Two hunters shoot at a duck at the same time. One hunter usually hits on half of his shots; the other hits on one quarter of his hits. The probability that the duck will be hit is a. 6/8 b. 5/8 c. 3/8 d. 1/8 e. none of these

Step-by-step explanation:

x to the power of 1/2 means sqrt(x) (square root).

so, 9 to the power of 1/2 = sqrt(9) = 3.

therefore, we are looking for expressions that are also 3.

3 to the power of 1/2 = sqrt(3).

sqrt(3) × sqrt(3) = 3

this is correct

27 = 3×3×3

so, the cubic root would be 3 and correct, but the 6th root is incorrect.

27 to the power of 1/3 means the cubic root of 27, which is 3. but this is still multiplied by 3 to the power of 1/2 (sqrt(3)). so, the result is not 3 and therefore incorrect.

81 to the power of 1/2 = sqrt(81) = 9

9×9 = 81 and not 3. this is therefore incorrect.

729 to the power of 1/6 is the 6th root of 729, which is 3. this is therefore correct.

81 to the power of 1/3 means the cubic root of 81. but 81 is not a cubic number, and also multiplying this again with the cubic root of 81 is not 3. this is therefore incorrect.

81 to the power of 1/4 means the 4th root of 81. which is the square root of the square root.

the square root of 81 = 9. and the square root of 9 = 3.

3×3 = 9 and not 3. this is therefore incorrect.

The given dataset provides information on salaries and cost of living adjustments in various categories. The goal is to determine the adjustment formula for salaries based on the specified adjustments

To determine the adjustment formula, we need to analyze the correlation between the salary and each category's adjustment. We are interested in finding the formula where the adjusted salary is positively or negatively affected by the adjustments in the respective categories.

By examining the given dataset, we can calculate the correlation between the salary and each category's adjustment using statistical techniques such as regression analysis. The adjustments with a significant positive or negative correlation with the salary should be included in the formula.

After calculating the correlations and determining the significant adjustments, we can create the adjustment formula for the salary. The formula should include the adjustments in the respective categories that have a statistically significant impact on the salary.

Given the options provided, we need to select the formula that incorporates the significant adjustments and aligns with the specified adjustments in groceries, housing, utilities, transportation, and healthcare.

To make a final determination, it is necessary to analyze the correlations, check for statistical significance, and compare the options provided. The formula that accurately captures the relationship between the salary and the cost of living adjustments will provide the desired adjustment for the salaries in the given dataset.

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Linear pairs are the angles which formed a straight line

Look at your figure

Which angle pairs formed a straight line

Angle 1 and angle 5 formed a straight line

The sum of them = 180 degrees

Angles 1, 2, and 3 formed a straight line

The sum of them = 180 degrees

Angles 2, 3, and 4 formed a straight line

The sum of them is 180 degrees

Angles 4 and 5 formed a straight line

The sum of them = 180 degrees

So, the linear pairs are

Angle 1 and angle 5

Angle 4 and angle 5

Traditionally, a region is defined as a desert if it receives less than 25 centimeters of rain per year. This is based on the fact that deserts are characterized by arid climates, which means that they receive very little rainfall. This lack of water creates a harsh and unforgiving environment that is inhospitable to most forms of life. However, it's important to note that this definition is not set in stone and can vary depending on the context. Some regions with higher rainfall amounts may still be considered deserts due to other factors, such as high evaporation rates and low humidity levels.

The definition of a desert is closely tied to its arid climate, which is characterized by very little rainfall. This lack of water creates a harsh and inhospitable environment that is unsuitable for most forms of life. As a result, the threshold for what is considered a desert is typically set at a certain level of rainfall. Traditionally, this level has been set at less than 25 centimeters per year, although there is some variation depending on the context. Other factors, such as high evaporation rates and low humidity levels, can also contribute to a region being classified as a desert.

In conclusion, a region is traditionally defined as a desert if it receives less than 25 centimeters of rain per year. This definition is based on the fact that deserts are characterized by arid climates, which are created by a lack of water. However, it's important to note that this definition can vary depending on the context and other factors, such as high evaporation rates and low humidity levels, can also contribute to a region being classified as a desert.

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The estimation of the equation 1/6 + 5/6  is 1 (option C).

For rounding a fraction to the nearest whole number, use the "rounding half up" rule if necessary.

To estimate the solution for the equation 1/6 + 5/6, we can round each fraction to the nearest whole number.

The fraction 1/6 is closer to 0 than it is to 1, so we will round it to 0.

The fraction 5/6 is closer to 1 than it is to 0, so we will round it to 1.

Now we can estimate the solution for the equation as follows:

0 + 1 = 1

Therefore, the estimated solution for the equation 1/6 + 5/6 is 1.

The correct answer is C. 1.

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Answer:

48%

Step-by-step explanation: multiply 4 with the numerator and denominator

The two factors that would give a product of 9.1 are option D: 7 and 1.3.

To find the two factors that would give a product of 9.1, we need to multiply two numbers together and obtain the result of 9.1. Let's examine each option:

A. 0.7 and 1.3: When we multiply 0.7 by 1.3, the result is 0.91, not 9.1. Therefore, option A is incorrect.

B. 7 and 0.13: Multiplying 7 by 0.13 gives us 0.91, which is the desired product. Thus, option B is a valid solution.

C. 0.7 and 13: The product of 0.7 and 13 is 9.1, satisfying the condition. Hence, option C is also a correct answer.

D. 7 and 1.3: The multiplication of 7 and 1.3 yields 9.1, which matches the required product. Therefore, option D is valid.

E. 0.7 and 0.13: When we multiply 0.7 by 0.13, we obtain 0.091, not 9.1. Thus, option E is incorrect.

In conclusion, options B (7 and 0.13), C (0.7 and 13), and D (7 and 1.3) are all pairs of factors that would give a product of 9.1.

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Answer:

b=-a

Step-by-step explanation:

Becaude when b is positive a will be negative

And when b is negative a will be positive.

Statement Problem: What is the answer to;

Solution:

Add 6t to both sides of the equation;

Divide both sides by 7;

\(14-6t=t\)

Simplify the equation:

\(14+-6t=t\)

\(-6t+14=t\)

Subtract t from both sides:

\(-6t+14-t=t-t\)

\(-7t+14=0\)

Subtract 14 from both sides:

\(-7t+14-14=0-14\)

\(-7t=-14\)

Divide both sides by -7:

\(\frac{-7t}{-7} =\frac{-14}{-7}\)

\(\fbox{t=2}\)

Hope this helps!

Answer:

8

Step-by-step explanation:

24/3 = 8

By hiring the top 90% of applicants for a given job, one is increasing the likelihood of making a Type II error, also known as a "false negative."

In the context of hiring, a Type II error occurs when a qualified and suitable candidate is mistakenly rejected or not selected for the job.

By only hiring the top 90% of applicants, there is a possibility that some highly qualified candidates who fall within the remaining 10% are overlooked or excluded.

This approach prioritizes specificity over sensitivity.

It aims to minimize the chances of hiring unqualified or unsuitable candidates (Type I error) but may inadvertently lead to missing out on potentially excellent candidates (Type II error).

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Answer:

\(\boxed{\boxed{\pink{\bf \leadsto Option \ second\ is \ correct . }}} \)

A linear inequality is given to us . And we need to find the correct number line. So the given linear inequality is :-

\(\bf\implies 3x -2 \leq 2x + 1 \\\\\bf\implies 3x -2x \leq 2 + 1 \\\\\bf\implies x \leq 2 + 1 \\\\\bf\implies\boxed{\red{\bf x \leq 3 }}\)

This means that the value of x can be less than or equal to 3 . That is it means x ≤ 3. So , the required solution set will be ,

\(\boxed{\purple{\bf \{x | x \in \mathbb{R} , x \leq 3 \}}}\)

Answer:

second option is correct:)

Step-by-step explanation:

To adjust the length of the pendulum, we need to make it 9.7922 times longer than its current length.

To adjust the length of the pendulum, we can use the formula for the period of pendulum, which is T = 2π√(L/g), where T is the period (time it takes for one swing), L is the length of the pendulum, and g is the acceleration due to gravity.

Since we don't know the exact value of g, we can use the fact that the clock loses 27 s per day, which means it runs at a rate of (24 hours - 27 s)/(24 hours) = 0.9990625 times the actual time. This means that the period of the clock is 0.9990625 times the actual period.

Setting the period of the clock equal to 0.9990625 times the actual period, we get:
0.9990625 T = 2π√(L/g)
Squaring both sides and rearranging, we get:
L = (g/4π^2) (0.9990625 T)²
Substituting T = 24 hours = 86400 s and solving for L, we get:
L = (g/4π²) (0.9990625 x 86400 s)²
L = (g/4π²) (86338.13 s)²
L = 9.7922(g) m

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A = w × (w + 2) is the simplified algebraic expression for the area of the rectangle in terms of its width (w).

Let's denote the width of the rectangle as 'w'. According to the given information, the length of the rectangle is two more units than its width, so the length can be represented as 'w + 2'.

The formula for the area of a rectangle is given by multiplying its length and width. Therefore, the area of the rectangle (A) can be expressed as:

A = width × length

Substituting the values for width (w) and length (w + 2), the algebraic expression for the area of the rectangle becomes:

A = w × (w + 2)

This is the simplified algebraic expression for the area of the rectangle in terms of its width (w).

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relation between two slopes of two perpendicular line are equal.

The relationship between the slopes of two perpendicular lines is that the product of the slopes of the two lines is equal to -1.

Two geometric objects are perpendicular in elementary geometry if they intersect at a right angle. When two lines cross at a straight angle, they are said to be perpendicular.

The relationship between the slopes of two perpendicular lines is that the product of the slopes of the two lines is equal to -1. Therefore, assuming that there are two lines that are perpendicular to each other such that the slope of the two lines is m₁ and m₂. Therefore, we can write the relation as,

m₁ × m₂ = -1

Hence, the relationship between the slopes of two perpendicular lines is that the product of the slopes of the two lines is equal to -1.

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Answer:Linear Algebra Examples ... Linear Algebra. Solve by Substitution y=x+3 , y=2x-1 ... Eliminate the equal sides of each equation and combine. ... Subtract 1 1 from 8 8 . ... The solution to the system of equations can be represented as a point.

Step-by-step explanation:

a) The amplitude of the function is 4 feet.

b) The function that represents the situation is .

a) The amplitude (A), in feet, is equal to the difference between highest and lowest point (\(\left(y_{\max }, y_{\min }\right.\)), in feet, divided by 2. The period (T), in seconds, is the time taken by the bottle to complete one cycle. In this case, the period is the time between two maxima. Hence, we proceed to determine each variable:

Amplitude \(\left(y_{\max }=14 \mathrm{ft}, y_{\min }=6 \mathrm{ft}\right)\)

\(\begin{array}{l}A=\frac{14 f t-6 f t}{2} \\A=4 f t\end{array}\)

The amplitude of the function is 4 feet.

Period

The period of the function is 20 seconds.

b) The function that represents the situation is based on this model:

\(y(t)=y_{o}+A \cdot \sin \frac{2 \pi \cdot t}{T}\)  ........(1)

Where:

\(y_{o}\)- Average height of the bottle, in feet.

\(t\) - Time, in seconds.

\(y(t)\) - Current height, in feet.

If we know that \(A=4 \mathrm{ft}, y_{o}=10 \mathrm{ft} \text { and } T=20 \mathrm{~s}\) then the function that represents the situation is:

\(y(t)=10+4 \cdot \sin \frac{\pi \cdot t}{10}\) ......(2)

The function that represents the situation is \(y(t)=10+4 \cdot \sin \frac{\pi \cdot t}{10}\).

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Answer:

A ∆ with an exterior angle :116° & two interior angles 7x+6 & 4x

The value of angle 7x+6

we know that ,

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non adjacent interior angles of the triangle.

so,

\(7x + 6 + 4x= 116 \\ 11x + 6 = 116 \\ 11x = 116 - 6 \\ 11x = 110 \\ x = 110 \div 11 \\ x = 10\)

so ,the measure of green angle would be

\(7x + 6 \\ placing \: the \: value \: of \: x \: as \: 10 \\ 7 \times 10 + 6 \\ = 70 + 6 \\ = 76\)

To verify our answer ,the sum of the resultant value of green angle and 4x should be 116°(the exterior opposite angle)

so,

\(7x + 6 + 4x = 116 \\ 7 \times 10 + 6 + 4 \times 10 = 116 \\ 70 + 6 + 40 = 116 \\ 76 + 40= 116 \\ 116 = 116 \\ \\ hence,\: verified\)

Solution:

Note that:

Simplify the equation to find x.

Substitute the value of x into the measure of the green angle.

The measure of the green angle is 76°.

Answer:

0.45

Step-by-step explanation:

You divided 2.25 by 5

Answer:

Step-by-step explanation:

Given:

Percent value of the distance travelled:

Interior Angle is 180n = 375 - x in given question.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

To determine the number of sides in a convex polygon given the sum of all but one of its interior angles, we can use the formula:

Sum of interior angles = (n - 2) * 180 degrees,

where n represents the number of sides in the polygon.

In this case, the sum of all but one of the interior angles is missing, so we need to subtract one interior angle from the total sum before applying the formula.

Let's denote the missing interior angle as x. Therefore, the sum of all but one of the interior angles would be the total sum minus x.

Given that the stamina is 15, we can express the equation as:

(15 - x) = (n - 2) * 180

Simplifying the equation, we have:

15 - x = 180n - 360

Rearranging the terms:

180n = 15 - x + 360

180n = 375 - x

Now, we need more information or an equation to solve for the number of sides (n) or the missing interior angle (x).

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Answer:

I believe its the third one, its makes a symmetrical line so that's my guess

Step-by-step explanation:

The rest don't make a line

Answer:

8

Step-by-step explanation:

Usually we would have to use a formula to find the distance between the two points, however the x values of both coordinates are the same therefore we can find the distance between the two points by subtracting the smaller y value (-3 ) from the larger y value ( 5 )

Distance = 5 - ( - 3 )

* the two negative signs cancels out *

5 + 3 = 8

The distance between the two points is 8 units

Answer:

8

Step-by-step explanation:

\(\sqrt{(6-6)^{2}+(-3-5)^{2}}\)

=> \(\sqrt{64}\)

=> 8

In this investigation, the dependent variable is the number of fish in the stream and the independent variable is the amount of pollution.

Variables are symbols or names that are used to represent values in a mathematical or scientific investigation. They allow us to describe and analyze patterns and relationships in data.

There are two main types of variables:

1. Independent variables are variables that are manipulated or controlled in an experiment to determine their effect on the dependent variable. The independent variable is also referred to as the predictor variable or the explanatory variable.

2. Dependent variables are variables that are being measured in an experiment and are dependent on the independent variable. The dependent variable is also referred to as the response variable or the outcome variable. It is the variable that is being affected by the independent variable.

The dependent variable is dependent on the independent variable, as changes in the amount of pollution are expected to affect the number of fish in the stream. The goal of the investigation is to determine the relationship between the two variables and see how changes in the amount of pollution affect the number of fish in the stream.

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Answer:

y=-2 8/9

x=31 1/2

Step-by-step explanation:

x-4y=15 --> x=4y+15

8x-5y=42

8(4y+15)-5y = 42

32y +120 - 5y = 42

27y = -78

y=-2 8/9

x=31 1/2

Answer:

y=-0.5x+2 (-4,0) (0,2)   y=0.5x+6 (0,6)(12,0)

Step-by-step explanation:

Desmos

Answer:

y = -1, x =4

Step-by-step explanation:

3x-`13=-2x+7

x = 4

y=3(4)-13

y = -1