distance from the town of Acton to the town of Bridgeton is 30,078 yards.

To find the total distance in yards, we need to convert the given distance from miles and yards to yards and then add them together.

Given:

Distance in miles = 17 miles

Distance in yards = 158 yards

To convert miles to yards, we multiply the number of miles by the conversion factor of 1760 yards/mile:

17 miles * 1760 yards/mile = 29,920 yards

Then, we add the distance in yards:

29,920 yards + 158 yards = 30,078 yards

Therefore, the total distance from the town of Acton to the town of Bridgeton is 30,078 yards.

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Answer:

Both angles are 51°

Step-by-step explanation:

By the Vertical Angles Theorem, both angles are congruent.

Step 1: Set up equation

68 - x = 3x

Step 2: Solve for x

68 = 4x

x = 17

Step 3: Find angles

68 - 17 = 51°

Answer:

4x=68

x=17

51°

Step-by-step explanation:

Answer:

the answer is c

Step-by-step explanation:

yes sir

Using proportions, it is found that the garage is 14 millimeters wide in the drawing.

The rule of three is:

7 millimeters - 4 meters

x millimeters - 8 meters

Applying cross multiplication:

\(4x = 7(8)\)

\(x = \frac{56}{4}\)

\(x = 14\)

The garage is 14 millimeters wide in the drawing.

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11 is the mean, and 2.3 is the standard deviation. 2.3^2/34 is the variance of the sample mean.

a) The distribution of individual ages when children learn to walk, denoted as X, is X ~ N(11, 2.3^2), where N represents a normal distribution, 11 is the mean, and 2.3 is the standard deviation.

b) The distribution of the sample mean ages when 34 people are randomly selected and asked about the age they learned to walk, denoted as ¯X, is ¯X ~ N(11, 2.3^2/34), where N represents a normal distribution, 11 is the mean, and 2.3^2/34 is the variance of the sample mean.

c) To find the probability that one randomly selected person learned to walk between 10.9 and 11.2 months old, we can calculate the area under the normal distribution curve within that range. Using z-scores, we can standardize the values and then use a standard normal distribution table or calculator to find the corresponding probabilities. The z-scores can be calculated as follows:

z1 = (10.9 - 11) / 2.3

z2 = (11.2 - 11) / 2.3

Using the z-scores, we can find the probabilities associated with each z-value and calculate the probability that the person learned to walk between 10.9 and 11.2 months old.

d) To find the probability that the average age the 34 people learned to walk is between 10.9 and 11.2 months old, we can follow a similar process as in part c). We calculate the z-scores based on the mean and standard deviation of the sample mean distribution, which is ¯X ~ N(11, 2.3^2/34). Then we find the probabilities associated with those z-values.

e) Yes, the assumption that the distribution is normal is necessary for calculating probabilities using the normal distribution. If the distribution is not normal or approximately normal, the calculations may not be accurate.

f) To find the interquartile range (IQR) for the average first-time walking age for groups of 34 people, we need to calculate the 25th percentile (Q1) and 75th percentile (Q3) of the sample mean distribution. Once we have Q1 and Q3, the IQR can be calculated as Q3 - Q1.

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Answer:

944 cm²

Step-by-step explanation:

get the area of each side: 12*10+10*16+12*16= 472

2 sets of each side: 944

The perimeter of the regular polygon is 70 inches

The sides of the regular polygon is given as:

Side = 10 in

The regular polygon has 7 sides

So, the perimeter of the polygon is calculated as:

P = Side lengths * Number of sides

This gives

P = 10 inches * 7

Evaluate

P = 70 inches

Hence, the perimeter of the regular polygon is 70 inches

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Using the unitary method, we found that the equivalent amount of 750 US Dollars in Egyptian pounds is 1100 Egyptian pounds.

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit and then multiplying that value to determine the required value. Therefore, the goal of this method is to establish values in relation to a single unit. Always write the things that need to be calculated on the right side and the things that are known on the left side to simplify things. The unitary approach must be applied whenever we need to determine the ratio of one quantity to another.

Given,

 The amount of money  in US dollars = 750 US Dollars

The conversion to Egyptian pounds can be done using the unitary method.

1 usd = 18.48 Egyptian pounds

The unitary method can be used to convert single units to multiple units.

So,

750 usd = 750 * 18.48 = 1110 Egyptian pounds.

Therefore using the unitary method, we found that the equivalent amount of 750 US Dollars in Egyptian pounds is 1100 Egyptian pounds.

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Answer:

\(Total = 11\frac{1}{8}\ cups\)

Step-by-step explanation:

Given

See attachment for plot

Required

Total number of cups used

The number of dot on each dataset represent the number of student

So, to get the total number of cups, we simply add the product of the number of cups and the number of student for each data item

So, we have:

\(Total = \frac{1}{8} * 6 + \frac{1}{4} * 5 + \frac{3}{8} * 2 + \frac{1}{2}*0 + \frac{5}{8} * 4 + \frac{3}{4} * 2 + \frac{7}{8} * 5\)

\(Total = \frac{6}{8} + \frac{5}{4} + \frac{6}{8} + 0+ \frac{20}{8} + \frac{6}{4} + \frac{35}{8}\)

Solve

\(Total = \frac{6+10+6+0+20+12+35}{8}\)

\(Total = \frac{89}{8}\)

\(Total = 11\frac{1}{8}\ cups\)

Thus, the test for homogeneity follows the same procedures as the test for independence because the assumptions for performing the chi-square test for independence and chi-square test for homogeneity are the same.

The procedures for the chi-square test of homogeneity are the same as for the chi-square test of independence. The data is different for both tests. Tests of independence are used to determine whether there is a significant relationship between two categorical variables from the same population. One population is segmented based on the value of two variables. So there will be a column variable and a row variable.

The chi-square test of homogeneity of proportions can be used to compare population proportions from two or more independent samples, determining whether the frequency counts are distributed identically among different populations.

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Answer:

figure it out

Step-by-step explanation:

Answer: y=-(4y-12)/2 + 3; x=0 y=3

a) If two points on a line are A(-5,7) and B(-2,1), the rise -6, the run is of 3, and then the slope is of -2.

b) If two points on a line are A(10,-3) and B(12,9), the rise 12, the run is of 2, and then the slope is of 6.

c) If two points on a line are A(4,6) and B(8,-8), the rise -14, the run is of 4, and then the slope is of -3.5.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

As the slope represents the rate of change of the output relative to the input, it is calculated as the change in the output y divided by the change in the input x, that is, the rise divided by the run.

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The probability distribution of X is 0.5, 0.25, 0.25, and 0.125. Mean value ∑ X × P (X) = 1.875. Standard Deviation of X = 1.0533

a) For a fair coin,

P(H) = P(T) = 0.5

Outcome  X                            Probability

T                  1                                  0.5

HT              2                       0.5×0.5 = 0.25

HHT          3                       0.5×0.5×0.5 = 0.125

HHHT          4                           0.5×0.5×0.5×0.5 = 0.0625

HHHH          4                           0.5×0.5×0.5×0.5 = 0.0625

So, probability distribution of X is

X P(X)

1 0.5

2 0.25

3 0.125

4 0.0625+0.0625 = 0.125

b)

X     P(X)    X×P(X)         X2×P(X)

1     0.5     0.5          0.5

2     0.25      0.5               1

3     0.125    0.375         1.125

4     0.125       0.5            2

sum 1     E(X) = 1.87

c) Variance = E(X²) - E(X)²

= 4.625 - 1.875²

= 1.1094

Standard Deviation of X = √ Variance

= √1.1094

= 1.0533

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10.59 is the value of the given side b.

In our case, we know that side A has a length of 15 units and is opposite angle A, which measures 27 degrees.

Using the sine rule, we can write:

b/sin(27°) = 15/sin(40°)

To find the value of b, we can rearrange the equation:

b = (15 * sin(27°)) / sin(40°)

evaluate the trigonometric functions and calculate b:

b ≈ 10.59

Therefore, using the sine rule of the triangle, we find that the value of side b is approximately 10.59 units.

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Answer:

The answer is below

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Dilation is the enlargement or reduction in size of a figure. If a figure with point A(x, y) is dilated by a scale factor k, the new point is at A'(kx, ky). If k > 1, it is an enlargement and if k < 1, it is a reduction.

Since ΔMNO maps to ΔRST with a transformation (x, y) = (3x, 3y), this means that ΔRST is three times the size of ΔMNO, hence all the sides of ΔRST are three times that of ΔMNO.

A. If RT = 3, MO = 9. A True B False B.

This is false because RT = 3 * MO = 3(9) = 27

B. If RT = 12, MO = 4. A True B False

This is true because RT = 3 * MO = 3(4) = 12

C. If RT = 9, MO = 27. A True B False

This is false because RT = 3 * MO = 3(27) = 81

The following distributions has a mean that varies

II. The distribution of sample data

III. The sampling distribution of the sample mean

The correct answer is option v) II and III."

Here, we have,

In the context of statistical distributions:

I. The population distribution refers to the distribution of a specific variable within the entire population. The mean of the population distribution which is fixed and does not vary.

II. The distribution of sample data refers to the distribution of a variable within a specific sample. The mean of the sample data can vary from one sample to another.

III. The sampling distribution of the sample mean refers to the distribution of sample means taken from multiple samples of the same size from a population. The mean of the sampling distribution of the sample mean is equal to the population mean, but the individual sample means can vary from sample to sample.

Therefore, the mean varies in both the distribution of sample data (II) and the sampling distribution of the sample mean (III), but not in the population distribution (I).

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In Milgram's first study of obedience, the majority of teachers initially complied but refused to deliver more than slight levels of shock.

In Milgram's first study of obedience, participants were assigned the role of 'teacher' and were instructed to administer electric shocks to a 'learner' whenever they answered a question incorrectly. The shocks ranged from mild to severe, with the highest level labeled as 'XXX.' The learner was actually an actor, and no real shocks were administered.

The study found that the majority of teachers initially complied with the experimenter's orders and delivered shocks, but they refused to deliver more than slight levels of shock. This suggests that while they were willing to follow the instructions to some extent, they had moral reservations about causing significant harm to another person.

It is important to note that the study has been criticized for ethical concerns and the potential psychological harm it may have caused to participants. However, it remains a significant contribution to our understanding of obedience and the power of authority figures.

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The Boolean duality principle is a fundamental concept in Boolean algebra which states that any statement or expression in the algebra can be transformed into an equivalent form by interchanging the roles of AND and OR operators, as well as 0's and 1's.

The Boolean duality principle, also known as De Morgan's laws, is a fundamental concept in Boolean algebra that states that every Boolean expression remains valid if you perform the following steps:
1. Swap AND (⋅) operators with OR (+) operators and vice versa.
2. Replace all 1's with 0's and all 0's with 1's.
3. Complement (invert) all variables.
In other words, the Boolean duality principle allows us to derive a dual expression from an original Boolean expression by applying these transformations. This principle is useful in simplifying Boolean expressions and designing digital circuits.

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Answer:

Inconsistent

Step-by-step explanation:

A system of linear equations that has at least one solution is called consistent, whereas a system of linear equations that has no solutions is called inconsistent.

A system of linear equations that has no solution is a set of inconsistent equations.

The correct answer is an option (B)

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

"It is a set of equations for which we find a common solution."

"A system of equations is consistent if there is at least one set of values that satisfies each equation in the system."

"A system of equations is inconsistent if there is no solution to the given system of equations."

From the definition, we can see that the system of equations is inconsistent if a system of equations has no solution.

Therefore, A system of linear equations that has no solution is a set of inconsistent equations.

The correct answer is an option (B)

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The problem involves maximizing profit in a factory that produces products X and Y. Constraints include labor time, material availability, testing equipment usage, and minimum production requirements.

(a) To maximize profit, we need to define the objective function. Let x be the number of units of product X and y be the number of units of product Y produced. The objective function can be expressed as Z = 6x + 4.5y, representing the total profit.

The constraints can be formulated as follows:

1. Labor time constraint: 30x + 15y ≤ 60 hours (converted to minutes)

2. Material constraint: 2.5x + 2y ≤ 500 kilograms

3. Testing equipment constraint: Testing time for X ≥ 8 hours (converted to minutes)

4. Minimum production requirement: x ≥ 40 units of product X, y ≥ 80 units of product Y

5. Non-negativity constraint: x ≥ 0, y ≥ 0

(b) By graphing the system of inequalities on graph paper, the feasible region can be shaded. The feasible region represents the intersection of all the constraints.

(c) To find the weekly production that maximizes profit, we need to optimize the objective function within the feasible region. This can be done using linear programming techniques.

By solving the problem, we can determine the values of x and y that maximize the objective function Z. The expected maximum profit will be the value of Z at the optimal solution.

Note: The specific calculations and graphical representation will require numerical values and graphing tools to provide an accurate solution.

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Answer: 9 and 8?

Step-by-step explanation:

Answer:

A.) combinations of the hours he can work at the two jobs and earn at least $300

Step-by-step explanation:

Answer:

A.

Step-by-step explanation: