When 20 employees were first hired in 2011 for an environmental engineering firm, Company A, the starting annual salary was $35,000. A competing environmental engineering firm, Company B, had the same starting salary for 20 employees hired the same year. In 2016, data was collected on the annual salaries of the same employees at each company. This data is displayed in the box plot shown. Part A: Compare the annual salary distributions. Part B: What are the pros and cons of working at each company? Explain using what you found in Part A.

Answer: Apple price = Rs 75 per kg & Orange price = Rs 45 per kg

Step-by-step explanation:

Creative Section- A

a) 4kg apples + 6 kg oranges = Rs 570

   3kg apple price = 5 kg orange price

Let, apple = x , orange = y

Now, 4x+6y= 570

         3x=5y ⇒ 3x-5y= 0

Subtract two equations,

x+11y=570

⇒ x + (33x/5) = 570

⇒  7.6x = 570

⇒ x = 75, y= 45

Apple price = Rs 75 per kg

Orange price = Rs 45 per kg

Answer:

f(x) = - 2x + 4

Step-by-step explanation:

Since we are only trying to move the graph up 3 units, the slope does not change. So, it would be -2.

We also know that the 1 in f(x)= -2x + 1 is the y-intercept (y=mx+b). But again, we are moving the graph 3 units up, so we have to add 3. That makes it 4 (3+1=4).

So, the new equation would be f(x) = -2x + 4

Step-by-step explanation:

it simply means that g(x) is f(x) just shifted 3 units upwards.

that means nothing else changes, only whatever y result f(x) produces is increased by 3.

so,

g(x) = f(x) + 3 = -2x + 1 + 3 = -2x + 4

therefore, as domain and range were the whole set of real numbers, the addition of 3 does not make any difference in relation to infinity. so, they remain unchanged.

the slope stays the same (g(x) is simply a parallel line to f(x)).

the y-intercept (the y-value when x = 0) also increases by 3, and is 4.

the x-intercept (the x-value when y = 0) changes :

0 = -2x + 4

2x = 4

x = 2

the x-intercept is 2.

Answer:

A) (1)/(7)

B) 33

Step-by-step explanation:

For (A), the sequence follows in 1 divided by numbers in a consecutive order, therefore after (1)/(6), the next term is (1)/(7)

For(B), the sequence follows in multiples of three but skips one in between

Example: Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36...

In the sequence, 6, 12, 18 and 24 are skipped, meaning that the next number to be skipped is 30, hence 33 is the next number in the sequence.

Because all the numbers in the sequence are odd numbers we can say that the sequence follows in odd consecutive numbers which are multiples of 3.

Answer:

Rational

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

400,000

Step-by-step explanation:

➟ 10 × 4 ten thousand

Since, a ten thousand = 10,000 therefore 4 ten thousand = 40,000

➟ 10 × 40,000

➟ 400,000

Answer:

y=-1

Step-by-step explanation:

-5y+8=-3y+10

+5y     +5y

       8=2y+10

     -10       -10

       -2=2y  Divide:

        -1=y

Hope this helps :)

Answer: y = -1  

Step-by-step explanation:

-5y + 8 = -3y + 10      Add  3y to both sides

+3y          +3y

 -2y + 8 =  10       Subtract 8 from both sides

       -8      -8

-2y =  2      Divide both sides by -2

y = -1

Answer:

A bearing of x. Hope this helped! :D

Answer:

Step-by-step explanation:

One characteristic of a reflection that is useful for answering this question is that it always reverses the clockwise/counterclockwise orientation of a figure. Rotation and translation have no effect on that orientation.

__

1. translation by reflection

Reflection across two parallel lines has the net effect of translating a figure twice the distance between the parallel lines. So, one way to effect a translation using two lines of reflection is to draw one of them through the perpendicular bisector of a point and its translated image. Then the other line would be drawn parallel to the first through the image point.

True: translation can be replaced by two reflections

__

2. translation by rotation

A single point can be moved from one set of coordinates to another by rotating around any point on the perpendicular bisector of the original and its image. To "undo" the change in direction of other points in the image, the image can be rotated an equal angle in the reverse direction about the point that is in its proper place.

That is, if we rotate figure ABC an amount of X° about a point on the perpendicular bisector of AA', so that A ends up at A', then the translation can be finished by rotating that figure by -X° about point A'.

The simplest case is an initial rotation of 180° about the midpoint of AA', followed by another rotation of 180° about A'.

True: translation can be replaced by two rotations

__

3. rotation by reflection

As discussed above, reflection changes orientation and rotation does not.

However, a rotation can be replaced by two reflections. The rotation angle is equal to twice the angle between the lines of reflection. The point where the lines of reflection meet is the center of rotation.

False: rotation can be replaced by reflection

__

4. reflection by rotation and translation

As discussed above, reflection changes orientation, but rotation and translation do not.

False: reflection can be replaced by rotation and translation

P= Total # of people who entered the park

t= The time in hours

P=2200t

6600 = 2200t

Divide both sides of the equation by 2200:

3=t

answer : 3 hours

9515 1404 393

Answer:

  2 8/11 hours ≈ 2.73 hours

Step-by-step explanation:

Assuming a constant rate, entries are proportional to time.

  time/people = 1 h/(2200 people) = t/(6000 people)

  t = (1 h)(6000/2200) = 2 8/11 h ≈ 2.73 h

It will take about 2.73 hours for 6000 people to enter.

Answer:

I think B but I'm not sure

Step-by-step explanation:

Answer:

B i think

Step-by-step explanation:

you're welcome <3

Answer:

6 yards

Step-by-step explanation:

she need 1 yard of ribbon for each hairbow and 6 friends to make them for

Answer:

a_n = 47 - 8n

Step-by-step explanation:

a_1 = 39

a_2 = 31

a_3 = 23

31 - 39 = -8

23 - 31 = -8

This is an arithmetic sequence with constant difference -8.

a_1 = 39

a_2 = 39 - 8

a_3 = 39 - 8 - 8 = 39 - 2(8)

a_4 = 39 - 8 - 8 - 8 = 39 - 3(8)

...

a_n = 39 - (n - 1)(8)

a_n = 39 - 8(n - 1)

a_n = 39 - 8n + 8

a_n = 47 - 8n

Answer:

\(a_n=47-8n\)

Step-by-step explanation:

Given sequence:

Calculate the differences between the terms:

\(39 \underset{-8}{\longrightarrow} 31 \underset{-8}{\longrightarrow} 23\)

As the differences are constant (the same), this is an arithmetic sequence with:

\(\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\end{minipage}}\)

Substitute the found values of a and d into the formula to create an equation for the nth term of the sequence:

\(\implies a_n=39+(n-1)(-8)\)

\(\implies a_n=39-8n+8\)

\(\implies a_n=47-8n\)

Answer: 1.To find the mean, we sum up all the scores and divide by the number of scores:

Mean = (5 + 12 + 8 + 14 + 11) / 5 = 50 / 5 = 10

To find the variance, we first find the deviation of each score from the mean:

5 - 10 = -5

12 - 10 = 2

8 - 10 = -2

14 - 10 = 4

11 - 10 = 1

We square each deviation and sum them up:

(-5)^2 + 2^2 + (-2)^2 + 4^2 + 1^2 = 26

Then, we divide by the number of scores to find the variance:

Variance = 26 / 5 = 5.2

Finally, we find the standard deviation by taking the square root of the variance:

Standard deviation = √5.2 = 2.28

2. To construct a simple random sample of size 2, we can choose any two scores from the population. The number of ways to do this is given by the combination formula:

C(5,2) = 5! / (2! * (5 - 2)!) = 10

Therefore, there are 10 simple random samples of size 2 that can be constructed.

3.The mean of the sampling distribution of the sample means is equal to the population mean, which we found to be 10. The variance of the sampling distribution is equal to the population variance divided by the sample size:

Variance of sampling distribution = Variance / Sample size = 5.2 / 2 = 2.6

The standard error of the sampling distribution is the square root of the variance:

Standard error = √2.6 = 1.61

4.The variance of the sampling distribution is 2.6, as we found in part

5. Since this is considered to be data from a simple random sample, we can use the sample mean as a point estimate of the population mean. Therefore, the point estimate of the population mean is 10.

Similarly, we can use the sample variance as a point estimate of the population variance. However, we need to correct for the bias in the sample variance by dividing by (n-1) instead of n:

Point estimate of population variance = Variance * (n / (n-1)) = 5.2 * (5 / 4) = 6.5

Step-by-step explanation:

Given statement solution is :- The correct answer is: The frequency is 3 more than expected.

To determine the expected frequency of landing on an even number when rolling a fair six-sided number cube, we need to calculate the probability of landing on an even number and multiply it by the total number of rolls.

The number cube has six possible outcomes: 1, 2, 3, 4, 5, and 6. Of these, three are even numbers: 2, 4, and 6. Therefore, the probability of rolling an even number is 3/6, which simplifies to 1/2 or 0.5.

The expected frequency can be found by multiplying the probability by the total number of rolls:

Expected frequency = Probability of landing on an even number × Total number of rolls

Expected frequency = 0.5 × 30 = 15

Now, we can compare the expected frequency (15) to the actual frequency (18) given in the problem statement.

The actual frequency is 18, and it is 3 more than the expected frequency (18 - 15 = 3).

Therefore, the correct answer is: The frequency is 3 more than expected.

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Answer:

I can see the picture re post it

Step-by-step explanation:

Answer:

The measure of angle F is the same as the measure of angle C.

BC is adjacent and AC is the hypotenuse. That means, use cosine.

Cos C = 15/17

C = cos-1(15/17) = 28.07... or 28.

Step-by-step explanation:

Answer:

e=h/r

Step-by-step explanation:

Answer:

see the picture there is the answer

Answer:228m

Step-by-step explanation: 19m x 12m = 228m

Answer: 228m

Step-by-step explanation: Just multiply 19m by 12m. That's how you find area.

\(\large\huge\red{\sf{➡ANSWER ⤵}}\)

The top angle is right (90 degrees, kinda looks like a bent elbow).

The 2nd is acute (smaller than 90, kind of 'cute' bc it's small).

The 3rd is obtuse (greater than 90, I have nothing corny to say, sorry).

4th is acute.

5th is straight because it's a straight line.

6th is also obtuse.

Have a good day :)

Answer: Outside the triangle

Step-by-step explanation:

Because one of the angles has a measure greater than 90 degrees, we know that the triangle must be obtuse. Therefore, the circumcenter must fall outside the triangle because in an obtuse triangle, the circumcenter is always located outside of the triangle.

Answer:

x ≤ 3

Step-by-step explanation:

\(\dfrac{1}{2}-\dfrac{1}{4}x \geq -\dfrac{1}{4}\)

Subtract 1/2 from both sides:

\(\implies \dfrac{1}{2}-\dfrac{1}{4}x-\dfrac{1}{2} \geq -\dfrac{1}{4}-\dfrac{1}{2}\)

\(\implies -\dfrac{1}{4}x \geq -\dfrac{3}{4}\)

Multiply both sides by 4:

\(\implies -\dfrac{1}{4}x \cdot 4 \geq -\dfrac{3}{4} \cdot 4\)

\(\implies -x \geq -3\)

Divide both sides by -1 (remembering to flip the sign):

\(\implies \dfrac{-x}{-1} \geq \dfrac{-3}{-1}\)

\(\implies x \leq 3\)

Answer:

Step-by-step explanation:

Answer:

1. 12

2. 10

3. 18

4. 6

Step-by-step explanation:

In Mathematics, substitution is a method used for solving algebraic equation by inputing the values of a given variable.

1) 4x - 4, when x = 5

4(4) - 4 =

16 - 4 = 12

2) 7 + m -2, when m = 5

7 + 5 - 2 =

12 - 2 = 10

3) 5+5h + 3, when h = 2

5 + 5(2) + 3 =

5 + 10 + 3 = 18

4) 3n - 6, when n = 4

3(4) - 6 =

12 - 6 = 6

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

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

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

Step-by-step explanation:

Use the Law of Sines

FE/sin38=18/sin90

FE=18sin38=11.08

DF/sin52=18/sin90

DF=18sin52=14.2

Answer:

Step-by-step explanation:

Use trigonometric ratios:

Apply to the given triangle

Side FE

Side DE

The quadratic equation that describes the function is  

f(x) = x² + 4x + 1

A quadratic equation is a equation that is of the form -

y = f{x} = ax² + bx + c

Given is the table that describes the quadratic function h(x) as follows -

{x}                h{x}

−3               −2

−2               −3

−1                −2

0                  1

1                   6

2                  13

3                  22

The quadratic equation is of the form given -

y = ax² + bx + c

For the point (0, 1), we can write -

1 = c                                                      ..... Eq{1}

For the point (1, 6), we can write -

6 = a + b + 1

a + b = 5                                               ...... Eq{2}

For the point (2, 13), we can write -

13 = 4a + 2b + 1

4a + 2b = 12                                               ...... Eq{3}

From Eq{2}, we can write -

a = 5 - b

So, the equation 3 can be written as -

4(5 - b) + 2b = 12

20 - 4b + 2b = 12

20 - 2b = 12

2b = 8

b = 4                                    ...... Eq{4}

then

a = 1                                ...... Eq{5}

So, we can write the quadratic equation as -

f(x) = x² + 4x + 1

Therefore, the quadratic equation that describes the function is  

f(x) = x² + 4x + 1

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Answer:

4(x + 3) / 4x + 12

Step-by-step explanation:

the image linked is showing 4 green whihc means 4x and 12 squares so I multiply 4 x 3 whihc is 12

Answer:

  C:  y = -(x +3)² -1

Step-by-step explanation:

You want the vertex-form equation of the parabola with vertex (-3, -1) and opening downward.

For vertex (h, k), the vertex form equation of a parabola is ...

  y = a(x -h)² +k

Given that (h, k) = (-3, -1), the equation will have the form ...

  y = a(x -(-3))² + (-1)

  y = a(x +3)² -1 . . . . . . . . . . matches choice C

The value of 'a' will be negative when the parabola opens downward. Here, its value is -1.

  y = -(x +3)² -1

__

Additional comment

Once you identify the left-shift of 3 units as resulting in an equation with (x +3)² as a component, you can make the appropriate answer choice without considering anything else. Of course, the fact that the curve opens downward immediately eliminates choices A and B.

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