Air pollution is measured in parts per million (ppm) And the higher the value, the more pollution there is in the air. Stephen is completing research for his senior project and records the amount of pollution in the air each day for two weeks. His results are show and the higher the value, the more pollution there is in the air. Stephen is completing research for his senior project and records the amount of pollution in the air each day for two weeks. His results are show in this stem and leaf plot below.

Stem and leaf
0_5,7,9
1_2,2,6,7
2_0,4,8
3_1,2,5,9

A. Calculate the mean, median and mode of the data represented in the plot. Show and explain your work.

B. Another student created the box and whisker plot shown below incorrectly. Explain where the error exists and what the correct answer should be. (Picture included)

C. Describe which quartile has the largest range. Show or explain your work.

D. Describe why this statement is false.
“ 75% of the days had 20 or more parts per million of pollution.”

Correct Statement:____________

Answer:

Ratio

Step-by-step explanation:

A ratio is a comparison of two numbers by division.

A ratio is a comparison of two numbers by division.  It compares two quantities measured in the same units.

Ratios compare two quantities measured in the same units. Ratios have no units. They are expressed as a fraction in simplest form.

A ratio compares two numbers by division. In scientific notation, you divide the numbers out front and subtract the exponents. For the logarithm of a number resulting from division, the difference between the logarithms of two numbers is calculated.

A ratio is what compares two numbers by division. It's a way of comparing or relating one amount to another. For example, if we have 10 apples and 5 oranges, the ratio of apples to oranges is 10 to 5, which can also be expressed through division as 10/5 (which simplifies to 2).

In cases involving scientific notation, division can be handled by performing the division upfront and then subtracting the exponents. When working with the logarithm of a number resulting from division, the result would be the difference between the logarithms of the two original numbers.

Consider the following scientific notation division example: given 106 and 103, you would first divide the 'numbers out front', in this case, 1 divided by 1 equals 1. Then you subtract the exponents, 6 minus 3, which equals 3. Thus, 106 divided by 103 equals 103.

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Answer:

Step-by-step explanation:

B because .06 + .12 = .18 which is 18% out of 250 people

Hello, I'm Eric. I'll be trying my best to assist you on your question today.

0.12 is 12 percent.

We also have the 0.06 percent which would just be 6 percent

We need to add up those percentages to get 18 percent, for the people surveyed that cannot swim would be 18 percent.  

Our final answer is D.

Not the right answer or confused? Reply to this question for help.

Enjoy your day - Eric

Answer:

[tex]d = \sqrt{80} = 8.94[/tex]

Step-by-step explanation:

We can find the distance using the distance formula:

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

We then substitute (1,7) as [tex](x_1,y_1)[/tex] and (-3,-1) as [tex](x_2,y_2)[/tex].

[tex]d=\sqrt{(-3-1)^2+(-1-7)^2} \\d=\sqrt{(-4)^2+(-8)^2} \\d=\sqrt{16+64}\\d=\sqrt{80}=8.94[/tex]

Answer with Step-by-step explanation:

The length of the line segments with end point (a,b) and (c,d) is:

[tex]\sqrt{(a-c)^2+(b-d)^2}[/tex]

Here, we have to find the length of the segment with endpoints A(1,7) and B(-3, -1)

i.e. (a,b)=(1,7)

and (c,d)=(-3,-1)

Length= [tex]\sqrt{(1+3)^2+(7+1)^2}[/tex]

          = [tex]\sqrt{4^2+8^2}[/tex]

          = [tex]\sqrt{16+64}[/tex]

          = [tex]\sqrt{80}[/tex]

Hence, Length of line segment is:

[tex]\sqrt{80}[/tex] or [tex]4\sqrt{5}[/tex]

Answer:  5

Step-by-step explanation:

[tex]f(x)=2(x)^2+5\\\\f(0)=2(0)^2+5\\\\.\qquad =0+5\\\\.\qquad =5[/tex]

Final answer:

You will have 8 slices from the 3-inch cucumber and 13 slices from the 5-inch cucumber.

Explanation:

To determine the number of slices you will have, you need to divide the length of each cucumber by the thickness of the slices. Let's start with the 3-inch cucumber:

3 inches / (3/8 inches) = 8 slices

Now let's calculate the slices for the 5-inch cucumber:

5 inches / (3/8 inches) = 13.33 slices

Since you cannot have a fraction of a slice, round down to the nearest whole number. Therefore, you will have 8 slices from the 3-inch cucumber and 13 slices from the 5-inch cucumber.

Answer:

12 minutes

Step-by-step explanation:

if it fills up in 4 minutes but empties in 6 minutes, that means there's a two minute gap of water sitting - meaning it would multiple attempts to get the bucket filled - taking 12 minutes to be exact - hope this helps!!

Is it 12 minutes good job

On a number line, a point that is 10 units away from 5 can be either 15 (if you move right) or -5 (if you move left). Both these points are 10 units away from 5.

In mathematics, if the value 5 is plotted on the number line, you can plot another point that is 10 units away from 5 by moving 10 places towards either the right or left on the number line. If you move to the right, 10 places ahead of 5 is 15. So, you can plot a point on 15. On the other hand, if you move to the left, 10 places behind 5 is -5. So, you can plot a point at -5. Either of these points (15 or -5) are 10 units away from 5.

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Answer:

The perimeter of the trapezoid is [tex]38.25\ units[/tex]

Step-by-step explanation:

we know that

The perimeter of the trapezoid is the sum of its four side lengths

so

In this problem

[tex]P=QR+RS+ST+QT[/tex]

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

[tex]Q(8, 8), R(14, 16), S(20, 16),T(22, 8)[/tex]

step 1

Find the distance QR

[tex]Q(8, 8), R(14, 16)[/tex]

substitute the values in the formula

[tex]d=\sqrt{(16-8)^{2}+(14-8)^{2}}[/tex]

[tex]d=\sqrt{(8)^{2}+(6)^{2}}[/tex]

[tex]d=\sqrt{100}[/tex]

[tex]QR=10\ units[/tex]

step 2

Find the distance RS

[tex]R(14, 16), S(20, 16)[/tex]

substitute the values in the formula

[tex]d=\sqrt{(16-16)^{2}+(20-14)^{2}}[/tex]

[tex]d=\sqrt{(0)^{2}+(6)^{2}}[/tex]

[tex]d=\sqrt{36}[/tex]

[tex]RS=6\ units[/tex]

step 3

Find the distance ST

[tex]S(20, 16),T(22, 8)[/tex]

substitute the values in the formula

[tex]d=\sqrt{(8-16)^{2}+(22-20)^{2}}[/tex]

[tex]d=\sqrt{(-8)^{2}+(2)^{2}}[/tex]

[tex]d=\sqrt{68}[/tex]

[tex]ST=8.25\ units[/tex]

step 4

Find the distance QT

[tex]Q(8, 8),T(22, 8)[/tex]

substitute the values in the formula

[tex]d=\sqrt{(8-8)^{2}+(22-8)^{2}}[/tex]

[tex]d=\sqrt{(0)^{2}+(14)^{2}}[/tex]

[tex]d=\sqrt{196}[/tex]

[tex]QT=14\ units[/tex]

step 5

Find the perimeter

[tex]P=10+6+8.25+14=38.25\ units[/tex]

Answer:

option C

ȳ = 9

Step-by-step explanation:

ȳ (yBar) is used to represent mean value of y

Mean, which is the average score of the population on a given variable

It is represented by = ( Σ Xi ) / N

There are two steps to calculate mean value

sum of all numbers = 3 + 7 + 8 + 11 + 16

                                = 45

    2. Divide by how number of ys (there are 5 numbers)

45 / 5 = 9

So ȳ = 9

Answer:

303

Step-by-step explanation:

I believe this is correct but I need to know the supplement.

Answer:

12 units

Step-by-step explanation:

by the pythagorean relation,

x^2 + 9^2 = 15^2

x^2 + 81   = 225

x^2           = 144

x               = 12 units

Answer:

x^2 = 15^2 – 9^2

Step-by-step explanation:

Answer:

44

Step-by-step explanation:

substitute k = 1, 2, 3, 4 into 2k² - 4 and sum the terms

k = 1 : 2(1)² - 4 = 2 - 4 = - 2

k = 2 : 2(2)² - 4 = 8 - 4 = 4

k = 3 : 2(3)² - 4 = 18 - 4 = 14

k = 4 : 2(4)² - 4 = 32 - 4 = 28

sum = - 2 + 4 + 14 + 28 = 44

Heya!

--------------------

Things to know before we solve:

The "4" at the top means that the the sequence only goes to the 4th term.

k = 1 represents that the sequence starts with the 1st term.

(2k² - 4) represents the rule of the sequence, we can substitute 1, 2, 3, and 4 to solve for the terms of the sequence.

--------------------

Solving for each term:

1st term:

2(1)² - 4

2(1) - 4

2 - 4

-2

2nd term:

2(2)² - 4

2(4) - 4

8 - 4

4

3rd term:

2(3)² - 4

2(9) - 4

18 - 4

14

4th term:

2(4)² - 4

2(16) - 4

32 - 4

28

--------------------

Simplifying:

Write these terms in expanded form:

(-2) + 4 + 14 + 28

Find the sum of the series:

(-2) + 4 + 14 + 28 = 44

--------------------

Answer:

The sum of the series is 44

--------------------

Best of Luck!

Cos(x)=20/25

X=cos-1(20/25)

=36.86989765

=B

Answer:

y=1/6x+3

the slope has to be negative reciprocal and it passes though (6,4)

Answer:

= 0.583

Step-by-step explanation:

Changing 7/12 as a decimal

we could use long method or convert to percentage

such that;

7/12 ×  100 = 700/12

                 =58.333%

This is equivalent to; 58.333/100

= 0.58333 ; to the nearest thousandth

= 0.583

Answer:

The correct answer is option A.    0.583

Step-by-step explanation:

It is given a fraction 7/12. This fraction is a proper fraction.

proper fraction :- Numerator is less than denominator

We have to convert this fraction into decimal number.

we can convert all proper fractions into decimal.

Convert 7/12 into decimal

7/12 = 0.58333333...

It is a non terminating rec-curing decimal number.

Therefore we can write, 7/12 = 0.583

The correct answer is option A.    0.583

28 less means subtract 28

7 times a number means7x

is means equals

20 more than a number means x +20

the equation is 7x-28 =x+20

to solve combine like terms

7x-x=20+28

6x=48 divide by 6 on both sides to isolate x

x=8

Answer: 28

Step-by-step explanation:

Yes

5/5 and then convert this to 100. so, you would multiply it by 20 which would equal 100/100. it’s a whole number, so it’d just be 100%.

Answer:

[tex]54-(p*s)[/tex]

Step-by-step explanation:

we know that

To find out how many pencils the teacher has left, subtract the quantity of p*s from 54

so

[tex]54-(p*s)[/tex]

Answer:

54-(p times s)

Step-by-step explanation:

The number obtained when it is added with 9, multiplied by 3, subtracted by 16 and then added with 7 is 3.

Suppose the number is x

An addition of  9 to x = 9+x

Multiplication of 9+x and 3 = 3(9+x)

According to the question

3(9+x)-16+7 = 27

By solving the above equation we will get x

An equation is a statement that equates to two expressions.

So, 3(9+x) = 36

9+x=12

x=3

So, the number is x=3

Thus, the required number that satisfies the question is 3.

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Answer:

X = 3.5

Step-by-step explanation:

First, we distribute the 4 inside of the parentheses.

4 * 6x = 24x

4 * -9.5 = -38

We now have 24x -38 = 46

Now, we will add 38 to each side to isolate the x.

24x - 38 = 46

+38 +38

We now have 24x = 84

Finally, we will divide each side by 24 to find out what x equals.

24x = 84

— —

24 24

We now have x = 3.5

So, our answer is x = 3.5

I hope I helped!

Let me know if you need anything else!

~ Zoe

Answer:

X = 3.5

Step-by-step explanation:

First, we distribute the 4 inside of the parentheses.

4 * 6x = 24x

4 * -9.5 = -38

We now have 24x -38 = 46

Now, we will add 38 to each side to isolate the x.

24x - 38 = 46

+38 +38

We now have 24x = 84

Finally, we will divide each side by 24 to find out what x equals.

24x = 84

— —

24 24

We now have x = 3.5

So, our answer is x = 3.5

Answer:  a) 27

Step-by-step explanation:

[tex]81^{\frac{3}{4}}=(3^4)^{\frac{3}{4}}=3^{\frac{12}{4}}=3^3=\boxed{27}[/tex]

Answer:

Part A. = 2,000,000,000

Step-by-step explanation:

To find the first measurements solve the equation.

10^3 = 1,000

So now 1,000 multiplied by 4

4 x 1,000 = 4,000

for the second side or measurement solve again.

10^5 = 100,000

5 x 100,000 = 500, 000

with both measurements 4,000 and 500,000 to find area we need to multiply both sides

4,000 x 500,000 = 2,000,000,000

See if you can solve the other one, if you can't I'll help!

Hope this helps!

Please mark as brainliest answer!! THanks!!

Answer:

x + y = 4

Step-by-step explanation:

To write the equation of the line use the point slope form. Then convert to the standard from. Begin by substituting m = -1 and (-2,6).

[tex]y - y_1 = m(x-x_1)\\y - 6 = -1(x --2)\\y - 6 = -1(x+2)\\y - 6 = -x -2\\x + y - 6 = -2\\x + y = 4[/tex]

Answer:

Step-by-step explanation:

The area would be 25 square centimeter

Here's how you solve this problem.

1) find how many kilometers equals 1 mile (16/10=1.6).

2) Divide 100 (from 100 km/h) by 1.6 (1.6×100=62.5).

3) solve for mph.

The answer is 62.5mph.

We know that the line is tangent at the point (2,8)

The derivative of the function at x=2 is

[tex]f'(x) = 6-2x \implies f'(2) = 6-4=2[/tex]

So, the tangent line passes through the point (2,8) and has slope 2. The equation is

[tex]y-8 = 2(x-2) \iff y = 2x+4[/tex]

This line crosses the x axis where y=0:

[tex]0 = 2x+4 \iff 2x = -4 \iff x = -2[/tex]

The coordinates of point P where the tangent to the curve y=6x-x² cuts the X-axis can be found by finding the x-value when the derivative of the curve is equal to zero. In this case, the x-coordinate of point P is 3, so the coordinates of point P are (3, 0).

In this question, we are asked to find the coordinates of point P on the X-axis where a tangent to the curve y=6x-x² cuts the X-axis. The equation of the curve is given as y = 6x - x². A tangent line to the curve intersects it at exactly one point. The equation of this tangent line can be written in slope intercept form y = mx + b. When the tangent line cuts the X-axis, y=0.

The first step is taking the derivative of the curve, which gives us the slope of the tangent line. The derivative of y = 6x - x² is y' = 6 - 2x. This gives us the slope of the tangent line.

The second step is finding the x-coordinate of point P where the tangent line intersects the X-axis. This is where the y-coordinate is zero, or when y = 6x - x² is equal to zero. Solving for x, we get x = 0 or x = 6. However, because the curve y = 6x - x² intersects the X-axis at the x-coordinate of 0 and 6, the x-coordinate of point P must be a different value.

The final step is to solve for the x-coordinate when y' = 0, or when 6 - 2x = 0. Solving this equation gives us x = 3. So, the tangent line will cut the X-axis at point P(3, 0).

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I will help if u help me pls

QUESTION 1

The tangent ratio is the ratio of the length of the opposite side to the length of the adjacent side.

[tex] \tan(M) = \frac{LN}{NM} [/tex]

[tex] \tan(M) = \frac{8}{6} = \frac{4}{3} [/tex]

QUESTION 2.

We again use the tangent ratio to find angle S.

[tex] \tan(S) = \frac{TU}{SU} [/tex]

[tex]\tan(S) = \frac{0.75}{3.5} [/tex]

[tex]\tan(S) = \frac{3}{14} [/tex]

[tex]S = { \tan}^{ - 1} ( \frac{3}{14} )[/tex]

[tex]S = 12.09 \degree[/tex]

to the nearest hundredth.

QUESTION 3

We can find CE using the tangent ratio.

[tex] \tan(27 \degree) = \frac{18}{CE} [/tex]

[tex]CE = \frac{18}{ \tan(27 \degree) } [/tex]

[tex]CE = 35.3 \degree[/tex]

to the nearest 0.1.

Answer:

(x-7)  (x+4)

Step-by-step explanation:

x^2 - 3x - 28

What two numbers multiply to -28 and add to -3

-7*4 = -28

-7+4 = -3

(x-7)  (x+4)

Answer:

on the top: -28

on the bottom: -3

on the sides: -7 and 4

(x-7)(x+4)

Step-by-step explanation:

Answer:

142

Step-by-step explanation:

The line underneath the straight angle is a straight line, meaning it is 180 degrees. 180-38= 142

A straight line is 180 degrees.

180-38=142

142 degrees is the answer.

A cosine function is simpler to model the situation of the changing tides because it starts at an extremum, aligning with the low tide occurring at t=0 (12:00 am). By calculating the amplitude, midline, and period, we can construct an approximate model for the tidal heights using a cosine function without a phase shift.

The phenomenon of tidal movements can be modeled through periodic functions, such as sine or cosine functions, which are suitable for representing recurring events over time.

In this scenario, since the low tide occurs at t=0 (12:00 am) and reaches the same low tide level at t=12.5 (12:30 pm), a cosine function would be more appropriate as it inherently starts at a maximum or minimum value.

On the other hand, a sine function starts from the middle of its range, making it necessary to introduce a phase shift in the function for accurate modeling of the tides in this case.

A simple cosine model for the tidal heights would look like: Depth(t) = A * cos(B * (t - C)) + D, where A represents the amplitude, B is related to the period of the tide cycle, C is the phase shift (in this model C would be zero), and D adjusts the midline to fit the average between high and low tides.

Considering the given data:

Amplitude (A): (High tide depth - Low tide depth) / 2 = (5.5m - 2.5m) / 2 = 1.5m

Midline (D): (High tide depth + Low tide depth) / 2 = (5.5m + 2.5m) / 2 = 4m

Period (Related to B): Since there are two high and two low tides every 24 hours, the period would be 12 hours. We would then find B by using the formula 2 * pi / period, yielding B = 2 * pi / 12.

So, the model would be approximately Depth(t) = 1.5 * cos((pi / 6) * t) + 4, accurately reflecting the transition from low to high tides and back over a 12-hour cycle.

Answer:

A cosine function would be a simpler model for the situation.

The minimum depth (low tide) occurs at t = 0. A reflection of the cosine curve also has a minimum at t = 0.

A sine model would require a phase shift, while a cosine model does not.