The ratio of juniors to seniors on the track team is 6:7. How many juniors are on the track team if there are 21 seniors on the team?


answer: 18

Answer:

B) x = √118 mi

Step-by-step explanation:

This is a right triangle, so we can the measure of x using the Pythagorean theorem, which is

a^2 + b^2 = c^2, where

Step 1:  Plug in x and √26 for a and b and 12 for c and simplify:

x^2 + (√26)^2 = 12^2

x^2 + 26 = 144

Step 2:  Subtract 26 from both sides to isolate x^2:

(x^2 + 26 = 144) - 26

x^2 = 118

Step 3:  Take the square root of both sides to isolate x:

√(x^2) = √118

x = √118 mi

A) The grant that will remain is; 3B + 6C - x = $75

B) The amount that each member needs to contribute is; 2M4W

C) The amount of money from the budget that remains to buy axles and gears is; $0

A) The grant will remain:

3B + 6C - x = $75

Where;

B = Beams

C = Channels

X = Balance which may or may not be Zero.

B) Corinne contributes

C + K + T = Cost of 2M4W

Where;

C = C's contribution

K = Kevin's contribution

T = Tomans contribution

2M4W is the cost of the Wheels and the motor controllers.

C) If all the Budget is spent on Sprockets, there will be $0 left to spend on Axles and Gears.

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The estimated crop yield from the simulation is 443 (option b).

To estimate the crop yield from the given random numbers, we need to assign a specific meaning to each random number. Let's assume that each random number represents the crop yield for a particular year.

Given random numbers: 37, 23, 92, 01, 69, 50, 72, 12, 46, 81

To find the estimated crop yield, we sum up all the random numbers:

37 + 23 + 92 + 01 + 69 + 50 + 72 + 12 + 46 + 81 = 443

Therefore, the estimated crop yield from the simulation is 443. The correct option is b.

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The cost of a whisky is GHC 0.85.

A linear equation is defined as an equation in which the highest power of the variable is always one.

Let x be the cost of brandy and y be the cost of a whisky.

As per the question, we have:

x = y + 0.10 (Brandy is 10p more expensive than whisky)

3x + 5y = 7.10 (A round of three Brandies and 5 whiskies cost GHC 7.10)

Substituting the value of x from the first equation into the second equation, we get:

3(y + 0.10) + 5y = 7.10

Expanding and simplifying, we get:

3y + 0.30 + 5y = 7.10

8y + 0.30 = 7.10

8y = 6.80

y = 0.85

Therefore, the cost of a whisky is GHC 0.85.

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The solution to the linear programming problem 0.3x₁ + 0.1x₂ ≤ 1.8 using the simplex method shows that the problem has optimal solutions.)

Convert the inequality into an equation by subtracting 1.8 from both sides:
0.3x₁ + 0.1x₂ - 1.8 ≤ 0

Introduce slack variables to convert the inequality into an equation:
0.3x₁ + 0.1x₂ + s₁ = 1.8

Set up the initial simplex tableau:

┌───┬───┬───┬───┬───┐
│   │ x₁ │ x₂ │ s₁ │  1│
├───┼───┼───┼───┼───┤
│  1│ 0.3│ 0.1│  1  │1.8│
└───┴───┴───┴───┴───┘
```

Select the pivot column. Choose the column with the most negative coefficient in the bottom row. In this case, it is the second column (x₂).

Select the pivot row. Divide the numbers in the rightmost column (1.8) by the corresponding numbers in the pivot column (0.1) and choose the smallest positive ratio. In this case, the smallest positive ratio is 1.8/0.1 = 18. So the pivot row is the first row.


The simplex method is an iterative procedure that systematically improves the solution to a linear programming problem. It starts with an initial feasible solution and continues to find a better feasible solution until an optimal solution is obtained. In each iteration, the simplex method selects a pivot column and a pivot row to perform row operations, which transform the current tableau into a new tableau with improved objective function values. The process continues until the objective function values cannot be further improved or the linear programming problem is unbounded.

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The correct answer is

0.3x1+0.1x2≤2.7→0.3x1+0.1x2≤1.8 Work Through The Simplex Method Step By Step. How The Solution Changes (I.E., LP Has Optimal

Answer: look up zodiac signs and if that dont work look up ailian signs

Step-by-step explanation:

Answer:

Answered

Step-by-step explanation:

Answer:

well you did the law of inverse on 6x you proved it by putting the one above it and switched the minus with a plus and divided 24 by 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

12 - 4 = 8 ⇒ sin x is shifted 8 units up.

k = ( 12 - 4 ) ÷ 2 = 4

The abscissa is ( \(\frac{x}{2}\) - \(\frac{\pi }{8}\) )

y = 4 sin ( \(\frac{x}{2}\) - \(\frac{\pi }{8}\) ) + 8

Possible cosine equation is

y = 4 cos ( \(\frac{x}{2}\) - \(\frac{\pi }{8}\) ) + 8

Answer:

I hope this works

Step-by-step explanation:

look at the picture

The probability that exactly 18 of the 25 smartphones selected are purchased with warranty is:  The probability that exactly 8 of the 25 smartphones selected are not purchased with warranty is: The probability that all 25 smartphones selected are purchased with warranty is:  

The probability that at most 15 of the 25 smartphones selected are purchased with warranty is: The probability that at least 14 of the 25 smartphones selected are purchased with warranty is: f) The probability that more than half (i.e. > 12) of the 25 smartphones selected are purchased with warranty is: 9) The probability that at least 14 but no more than 23 of the 25 smartphones selected are purchased with warranty is:

h) The probability that less than 12 or more than 19 of the 25 smartphones selected are purchased with warranty is: Part 2Mean = Standard Deviation =  Part 3To find the minimum sample size required to expect to find exactly 72 smartphones that are purchased with warranty, we use the following formula: N = [(Z * σ) / E]^2 where Z is the z-score corresponding to the desired level of confidence, σ is the standard deviation, and E is the maximum error of estimation. Using a 95% level of confidence, Z = 1.96.Using the calculated standard deviation of 2.91 and expecting to find exactly 72 smartphones, the maximum error of estimation is 0.5.N = [(1.96 * 2.91) / 0.5]^2N

= 337.11

Therefore, the minimum sample size required to expect to find exactly 72 smartphones that are purchased with warranty is 338.

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Answer:

Step-by-step explanation:

So there is this property,

Sum of two angle of triangle = exterior angle

So based on this we can form an algebraic equation (NOTE: this is an equilateral triangle so all the sides are 60°)

\(4x + 20 = 60 + 60 \\ 4x = 120 - 20 \\ 4x = 100 \\ x = \frac{100}{4} \\ x = 25\)

So it's option B.

Answer:

Sure with what ?

Step-by-step explanation:

Any value between 110 and 250 is within 2 standard deviations of the mean. In other words, any data point between 110 and 250 is considered within this range.

Within 2 standard deviations of the mean refers to the range that includes data points within two units of standard deviation from the mean. In this case, the mean is 180 and the standard deviation is 35.

To find the range within 2 standard deviations of the mean, we need to calculate the upper and lower bounds.

The upper bound can be found by adding 2 standard deviations (2 * 35 = 70) to the mean: 180 + 70 = 250.

The lower bound can be found by subtracting 2 standard deviations (2 * 35 = 70) from the mean: 180 - 70 = 110.

Therefore, any value between 110 and 250 is within 2 standard deviations of the mean. In other words, any data point between 110 and 250 is considered within this range.

It's important to note that this answer is specific to the given mean and standard deviation. If the mean and standard deviation were different, the range within 2 standard deviations would also be different.

Always calculate the upper and lower bounds based on the provided mean and standard deviation to determine the range within 2 standard deviations accurately.

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Answer:

x+35/5=2

x+35=10

x=-25

Answer:

\(\frac{1}{5} x\)+7=2, x=-25

\(\frac{m}{7} -7=3\), m= 105

\(\frac{3}{5} x+7=-20, x= -45\)

\(-\frac{2}{7} t+5=17, t=-42\)

4.9x+4.2=9.1, x=1

Explanation for last two:

\(-\frac{2}{7}t+5=17\)  

Step 1: Subtract 5 from both sides.

\(\frac{-2}{7} t+5-5=17-5\)

\(\frac{-2}{7} t=12\)

Step 2: Multiply both sides by 7/(-2).

\((\frac{7}{-2} )*( \frac{-2}{7}t )= (\frac{7}{-2} )*(12)\)

t=−42

4.9x+4.2=9.1

Step 1: Subtract 4.2 from both sides.

4.9x+4.2−4.2=9.1−4.2

4.9x=4.9

Step 2: Divide both sides by 4.9.

\(\frac{4.9x}{4.9} \frac{4.9}{4.9}\)

x=1

Answer:

X=4 , Y=3

Step-by-step explanation:

suppose,

2x-3y=-1...(I) and

y=x-1

or, x-y=1...(ii)

let's do: (ii)×2-(i)

2x-2y=2

2x-3y=-1

(-) (+) (+)

_______

y =3

let's put the value of y in (ii)

x-3=1

or, X=1+3

so, X=4

Answer:

Number 2

Step-by-step explanation:

Predation refers to a flow of energy between two organisms, predator and prey. In this interaction, the prey loses energy, and the predator gains energy

A) The new values for the mean and standard deviation, after adding 3 points to every score, would be a mean of 53 and a standard deviation of 10. B) The new values for the mean and standard deviation, after multiplying every score by 2, would be a mean of 100 and a standard deviation of 20.

A) Adding 3 points to every score in the population would result in a shift of the entire distribution. The new mean would be the original mean plus 3, so the new mean would be 50 + 3 = 53. The standard deviation would remain the same since it measures the spread of the data relative to the mean. Therefore, the new standard deviation would still be 10.

B) Multiplying every score in the population by 2 would affect both the mean and the standard deviation. The new mean would be the original mean multiplied by 2, so the new mean would be 50 * 2 = 100. The new standard deviation would also be multiplied by 2 since it measures the spread of the data relative to the mean. Therefore, the new standard deviation would be 10 * 2 = 20.

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The first step in developing a competency-model is to gather background information and analyze the existing standards within the workplace.

The first-step involves conducting a thorough examination of the organization's goals, strategies, and the specific job roles or positions for which the competency-model will be developed.

By gathering background information, organizations can understand the context in which the competency-model will be applied.

Analyzing existing standards within the workplace involves assessing the current performance expectations, competencies, and criteria used for evaluating employees in their respective roles.

The purpose of this step is to identify any gaps or areas for improvement in the existing standards and to ensure that the development of the competency model aligns with the organization's overall objectives.

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The first step in developing a competency model is conducting a job analysis.

developing a competency model is a systematic process that helps organizations define the key competencies needed for their employees. The first step in this process is conducting a job analysis.

A job analysis involves gathering information about the job, such as its purpose, tasks, responsibilities, and required qualifications. This information can be collected through methods like interviews, observations, and surveys. By analyzing the job, organizations can identify the critical competencies that are necessary for effective job performance.

These competencies can then be used to guide various HR processes, including recruitment, selection, training, and performance management. By aligning the competencies with job requirements, organizations can ensure that they have the right people with the right skills in the right positions.

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Let x be the hottest temperature.

Equation: x - (-35.67) = 148.98

So,

x - (-35.67) = 148.98

=> x + 35.67 = 148.98

=> x = 148.98 - 35.67

=> x = 113.31

Answer:

x = 2

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

x² + x² = (2\(\sqrt{2}\) )² , that is

2x² = 8 ( divide both sides by 2 )

x² = 4 ( take the square root of both sides )

x = \(\sqrt{4}\) = 2

Answer:

X= 5cm

Y=15cm

Step-by-step explanation:

Using by Pythagoras theorem .

The following relation hold for the dimensions of the triangle;

(Hypotenuse)²=(height)²+(base)²

=> H²=h²+b²

On first triangle the unknown X is the hypotenuse, therefore

X² = 3²+4²

=9+16

x² =25

X=√25

X=5cm

On the second triangle, the unknown Y is the height which is given by ;

h²=H²-b²

=>. Y²= 25²-20²

625-400

Y= √225

=15cm

The main bearing clearance (in mm) in a certain type of engine is a random variable with a probability density function (PDF).

A probability density function (PDF) is a mathematical function that describes the likelihood of a continuous random variable taking on a specific value within a given range. In this case, the main bearing clearance in a certain type of engine is a continuous random variable, and its PDF provides information about the probability distribution of the clearance values.

To fully describe the main bearing clearance's PDF, we would need the specific mathematical expression for the function. The PDF should satisfy two conditions: it must be non-negative for all values of the clearance, and the total area under the curve of the PDF must equal 1, as the probability of the clearance being within the entire possible range is 1 (100%).

Without the specific form of the PDF, we cannot provide further details, such as the mean, variance, or other properties of the main bearing clearance's probability distribution.

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Answer:

f(-5) = -43

Step-by-step explanation:

Step 1: Define

f(x) = -2x² + 7

f(-5) is x = -5

Step 2: Substitute and Evaluate

f(-5) = -2(-5)² + 7

f(-5) = -2(25) + 7

f(-5) = -50 + 7

f(-5) = -43

(a) The interval on which f is increasing: (0, ∞)

The interval on which f is decreasing: (0, 1)

(b) Local minimum: At x = 1, f(x) has a local minimum value of -1.

There is no local maximum value.

(c) Inflection point: At x ≈ 0.293, f(x) has an inflection point.

The function f(x) = x^2 - x - ln(x) is a quadratic function combined with a logarithmic function.

To find the interval on which f is increasing, we need to determine where the derivative of f(x) is positive. Taking the derivative of f(x), we get f'(x) = 2x - 1 - 1/x. Setting f'(x) > 0, we solve the inequality 2x - 1 - 1/x > 0. Simplifying it further, we obtain x > 1. Therefore, the interval on which f is increasing is (0, ∞).

To find the interval on which f is decreasing, we need to determine where the derivative of f(x) is negative. Solving the inequality 2x - 1 - 1/x < 0, we get 0 < x < 1. Thus, the interval on which f is decreasing is (0, 1).

The local minimum is found by locating the critical point where f'(x) changes from negative to positive. In this case, it occurs at x = 1. Evaluating f(1), we find that the local minimum value is -1.

There is no local maximum in this function since the derivative does not change from positive to negative.

The inflection point is the point where the concavity of the function changes. To find it, we need to determine where the second derivative of f(x) changes sign. Taking the second derivative, we get f''(x) = 2 + 1/x^2. Setting f''(x) = 0, we find x = 0. Taking the sign of f''(x) for values less than and greater than x = 0, we observe that the concavity changes at x ≈ 0.293. Therefore, this is the inflection point of the function.

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Answer:

The length of the side of the square is 26.87 yards

Step-by-step explanation:

The sides of the square and the diagonal will form an Isosceles right angled triangle

Let the length of the side be x

From Pythagoras’ theorem, the square of the side of the hypotenuse is equal to the sum of the squares of the two other sides

x^2 + x^2 = 38^2

2x^2 = 1,444

x^2 = 722

x = square root of 722

x = 26.87 yards

Answer:

B: 340

Step-by-step explanation:

We are told that her walls are 8 ft high.

Now, Two walls are 10 feet wide. Thus, area of the first two walls will be;

A1 = 2 × (10 × 8) = 160 sq.ft

Also, the other 2 walls are 15 feet wide.

Thus, Area of other two walls will be;

A2 = 2 × (15 × 8) = 240 sq.ft

We are told that the combined area of the 1 window and the 1 door in her room in 60 square feet.

This means that we will subtract 60 Sq.ft from the sum of the area of the 2 walls earlier calculated to get the total area to be painted.

Thus;

Area to be painted = 160 + 240 - 60 = 340 Sq.ft

Answer:

340

Step-by-step explanation:

2 × (10 × 8) = 160

2 × (15 × 8) = 240

160 + 240 - 60 = 340 square feet

Answer:

Hey there!

The domain is the range of all the x values.

Thus, the domain would be from -3 to 5 and would be written as -3≤x≤5.

Let me know if this helps :)

A z-score represents the number of standard deviations a data point is away from the mean. A score that is 2.5 standard deviations below the mean would have a z-score of -2.5 that is option D.

A z-score is a statistical measure that indicates how many standard deviations a particular data point is away from the mean of a distribution. It is calculated using the formula:

z = (x - μ) / σ

Where:

z is the z-score,

x is the value of the data point,

μ is the mean of the distribution, and

σ is the standard deviation of the distribution.

If a score is 2.5 standard deviations below the mean, it means that the value of x is 2.5 times the value of σ below the mean. In other words, it is located in the left tail of the distribution.

Since the z-score represents the number of standard deviations away from the mean, a score that is 2.5 standard deviations below the mean would have a z-score of -2.5. The negative sign indicates that the score is below the mean.

So, if we substitute the values into the z-score formula:

z = (x - μ) / σ

-2.5 = (x - μ) / σ

This equation represents the z-score being -2.5, indicating that the score is 2.5 standard deviations below the mean.

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Answer:

Option d

Step-by-step explanation:

The zeroes of given function can be obtained from graph when the graph intersects at x axis