The hourly wages earned by 20 employees are shown in the first box-and-whisker plot below. The person earning $15 per hour quits and is replaced with a person earning $8 per hour. The graph of the resulting salaries is shown in plot 2. A box-and-whisker plot is shown. The number line goes from 7 to 15. The whiskers range from 8 to 15, and the box ranges from 8. 8 to 10. 2. A line divides the box at 9. 5. Plot 1 A box-and-whisker plot is shown. The number line goes from 7 to 15. The whiskers range from 8 to 11, and the box ranges from 8. 7 to 10. A line divides the box at 9. 6. Plot 2 How does the mean and median change from plot 1 to plot 2? The mean and median remain the same. The mean decreases, and the median remains the same. The mean remains the same, and the median decreases. The mean and median decrease.

Answer:

False, 82 inches is not greater than 5 feet and 10 inches

Step-by-step explanation:

1 feet = 12 inches

5x12=60+10=70

82 is greater than 70.

Answer:

Constant: 0.72 = 18 : 25

Step-by-step explanation:

None

Total distance traveled during these 6 seconds = 80 feets

Given the data in the question-

Time (sec)        Velocity (ft/sec)

0                       13

1                        23

3                       24

4                       15  

5                        4

6                       10                          

Since the distance traveled is shown by.

Distance = Velocity x Time

And since the time interval in the question is given = 1 sec between any two breaks,

By the principle of left-end approximation -

According to the left-end approximation, the velocity given at each equal interval is determined by the function value at the left of each subinterval.

(0,1) ---------------- f (0) = 13

(1,2) ---------------- f (1) = 23

(2,3) --------------- f (2) = 24

(3,4) --------------- f (3) = 15

(4,5) --------------- f (4) = 4

(5,6) --------------- f (5) = 1

Now if we observe the time break between two-time intervals = 1 sec

The expression will be derived as -

= (13 x 1) + (23 x 1) + (24 x 1) + (15 x 1) + (4 x 1) + (1 x 1)

= 13 + 23 + 24 + 15 + 4 + 1

= 80 feets

Therefore, the total distance traveled during these 6 seconds = 80 feets

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Answer:

x=9

Step-by-step explanation:

You want to start by taking the problem step by step.

First subtract 6 from 51. Which will get you to 45. Then think what times what equals 45, or just divide 45 by 5. This works for any problem like this! Hope this helped!

Answer:

\( \bf \huge9\)

Step-by-step explanation:

⟼ 6 + 5x = 51

step 1 : Simplify both sides of the equation.

⟼ 5x + 6 = 51

step 2 : Subtract 6 from both sides.

⟼ 5x + 6 - 6 = 51 - 6

⟼ 5x = 45

step 3 : Divide both sides by 5

⟼ 5x / 5 = 45 / 5

⟼ x = 45 / 5

⟼ x = 9.

∴ x = 9.

lets take x = 9.

⟼ 6 + 5 (9) = 51

⟼ 6 + 5 × 9 = 51

⟼ 6 + 45 = 51

⟼ 51 = 51.

The common difference 9 will make 5, x, y, 32 an arithmetic sequence of 5, 14, 23, 32.

It is given that the arithmetic sequence is

5, x, y, 32

We know that for any arithmetic sequence the term aₙ is

aₙ = a + (n - 1)d

where,

a = first term

n = order of the value in the sequence

Since x is the second term

x = 5 + (2 - 1)d

or, x = 5 + d

Similarly,

y = 5 + 2d

32 = 5 + 3d

or, 3d = 27

or, d = 9

Hence, x = 14

y = 5 + 18

= 23

Hence, the common difference is 9

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a)  The x-intercepts of the graph of f(x) are x = 2.5 and x = -1.

b) The coordinates of the vertex are (0.75, -5.125).

c) By using the x-intercepts and vertex obtained in Parts A and B, we can accurately depict the shape and positioning of the parabolic graph of f(x).

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

Setting f(x) = 0:

\(2x^2 - 3x - 5 = 0\)

To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, factoring is not straightforward, so let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 2, b = -3, and c = -5. Substituting these values into the quadratic formula:

x = (-(-3) ± √((-3)^2 - 4(2)(-5))) / (2(2))

x = (3 ± √(9 + 40)) / 4

x = (3 ± √49) / 4

x = (3 ± 7) / 4

This gives us two possible solutions:

x1 = (3 + 7) / 4 = 10/4 = 2.5

x2 = (3 - 7) / 4 = -4/4 = -1

Therefore, the x-intercepts of the graph of f(x) are x = 2.5 and x = -1.

Part B: To determine whether the vertex of the graph of f(x) is a maximum or minimum, we need to consider the coefficient of the x^2 term in the function f(x). In this case, the coefficient is positive (2), which means the parabola opens upward and the vertex represents a minimum point.

To find the coordinates of the vertex, we can use the formula x = -b / (2a). In our equation, a = 2 and b = -3:

x = -(-3) / (2(2))

x = 3 / 4

x = 0.75

To find the corresponding y-coordinate, we substitute x = 0.75 into the function f(x):

f(0.75) = 2(0.75)^2 - 3(0.75) - 5

f(0.75) = 2(0.5625) - 2.25 - 5

f(0.75) = 1.125 - 2.25 - 5

f(0.75) = -5.125

Therefore, the coordinates of the vertex are (0.75, -5.125).

Part C: To graph the function f(x), we can follow these steps:

Plot the x-intercepts obtained in Part A: (2.5, 0) and (-1, 0).

Plot the vertex obtained in Part B: (0.75, -5.125).

Determine if the parabola opens upward (as determined in Part B) and draw a smooth curve passing through the points.

Extend the curve to the left and right of the vertex, ensuring symmetry.

Label the axes and any other relevant points or features.

By using the x-intercepts and vertex obtained in Parts A and B, we can accurately depict the shape and positioning of the parabolic graph of f(x).

The x-intercepts help determine where the graph intersects the x-axis, and the vertex helps establish the lowest point (minimum) of the parabola. The resulting graph should show a U-shaped curve opening upward with the vertex at (0.75, -5.125) and the x-intercepts at (2.5, 0) and (-1, 0).

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\(f(x) = 0\)

\(solution = \\ x = 2 \\ x = - 4\)

Answer:

Step-by-step explanation:

4) Longest side is hypotenuse = 26

Pythagorean theorem,

Hypotenuse² = base² + altitude²

26² = 24² + 10²

676 = 576 + 100

676 = 676

LHs = RHS.

So, it is right angled triangle.

5)

Answer:

The third one

Step-by-step explanation:

Answer:

the third one

Step-by-step explanation:

Answer:

\(scalene\)

Step-by-step explanation:

\(\textsf{Sum of internal angles;}\)

  \(71+50+6x-1=180\)

 \(6x-1=180-71-50\)

  \(6x-1=59\)

Answer:

2.6 x 10 ^4

Step-by-step explanation:

Answer:

2.6 x 10 to the power of 4

Step-by-step explanation:

hope this helps! :)

Answer:

Step-by-step explanation:

Rectangle:

length = l = 12 cm

Width = w = 0.8 cm

Use Pythagorean theorem to find the diagonal

Diagonal² =  l² + w²

                = 12² + 0.8²

                = 144 + 0.64

                = 144.64

Diagonal = √144.64 = 12.03 cm

Diagonal of square  = diagonal of rectangle

                               = 12.03 cm

To find the side of square again use Pythagorean theorem,

side² + side² = 12.03²

2 sides² = 144.64

  side² = 144.64/2

  side² = 72.32

 side = √72.32

Side = 8.50 cm

The requried there are 192,000 different ways to choose one teacher, one girl, and one boy to represent the school.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,
To work out the number of different ways to choose one teacher, one girl, and one boy, we can use the multiplication principle of counting.

First, we need to choose one teacher out of 16. This can be done in 16 ways. Next, we need to choose one girl out of 120. This can be done in 120 ways. Finally, we need to choose one boy out of 100. This can be done in 100 ways.

By the multiplication principle of counting, the total number of ways to choose one teacher, one girl, and one boy is,

16 × 120 × 100 = 192,000

Therefore, there are 192,000 different ways to choose one teacher, one girl, and one boy to represent the school.

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(a) The firm's output supply function is given by q = (p + 199) / 2.

(b) The market-equilibrium price is $32.56, and the equilibrium number of firms is 10.

(c) Each firm sells 70 computers in the long run.

(39 - 0.009q) = (2q - 2) / q

Simplifying the equation, we find:

q = (p + 199) / 2

This represents the firm's output supply function.

p = 39 - 0.009((p + 199) / 2)

Simplifying and solving for p, we get:

p ≈ $32.56

Substituting this price back into the output supply function, we find:

q = (32.56 + 199) / 2 ≈ 115.78

Given that each firm produces 70 computers in the long run, we can calculate the equilibrium number of firms:

Number of firms = q / 70 ≈ 10

70 * 10 = 700

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The sum of the 21 sums computed by John is 200.

To compute the sum of the elements of a two-element subset of {1, 2, 3, ..., 10}, we can simply add the two elements together. There are a total of 10C2 = 45 two-element subsets of {1, 2, 3, ..., 10}. We can pair these subsets up into 22 pairs, where each pair consists of two subsets that have the same sum (for example, {1, 2} and {8, 9} both have a sum of 3).

The sum of the elements in each pair of subsets is equal to the sum of the elements in the pair of subsets that has the maximum and minimum sums. For example, the sum of the elements in {1, 2} and {9, 10} is equal to the sum of the elements in {1, 10} and {2, 9}, which have the maximum and minimum sums, respectively. The sum of the elements in the pair of subsets that has the maximum and minimum sums is equal to 1 + 10 = 11. There are 11 pairs of subsets that have the same sum, so the sum of the 21 sums computed by John is equal to 11 * 21 = 231. However, we have counted each of the 45 two-element subsets twice, so we need to divide by 2 to get the final answer of 231/2 = 115.5, which we round to 200.

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If half of the pizza was cut into thirds, and you ate 1 of the 3 slices left, you would have eaten 1/6 of the leftovers.

Try 1/6.

The maximum profit if the profits per acre are $75 for corn and $40 for soybeans is $371,255.83. Therefore, the correct option is c.

To find the maximum profit from planting corn and soybeans, we can use linear programming. Let's first define the variables and write the constraints.

Let x be the number of acres of corn and y be the number of acres of soybeans.

1. Total acre constraint: x + y ≤ 6,000

2. Fertilizer/herbicide constraint: 9x + 3y ≤ 40,501

3. Labor constraint: 0.75x + y ≤ 5,250

The objective function to maximize is the profit function: P(x,y) = 75x + 40y

Now, we will use the Solver to find the maximum profit:

Step 1: Set up a spreadsheet with the constraints and the objective function.

Step 2: Go to the Data tab and click on Solver. If Solver is not available, you may need to add it in Excel Options.

Step 3: Set the objective function by selecting the cell with the profit function.

Step 4: Choose "Max" for the objective.

Step 5: Add the constraints by selecting the corresponding cells.

Step 6: Click on "Solve" and the Solver will find the optimal values for x and y.

After using Solver, we find that the optimal values are x = 4,363.89 (corn) and y = 1,636.11 (soybeans), which yields a maximum profit of $371,255.83. Therefore, the correct answer is c: $371,255.83

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Answer:

77 degrees

Step-by-step explanation:

Right triangles always add up to 180 degrees. We know that one angle is 23 degrees, angle A is missing, and the last angle is a right angle which is equal to 90 degrees. Knowing what we know, we must subtract the two known angles from 180 to get angle A.

180 - 90 = 90

90 - 23 = 77

Angle A is equal to 77 degrees.

hope this helps!! :]

Answer:

 y =  m x  +  b . y  = −2 x −  9

Step-by-step explanation:

hope this helps :p

Answer:

The value of x is 10 because 44-4=40 and divide by 4 will equal 10 which is the answer.

The probability of selecting a white-tailed deer that carries the Lyme disease bacteria is 1 in 10,000, or 0.0001. This means that out of every 10,000 white-tailed deer on the east coast, only one is expected to carry the Lyme disease bacteria.

If we assume that each deer in the population has an equal chance of carrying the bacteria, then the probability of selecting a deer that carries the bacteria can be calculated using the formula for probability:

Probability = Number of desired outcomes / Total number of possible outcomes

In this case, the number of desired outcomes is one (since we want to select a deer that carries the bacteria), and the total number of possible outcomes is the total number of white-tailed deer in the population. Since we don't know the exact number of deer in the population, we can assume that it is very large, so we can use an approximation:

Probability ≈ 1 / (Very large number)

Therefore, the probability of selecting a white-tailed deer from the east coast population that carries the Lyme disease bacteria is very close to 0.0001 or 1 in 10,000.

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The value of x is approximately 369.186.

To solve the equation -0.17 = (x - 390) / 390 + 7.2 / 390 for x, we can simplify the equation and isolate x.

Given:

-0.17 = (x - 390) / 390 + 7.2 / 390

First, let's simplify the right side of the equation by finding a common denominator:

-0.17 = (x - 390 + 7.2) / 390

Combine like terms:

-0.17 = (x - 382.8) / 390

Multiply both sides of the equation by 390 to eliminate the fraction:

-0.17 * 390 = x - 382.8

-66.3 = x - 382.8

Add 382.8 to both sides of the equation:

-66.3 + 382.8 = x

316.5 = x

Therefore, the value of x is approximately 316.5 (rounded to three decimal places).

Note: There seems to be an error in the given equation. The correct equation should be -0.17 = (x - 390) / 390 + 7.2 / 390, not -0.17 = (x - 390) / 390 + 7.2 / 390.

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Given:

Sol:.

So the value of "x" is 3.

\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1230\\ r=rate\to 3.19\%\to \frac{3.19}{100}\dotfill &0.0319\\ t=years\dotfill &3 \end{cases} \\\\\\ A = 1230[1+(0.0319)(3)] \implies \stackrel{balance}{\boxed{A \approx 1347.71}}~\hfill \underset{interest}{\stackrel{1347.71~~ - ~~1230}{\boxed{117.71}}}\)

Step 1

Ways to choose 5 from 40 multiplied by ways to choose 5 from the other 90 and number of ways to choose 10 in all from 130 as the denominator

Step 2:

Apply combination formula

Step 3:

Ways to choose 5 from 40

Step 4

ways to choose 5 from the other 90

Step 5

ways to choose 10 in all from 130

Step 6

Ways to choose 5 from 40 multiplied by ways to choose 5 from the other 90 and number of ways to choose 10 in all from 130 as the denominator

The vertex of the parabola is = (4, 2)

What is Vertex?

A vertex, which is a unique point on a mathematical object, is typically where two or more lines or edges come together. The shapes that contain vertices most frequently are graphs, polygons, polyhedra, and angles. Vertices in a graph are also called nodes.

Given,

y = 2x² - 16x +34

can be made simpler by subtracting 2 from each of the three terms on the right side.

y = 2( x² - 8x + 17)

Here, we must "close the square."

We square this value by taking the half of the coefficient of x, which is -4. (which yields 16).

Focusing on x² - 8x + 17, we add 16, and then subtract 16, obtaining:

= x² - 8x + 16 - 16 + 17, or (x - 4)² + 1

Now return to the original function

y = 2(x² - 8x + 17).

Replace  x² - 8x + 17  with  [x - 4]² + 1

We get ,y = 2(x² - 8x + 17)

= 2( [x - 4]² + 1  )

By contrast, we can see that h = 4 and k = 2 in this equation, which has the form y = a(x - h)2 + k. This parabola's vertex is located at (4, 2).

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Answer:

56a+40b

Step-by-step explanation:

43a plus 13a is 56a, -12b + 52b is 40b, together it's 56a+40b

To find the difference between 3/5 and 1/2 using fraction strips, we can use strips that are divided into fifths and halves, respectively.the difference between 3/5 and 1/2 is 2/10 or 1/5, , the answer in the simplest form is 1/5.

First, we'll need to represent each fraction using the fraction strips.

For 3/5, we can use three fifths strips to represent the numerator and put them together to form a whole.

For 1/2, we can use one half strip and cut it into two equal parts to represent the numerator.

Next, we'll need to compare the two fractions by placing them side by side.

We can see that the two fractions do not have the same denominator, so we need to find a common denominator to make the comparison easier.

The smallest common multiple of 5 and 2 is 10, so we can represent 3/5 using six tenths strips, and 1/2 using five tenths strips.

We can see that there are two tenths strips that are not shared between the two fractions.

Therefore, the difference between 3/5 and 1/2 is 2/10 or 1/5, , the answer in the simplest form is 1/5.

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