Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of 1650 . What was the rate charged per hour by each mechanic if the sum of the two rates was 135 per hour?

The company should produce 5 units of Metakeb tractors, 8 units of Mewesson tractors, and 16 units of Metekem tractors in a month to use up all the available resources.

What is equations ?

An equation is a mathematical statement that shows that two expressions are equal. It consists of two expressions separated by an equals sign. For example, 3x + 5 = 14 is an equation that states that the sum of 3 times x and 5 is equal to 14.

Let x, y, and z be the number of units of Metakeb, Mewesson, and Metekem tractors produced, respectively.

Then we have the following system of equations based on the time required in each department:

\(1200x + 1800y + 3000z &\leq 63000 \\&&\text{(machining department)}\2400x + 1200y + 1200z &\leq 69600 \\&&\text{(assembly department)}\600x + 3000y &\leq 49800 \\&&\text{(inspection department)}\)

Converting the hours to minutes, we get:

Machining department: 1050 hours = 63,000 minutes

Assembly department: 1160 hours = 69,600 minutes

Inspection department: 830 hours = 49,800 minutes

We can rewrite the system of equations as follows:

\(20x + 30y + 50z &\leq 1050 &&\text{(machining department)}\\ \\10x + 5y + 5z &\leq 580 &&\text{(assembly department)}\\ \\x + 5y &\leq 83 &&\text{(inspection department)}\\ \\\)

To use Gaussian elimination to solve the system of equations, we first write the augmented matrix:

\(\begin{bmatrix}20 & 30 & 50 & | & 1050 \\10 & 5 & 5 & | & 580 \\1 & 5 & 0 & | & 83\end{bmatrix}\)

Performing row operations to obtain row echelon form:

\(\begin{bmatrix}20 & 30 & 50 & | & 1050 \\0 & -55 & -95 & | & -790 \\0 & 1 & -5/4 & | & -1.35\end{bmatrix}\)

Next, perform additional row operations to get the matrix in reduced row echelon form:

\(\begin{bmatrix}20 & 30 & 50 & | & 1050 \\0 & 1 & 19/55 & | & -14.36 \\0 & 0 & 367/55 & | & 105.36\end{bmatrix}\)

Finally, solve for the variables:

\(z &= \frac{105.36}{367/55} = 16 \\ \\y + \frac{19}{55}z &= 14.36 \\ \\y + \frac{19}{55}(16) &= 14.36 \\ \\y &= 8 \\ \\20x + 30y + 50z &= 1050 \\ \\20x + 30(8) + 50(16) &= 1050 \\ \\20x &= 90 \\ \\x &= 4.5\)

Therefore, the company should produce 4.5 units of Metakeb tractors, 8 units of Mewesson tractors, and 16 units of Metekem tractors in a month to use up all the available resources. Since we cannot produce fractional units, we can round up the values of x and y to obtain a feasible production plan of 5 units of Metakeb tractors and 8 units of Mewesson tractors.

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Considering the given graph,  we infer that while rolling a dice is random, the median values do exhibit some patterns that can be analyzed and used to make predictions about the expected values.

Looking at the median data from the graph, we can infer that option A is not true, as the median appears to be equally likely to fall between any two numbers from 1 to 6. However, we can also infer that option B is not entirely accurate.

While it is true that rolling a dice is random and each roll is independent, we can observe patterns in the median data.

For example, the median values are more likely to be closer to 3.5, which is the theoretical median value of a fair six-sided dice. This suggests that the more times the dice is rolled, the more likely the median value will approach the expected value.

We can also observe that the spread of the median values tends to decrease as the number of rolls increases, indicating that more rolls lead to more consistent results.

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Answer:

11.8125 cups of flour

Step-by-step explanation:

4 dozen = 48 cookies

126/48=2.625 batches of 48 cookies

2.625 x 4.5 = 11.8125 cups of flour

Answer:

0.8948 = 89.48% probability that the mean of a sample of 43 cars would differ from the population mean by less than 111 miles

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean number of miles between services is 4959 miles, with a standard deviation of 448 miles

This means that \(\mu = 4959, \sigma = 448\)

Sample of 43:

This means that \(n = 43, s = \frac{448}{\sqrt{43}}\)

What is the probability that the mean of a sample of 43 cars would differ from the population mean by less than 111 miles?

p-value of Z when X = 4959 + 111 = 5070 subtracted by the p-value of Z when X = 4959 - 111 = 4848, that is, probability the sample mean is between these two values.

X = 5070

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{5070 - 4959}{\frac{448}{\sqrt{43}}}\)

\(Z = 1.62\)

\(Z = 1.62\) has a p-value of 0.9474

X = 4848

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{4848 - 4959}{\frac{448}{\sqrt{43}}}\)

\(Z = -1.62\)

\(Z = -1.62\) has a p-value of 0.0526

0.9474 - 0.0526 = 0.8948

0.8948 = 89.48% probability that the mean of a sample of 43 cars would differ from the population mean by less than 111 miles

Answer:

Step-by-step explanation:

1 cat + 20 dogs + 60 men + 5 shark=​ 86

Answer:

86 baby sharks

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

ok so first you divide 40 hour by the 5 day work week it = 8 so take away the hours from the morning 8 take away 3 and that = 5 so there is your answer I'm not sure if I did it right but I think I did it just makes sense.

Answer:

6 represents the number of people among which the balls and jacks will be split.

4 represents the number of balls.

10 represents the number of jacks.

Step-by-step explanation:

This is the PLATO answer, hope it helps :)

Answer:

6

Step-by-step explanation:

Answer:

26) 70

27) 12.86 sec

28) 350 feet

Step-by-step explanation:

26) Given points A(0, 0) and B(16, 1120)

slope m = \(\frac{y_2-y_1}{x_2-x_1}\)

\(=\frac{1120-0}{16-0}\\ \\=\frac{1120}{16}\\ \\=70\)

slope = 70

27) eq of a line is :

y = mx + c

y = 70x + c

Since the line passes through A(0,0) substituting the points in the equation,

0 = 70(0) + c

⇒ c = 0

eq of line: y = 70x

given distance is 900 ft

y = distance and x = time

⇒ y = 900

sun in eq,

900 = 70x

⇒ x = 900/70

⇒ x = 12.86

28) time is 5 sec

⇒ x = 5

sub in eq

y = 70(5)

⇒ y = 350

Answer:

47 hours

Step-by-step explanation:

[606 -(12×40)]/(1½×12) =

(606-480)/(18) =

126/18 = 7

the total working hours = 40+7 = 47 hours

Answer:

47 hours

Step-by-step explanation:

First, we do 12 times 40, the answer we get is 480 dollars.

Then, we do 606 minus 480, the answer we get is 126.

Next, we do 126 divided by 18, and we get 7

Therefore, the total hours is 47 hours.

Answer:

316 ls the next term greater than 312. in the sequence you are adding 4 to the preceding term

Take 2 points

\(\\ \sf\longmapsto m=\dfrac{12-10}{2-1}=2\)

\(\\ \sf\longmapsto y=mx+b\)

\(\\ \sf\longmapsto 10=2(1)+b\)

\(\\ \sf\longmapsto b=8\)

Function:-

\(\\ \sf\longmapsto f(x)=2x+8\)

Answer:

25.13

Step-by-step explanation:

the inner circle is 1570.8 and the outer is 1595.93

Hope this helps! :)

Have a great weekend!! :)

Answer:

50.24 ft

Step-by-step explanation:

diameter = 250  -----  radius = 125  (radius of the smaller circle)

125+4 = 129  ( radius of the bigger circle)

129-125 = 4

4² x pi   =  16x 3.14  = 50.24

A) The type of triangles are congruent triangles

B) By the use of SAS Congruency Postulate

C) The distance across for the sink hole is: 52.2 ft

D) The perimeter of triangle ABC is: 172.2 feet.

A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.

B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.

C) We know that:

AB = ED = 52.2

AB is the distance across the sink hole. Thus, it is 52.2 feet

D) AB = 52.2

BC = 70

AC = 50

Thus:

Perimeter of triangle ABC = AB + BC + AC

Perimeter of triangle ABC = 52.2 + 70 + 50

Perimeter of triangle ABC = 122.2 + 50

Perimeter of triangle ABC = 172.2

The perimeter of triangle ABC is 172.2 feet.

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Answer:

Step-by-step expA) The type of triangles are congruent triangles

B) By the use of SAS Congruency Postulate

C) The distance across for the sink hole is: 52.2 ft

D) The perimeter of triangle ABC is: 172.2 feet.

How to solve congruent triangles?

A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.

B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.

C) We know that:

AB = ED = 52.2

AB is the distance across the sink hole. Thus, it is 52.2 feet

D) AB = 52.2

BC = 70

AC = 50

Thus:

Perimeter of triangle ABC = AB + BC + AC

Perimeter of triangle ABC = 52.2 + 70 + 50

Perimeter of triangle ABC = 122.2 + 50

Perimeter of triangle ABC = 172.2

The perimeter of triangle ABC is 172.2 feet.

lanation:

Answer:

Number of ways to chose rolls = 5,527,200

Step-by-step explanation:

Given:

Total number of films rolls (n) = 50

Selected number of films rolls (r) = 4

Find:

Number of ways to chose rolls.

Computation.

Permutation problem.

Number of ways to chose rolls = n! / (n! - r!)

Number of ways to chose rolls = 50! / (50! - 4!)

Number of ways to chose rolls = 50! / (46!)

Number of ways to chose rolls = 50 × 49 × 48 × 47

Number of ways to chose rolls = 5,527,200

84.13% of the printing jobs will be acceptable.

The new standard deviation required to achieve a minimum of 95% of jobs acceptable is 0.121.

The darkness of the print is measured quantitatively using an index. If the index is greater than or equal to 2.0 then the darkness is acceptable. Anything less than 2.0 means the print is too light and not acceptable. The machines print at an average darkness of 2.2 with a standard deviation of 0.20.

The mean of the darkness of the print is µ = 2.2 and the standard deviation is σ = 0.20.Therefore, the z-score can be calculated as; `z = (x - µ) / σ`.The index required for acceptable prints is 2.0. Thus, the percentage of prints that are acceptable can be calculated as follows;P(X ≥ 2.0) = P((X - µ)/σ ≥ (2.0 - 2.2) / 0.20)P(Z ≥ -1) = 1 - P(Z < -1)Using the standard normal table, P(Z < -1) = 0.1587P(Z ≥ -1) = 1 - 0.1587= 0.8413.

To find the new standard deviation, we can use the z-score formula.z = (x - µ) / σz = (2.0 - 2.2) / σz = -1Therefore, P(X ≥ 2.0) = 0.95P(Z ≥ -1) = 0.95P(Z < -1) = 0.05Using the standard normal table, the z-score value of -1.645 corresponds to a cumulative probability of 0.05. Hence,z = (2.0 - 2.2) / σ = -1.645σ = (2.0 - 2.2) / -1.645= 0.121.

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Answer:

Ameliorate retort, pertaining to preceding albeit contingent interrogate proximates subject to x = 12.

Step-by-step explanation:

Availing, exploiting, albeit maneuvering the Mathematic convention, Order of Operations (OO), the contiguous albeit proximate equation may ascertain as the preeminent imminent:

Groups: Not identified.

Exponents: Not identified, disparaging ₁.

Multiplication: Derived, pertaining to subtraction, 4 · (7/4x) = 4 · 21  7x = 84

Division: Derived, pertaining to multiplication, 7x = 84 ⇒ x = 12

Addition: Aggregate constants ⇒ 5/2x = 3/4x +21

Subtraction: Abate algebraic groups ⇒ 7/4x = 21

Check the picture below.

Bearing in mind that the angle is not changing all the wihle, namely is constant

\(tan(32^o)=\cfrac{y}{x}\implies x = \cfrac{y}{tan(32^o)}\implies x = \cfrac{1}{tan(32^o)}y \\\\\\ \stackrel{\textit{taking the derivative on bot sides}}{\cfrac{dx}{dt}=\cfrac{1}{tan(32^o)}\cfrac{dy}{dt}}\implies \cfrac{dx}{dt}=\cfrac{1}{tan(32^o)}200\implies \cfrac{dx}{dt}\approx 320.07~\frac{km}{hr}\)

Answer

D. The number of goals scored by each member of a soccer team.

Explanation

Discrete data is information that can only take certain values. That is discrete data are data that can be counted and involves integers. In order words, only a limited number of values can be assigned to the data.

Examples of discrete data are variables that are numeric, non-negative numbers, countable, and finite.

Therefore, an example of discrete data that is finite and countable is: D. The number of goals scored by each member of a soccer team.

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

8

Step-by-step explanation:

scince it has the lines that mean that it will always be positive.

Answer:

8

Step-by-step explanation:

Have a nice day!

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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I. The solution to the system of equations using Gaussian elimination is x = 1, y = -1, and z = 2.

II. For the LU-decomposition method, we need to have a square coefficient matrix, which is not the case in the given system. Therefore, we cannot directly apply the LU-decomposition method.

III. For this method to converge, the coefficient matrix must be diagonally dominant, which is not the case in the given system. Therefore, the Gauss-Jacobi method cannot be directly applied either.

IV. It requires the coefficient matrix to be diagonally dominant, which is not satisfied in the given system. Hence, the Gauss-Seidel method cannot be directly used.

I. Gaussian Elimination Method:

To solve the system of linear equations using Gaussian elimination, we perform row operations to reduce the system into upper triangular form. The augmented matrix for the given system is:

| 6 2 -1 | 4 |

| 1 5 1 | 3 |

| 2 1 4 |27 |

We can start by eliminating the coefficients below the first element in the first column. To do this, we multiply the first row by a suitable factor and subtract it from the second and third rows to eliminate the x coefficient below the first row. Then, we proceed to eliminate the x coefficient below the second row, and so on.

After performing the necessary row operations, we obtain the following reduced row-echelon form:

| 6 2 -1 | 4 |

| 0 4 2 | -1 |

| 0 0 3 | 6 |

From this form, we can easily back-substitute to find the values of x, y, and z. We have z = 2, y = -1, and x = 1.

II. LU-Decomposition Method:

LU-decomposition is a method that decomposes a square matrix into a product of two matrices, L and U, where L is lower triangular and U is upper triangular.

III. Gauss-Jacobi Method:

The Gauss-Jacobi method is an iterative numerical method to solve systems of linear equations.

IV. Gauss-Seidel Method:

Similar to the Gauss-Jacobi method, the Gauss-Seidel method is an iterative method for solving linear systems.

Therefore, out of the four methods mentioned, only the Gaussian elimination method can be used to solve the given system of linear equations.

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The probability of rolling a total of 9 is 1/9.

The probability of rolling a total of 10 is 1/12.

The probability of rolling a total of 11 is 1/18.

We have,

To calculate the probabilities of rolling specific totals with a pair of dice, we need to consider all possible combinations of numbers on each die.

Probability of rolling a total of 9:

There are four combinations that can result in a total of 9: (3, 6), (4, 5), (5, 4), and (6, 3).

Since each die has six sides, there are 6 * 6 = 36 equally likely outcomes when rolling two dice.

The probability of rolling a total of 9 is 4/36, which can be simplified to 1/9.

Probability of rolling a total of 10:

There are three combinations that can result in a total of 10: (4, 6), (5, 5), and (6, 4).

The probability of rolling a total of 10 is 3/36, which can be simplified to 1/12.

Probability of rolling a total of 11:

There are two combinations that can result in a total of 11: (5, 6) and (6, 5).

The probability of rolling a total of 11 is 2/36, which can be simplified to 1/18.

Thus,

The probability of rolling a total of 9 is 1/9.

The probability of rolling a total of 10 is 1/12.

The probability of rolling a total of 11 is 1/18.

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The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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Answer:

12

Step-by-step explanation:

13x-21=5x+75

8x=96

x=96/8=12

Answer:

x=12

Step-by-step explanation:

Since the 2 lines are parallel we can use the rules of transversals. These 2 angels are alternate side interior. This means that they are congruent and have the same measurement. Because they have the same measurement, we can set them equal to each other and solve for x.

13x-21 = 5x+75

13x = 5x+96

8x = 96

x=12

Answer:

Jet: 415 mph

Wind: 25 mph

Step-by-step explanation:

If x is the speed of the jet in still air, and y is the speed of the wind, then:

x + y = 1320 / 3 = 440

x − y = 1170 / 3 = 390

Solve the system of equations with substitution or elimination.  Using elimination:

2x = 830

x = 415

y = 25

The sequence of steps that translates figure W to figure X are -

Refer to the image attached. It shows figure W and figure X. We can write the sequence of steps for the given translation as -

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