The age distribution of a sample of part-time employees at Lloyd's Fast Food Emporium is: Ages Number 18 up to 23 6 23 up to 28 13 28 up to 33 33 33 up to 38 9 38 up to 43 4 What type of chart should be drawn to present this data

The graph of f(x) relate to its parent function by B. The parent function has been translated up.

Given that

f(x) = 3x +2 +4

When evaluated, we have

f(x) = 3x + 6

The parent function of the above is

f(x) = 3x

When f(x) = 3x is compared to f(x) = 3x + 6, we have

Difference = 6

This means that the parant function is translated up by 6 units

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Answer:

  (b)  x + 6

Step-by-step explanation:

You want the rule for the x-coordinate when the transformation is a right shift of 6 units.

A point that is the image of a pre-image point with x-coordinate x will be 6 units farther right of the y-axis than the pre-image point.

The x-coordinate measures how far right of the y-axis a point is. When that distance increases by 6 units, the x-coordinate increases by 6 units:

  x ⇒ x+6 . . . . . . the x-coordinate transformation rule

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If we restrict the domain of the function to the portion of the graph with a positive slope, the domain of the inverse function will be the range of the original function for values of x greater than 4, and its range will be all real numbers greater than or equal to 4.

The given function f(x) = |x – 4| + 6 is a piecewise function that contains an absolute value. The absolute value function has a V-shaped graph, and the slope of the graph changes at the point where the absolute value function changes sign. In this case, that point is x=4.

If we restrict the domain of f(x) to the portion of the graph with a positive slope, we are essentially considering the piece of the graph to the right of x=4. This means that x is greater than 4, or x>4.

The domain of the inverse function, f⁻¹(x), will be the range of the original function f(x) for values of x greater than 4. This is because the inverse function reflects the original function over the line y=x. So, if we restrict the domain of f(x) to values greater than 4, the reflected section of the graph will be the range of f⁻¹(x).

The range of f(x) is all real numbers greater than or equal to 6 because the absolute value function always produces a positive or zero value and when x is greater than or equal to 4, we add 6 to that value. The range of f⁻¹(x) will be all real numbers greater than or equal to 4, as this is the domain of the reflected section of the graph.

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The function g(x) is defined as follows:

D. g(x) = f(x) + 4.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The y-intercept for each function is given as follows:

Meaning that g(x) is a translation up four units of function f(x), hence it is defined as follows:

g(x) = f(x) + 4.

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Answer: D

Step-by-step explanation:

The function g(x) is defined as follows:

D. g(x) = f(x) + 4.

What is a translation?

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

Translation left a units: f(x + a).

Translation right a units: f(x - a).

Translation up a units: f(x) + a.

Translation down a units: f(x) - a.

The y-intercept for each function is given as follows:

f(x): y = -5.

g(x): y = -1.

Meaning that g(x) is a translation up four units of function f(x), hence it is defined as follows:

g(x) = f(x) + 4.

The answer choice which belongs in the green box and is the longest side of the triangle as required is; 11.06.

It follows from the task content that since the sum of angles in a triangle is; 180°, the missing angle measure is; 180 - 51 - 109° = 20°.

Consequently, it follows from the sine law that;

4 / sin 20° = x / sin 109°

x = 4 sin 109° / sin 20°

x = 11.06.

Ultimately, the number that belongs in the green box is; 11.06.

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Step-by-step explanation:

Given that

To find

So, according to the question

The division of subjects into units known as blocks was a component of the randomized block design. the random application of treatment to each block's components or subjects.

Here, we divide the 30 mature trees into 3, resulting in three blocks, each with 10 mature trees. Then, each of the three units receives a random application of citrus fertilizers A, B, and C.

So, All steps are needed to analyse which of three fertilizers (A, B, and C) is most effective for increasing the number of oranges on his trees.

Step 1: will divide his 30 trees based on sizes.

Step 2: will be give the results of fertilizer A,B and C on the small trees.

Step 3: will be give the results of fertilizer A,B and C on the medium and large sized trees.

Step 4: is the part of measurement, which is give the final results which of three fertilizers (A, B, and C) is most effective and farmer can use one of that fertilizer for increase their production.

Answer:

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Using the concept of simple interest and compound interest, the first equation is \(S = 200(1.1)^t\), while the second is S = 250 + 20t

c. It will take over 7 years for the accounts to be equal.

The similarities between simple interest and compound interest is that both deals with saving of money over certain period of time with a fixed rate. While the difference between both is that in compound interest, the interest are compounded while in simple interest it is not. This implies that compound interest is an exponential function while simple interest is a linear function.

Simple interest = P(1 + rt)

Compound interest = P(1 + r/n)ⁿˣ

To solve this, we can write equations;

For the first scenario;

\(S = 200(1.1)^t\)

For the second scenario;

S = 250 + 20t

NB: The first case is a compound interest while the second is a simple interest.

c. To determine when the two accounts will be equal;

\(250 + 20t = 200(1.1)^t\)

Solving for t;

t = 7.01 ≈ 7 years

Therefore, it will take over 7 years for the accounts to be equal

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Using the concept of perimeter of polygon, the perimeter of figure C is 27cm shorter than total perimeter of A and B

To solve this problem, we have to know the perimeter of the polygon C.

The perimeter of a polygon is the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The perimeter of the figures are;

Using the concept of perimeter of a rectangle;

a. figure A = 2(4 + 11) = 30cm

b. figure B = 2(8 + 4) = 24cm

c figure C = 11 + 4 + 8 + 4 = 27cm

Now, we can add A and B and then subtract c from it.

30 + 24 - 27 = 27cm

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Answer:

8x/5

Step-by-step explanation:

The value of the inverse of the equation is this: x³ -3 = y

To find the inverse of the equation follow these steps:

1. Replace H(x) with y.

y = (x + 4)³ - 1

2. Interchange the values of X and Y.

X = (y + 4)³ - 1

3. Find the cube root of both sides

x³ = y + 4  - 1

4. Find the value of y

x³ - 4 + 1 = y

x³ -3 = y

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Answer:

X, Process, Y

-2, 2(-2)-1, -5

-1, 2(-1)-1, -3

0, 2(0)-1, -1

1, 2(1)-1, 1

2, 2(2)-1, 3

X = -2, -1, 0, 1, 2

Y = -5, -3, -1, 1, 3

Step-by-step explanation:

Coordinates for the graph are (-2,-5), (-1,-3), (0,-1), (1,1), (2,3)

graph is the image attached

Solve for Y

2(-2)-1 = -5

2(-1)-1 = -3

2(0)-1 = -1

2(1)-1 = 1

2(2)-1 = 3

Hope this helps

Answer:

(x + 2)² + (y - 2)² = 3²

Step-by-step explanation:

Equation of a circle is (x - a)² + (y - b)² = r²,

where a is the x-coordinate of the centre of the circle, b is the y-coordinate of the centre of the circle, r is the circle's radius.

So, we have (x - -2)² + (y - 2)² = 3²

subtract a minus means we add.

(x + 2)² + (y - 2)² = 3²

A. Divide number of people in the shop by total people walking by:

66/125 = 0.528 = 0.53

B. Divide people who bought something by total people walking by:

21/125 = 0.168 = 0.17

d. 66 -21 = 45 people don’t buy anything.

45/66 = 0.68

Answer:

4710

Step-by-step explanation:

6580 minus

1870

4710

Then, the number of pounds of food that an adult manatee can eat in "d" days can be represented by the equation: p = r x d.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

Let's assume that an adult manatee eats "r" pounds of food per day on average. Then, the number of pounds of food that an adult manatee can eat in "d" days can be represented by the equation: p = r x d

Here, "p" represents the number of pounds of food, "r" represents the average amount of food consumed per day, and "d" represents the number of days. So, if we know the average amount of food consumed by an adult manatee per day, we can use this equation to calculate how much food it will eat in any given number of days.

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Step-by-step explanation:

y = 2x

if x = 1 y = 2(1) = 2

if x = 2 y = 2(2) =4

Answer:

Pls. correct me if I'm wrong.

I hope it helps.

If you don't like it just ignire it. okay.

By applying the rule of sin, it can be concluded that the length of the sides of the triangle is 15.48 cm, 39.68 cm, and 44.84 cm.

Triangle is a 2D shape that is bounded by three sides and has three vertices. The perimeter of a triangle is the sum of the lengths of the three sides of the triangle.

Perimeter = a + b + c, where a, b, and c are the sides of the triangle

One of the most important properties of a triangle is that the sum of the angles in a triangle equals 180°.

The rule of sin describes the ratio of the angles corresponding to the side lengths of the sine function.

a / sin A = b / sin B = c / sin C, where A, B, and C are the angles of the triangle

If the ratio of the angles is 1 : 3 : 5 and let x be the smallest angle, then we can put this information into the following equation:

Total angle = A + B + C

           180° = x + 3x + 5x

           180° = 9x

                x = 20°

Then we can calculate the other angles:

A = 20°

B = 3x = 3 * 20° = 60°

C = 5x = 5 * 20° = 100°

Now we put the value of A, B, and C into the rule of sin equation:

  a / sin A = b / sin B

a / sin 20° = b / sin 60°

   a / 0.34 = b / 0.87

              a = 0.34 * b / 0.87

              a = 0.39b

    c / sin C = b / sin B

c / sin 100° = b / sin 60°

    c / 0.98 = b / 0.87

               c = 0.98 * b / 0.87

               c = 1.13b

Then we go back to the perimeter formula:

perimeter = a + b + c

          100 = 0.39b + b + 1.13b

          100 = 2.52b

              b = 39.68 cm

Then we can calculate the length of the other sides, a and c:

a = 0.39b

  = 0.39 * 39.68

  = 15.48 cm

c = 1.13b

  = 1.13 * 39.68

  = 44.84 cm

Thus, the length of the sides of the triangle is 15.48 cm, 39.68 cm, and 44.84 cm.

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To check if x = 49 is a solution of an equation, you have to replace the x-value into the equation as follows:

x - 23 = 26

49 - 23 = 26

26 = 26

Given that there is the same number on both sides of the equal sign, then x = 49 is a solution to the equation

Answer:

0.4246

Step-by-step explanation:

Given data:

mean ( u ) = 15 inches

std ( б )= 6 inches

sample size( n ) = 46

ux = mean sample length

Determine the probability that x within 0.5 inch of the claimed population mean

ux = u = 15

бx = б/ √ 46 =  6 /√ 46 = 6 / 6.78 = 0.88

Hence the   P( 14.5 < x < 15.5 )

= P ( [14.5 - 15 / 0.88 ] < z < (15.5 - 15) / 0.88) )

= P ( -0.5682 < z <  0.5682 )

= P ( z < 0.5682 ) - P ( z < -0.5682 )

= 0.7123 - 0.2877  ( from Z table )

= 0.4246

Answer:

Equal to 1.

Step-by-step explanation:

3/1 x 1/3 = 3/3 = 1

1 = 1

a. The feasible region is a triangle in the x1-x2 plane with vertices at (0,0), (1,0), and (2/3,1/3).

b. The slack variables x3 and x4 are zero on the boundaries of the feasible region.

c. The maximum value of x is 2/3 and is attained at x1 = 2/3 and x2 = 1/3.

d. The requirement space is the region satisfying the given constraints, and feasibility means that a solution exists within this region.

For a. To sketch the feasible region, we first find the boundary curves of the region by setting each constraint equal to zero. The resulting curves are x2 = 0, -x1 + 3x2 = 0, and -3x1 + 2x2 = 0. The feasible region is the area in the x1-x2 plane that satisfies all the constraints, which is a triangle with vertices at (0,0), (1,0), and (2/3,1/3).

For b. The slack variables x3 and x4 are introduced to convert the inequality constraints to equations. They represent the amount by which the left-hand side of each constraint is less than the right-hand side. When a slack variable is zero, it means that the corresponding inequality is an equality and the point lies on the boundary of the feasible region. In this case, x3 = 0 corresponds to the line x2 = 0, and x4 = 0 corresponds to the line -x1 + 3x2 = 0.

For c. To solve the problem geometrically, we find the corner points of the feasible region and evaluate the objective function at each point. The maximum value of x occurs at the point (2/3,1/3), where x = 2/3.

For d. The requirement space is the region of the x1-x2 plane that satisfies all the constraints. Feasibility means that there exists a solution to the problem within this region. The feasible region is a subset of the requirement space and is defined by the intersection of the constraint curves.

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Answer:

B

Step-by-step explanation:

So, a function is increasing when the y-values increase with the x-values. Ok?

So, A is constant, because while the x-values are increasing, the y-values aren't changing at all.

B is increasing because both the x and y values are increasing.

C is once again constant, for the same reason as A.

D is decreasing because as x-values increase, y-value decrease.

Answer:

I agree that’s your answer

Step-by-step explanation:

Answer: 24n + 18

Step-by-step explanation:

     To simplify, we will distribute and combine like terms using the Order of Operations.

  Given:

3n + 3(6 + 7n)

  Distribute:

3n + 18 + 21n

  Combine like terms:

24n + 18

Answer:

The absolute first thing you want to simplify when dealing with a problem is to ALWAYS start at the parentheses.
SO, this is what you'll have to do

We'll only be focusing the parenthetical part of the problem so lets put it here:
3(6 + 7n)

This is another way of saying: What is 3 times (6+7n)?

This is how:

3 x 6 = 18
3 x 7n = 21n

so now we have the simplified version of:

3n+18+21n

OR

24n+18

Your Welcome!

Step-by-step explanation:

The inequality is used to find the domain of the given function is

5x-5 ≥ 0

A function is a relation from a set of inputs to a set of possible outputs, where each input is related to exactly one output.

Given is function y = √(5x-5)+1, we have to find which inequality can be used to find the domain.

Since, the function is a square root function.

We know that,

The square root function is defined only for the positive values, including 0. i.e. the expression inside the square root must be greater than or equal to 0.

The expression inside the square root is (5x-5) so that must be greater than or equal to 0 which can be written as :

5x-5 ≥ 0

Hence, the inequality is used to find the domain of the given function is 5x-5 ≥ 0

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The probabilities are

i. P(male) ≈ 0.503

ii. P(hybrid) ≈ 0.324

iii. P(hybrid|male) ≈ 0.208

iv. P(hybrid|female) ≈ 0.441

v. P(female|hybrid) ≈ 0.677

P(hybrid|male) and P(male|hybrid) are not equal because the sample may not be representative of the entire population.

What is probability?

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event.

a.

i. P(male) = number of males in the sample / total number in the sample = 154 / 306 ≈ 0.503

ii. P(hybrid) = number of hybrid cars purchased / total number in the sample = 99 / 306 ≈ 0.324

iii. P(hybrid|male) = number of males who purchased a hybrid / total number of males in the sample = 32 / 154 ≈ 0.208

iv. P(hybrid|female) = number of females who purchased a hybrid / total number of females in the sample = 67 / 152 ≈ 0.441

v. P(female|hybrid) = number of females who purchased a hybrid / total number of people who purchased a hybrid = 67 / 99 ≈ 0.677

b.

i. P(male) represents the probability of randomly selecting a male from the sample of 306 people who purchased a Honda Civic.

ii. P(hybrid) represents the probability of randomly selecting a car from the sample that has a hybrid engine.

iii. P(hybrid|male) represents the probability of selecting a hybrid car given that the person selected is male.

iv. P(hybrid|female) represents the probability of selecting a hybrid car given that the person selected is female.

v. P(female|hybrid) represents the probability of selecting a female given that the car selected has a hybrid engine.

c. No, P(hybrid|male) and P(male|hybrid) are not equal. P(hybrid|male) represents the probability of selecting a hybrid car given that the person selected is male, while P(male|hybrid) represents the probability of selecting a male given that the car selected has a hybrid engine. These probabilities are different because the sample is not necessarily representative of the entire population.

Hence, the probabilities are

i. P(male) ≈ 0.503

ii. P(hybrid) ≈ 0.324

iii. P(hybrid|male) ≈ 0.208

iv. P(hybrid|female) ≈ 0.441

v. P(female|hybrid) ≈ 0.677

P(hybrid|male) and P(male|hybrid) are not equal because the sample may not be representative of the entire population.

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To find the values of ab, bc, and ca, we simply need to multiply the corresponding variables.

ab = 2 * 3 = 6

bc = 3 * 4 = 12

ca = 4 * 2 = 8

Therefore, ab = 6, bc = 12, and ca = 8.

Answer:

angle XYZ = 118 degrees

Step-by-step explanation:

all interior angles of ma quadrilateral add up to 360 degrees.

W = 90 degrees

90 + 84 + (2x + 118) + (2x + 68) = 360

simplify:

4x = 0

x = 0

angle XYZ = 118 degrees

See the picture below for a way to construct a right triangle that makes that piece the longest side of the triangle your line segment.

With that setup, you can use they Pythagorean Theorem.

    \(7^2 + 6^2 = c^2\)

And then solve that for c, keeping in mind c must be positive.

   \(\begin{aligned}49 + 36 &= c^2\\85 &= c^2\\\sqrt{85} &= c\end{aligned}\)

If you want to use the distance formula, that is just the Pythagorean theorem solved for c:

    \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Applying that to your situation

   \(d = \sqrt{(5-(-2))^2+(-5-1)^2} = \sqrt{(7)^2+(-6)^2} = \sqrt{49+36} = \sqrt{85}\)

Answer:

y \(\leq\) -7

Step-by-step explanation:

6x + 2y \(\leq\) -8   Subtract 6x from both sides

6x - 6x + 2y \(\leq\) -8 - 6

2y \(\leq\) -14  Divide both sides by 2

y \(\leq\) -7