Health department lab officials detected 120,000 bacteria on a dessert plate that has a diameter of 6 inches. What's the approximate population density of the bacteria on the dish?

A. 1,062 bacteria/square inch
B. 1,111 bacteria/square inch
C. 12,739 bacteria/square inch
D. 4,246 bacteria/square inch

[tex]\dfrac{2}{3}x=26\\\\x=26\div \dfrac{2}{3}=26\cdot\dfrac{3}{2}=39[/tex]

ANSWER

The possible rational roots are:

[tex]\pm\frac{1}{2},\pm2,\pm \frac{5}{2}[/tex]

EXPLANATION

According to the rational root theorem, the possible rational roots of the polynomial,

[tex]4x^3+9x^2-x+10=0[/tex]

are all the possible factors of the constant term divided by all the possible factors of the coefficient of the highest degree of the polynomial.

Therefore we examine the numerator and denominator of the options provided to see if they are factors of 10 and 4 respectively.

For

[tex]\pm\frac{1}{2}[/tex], we can see that 1 is a factor of 10 and 2 is a factor of 4, hence it is a possible rational root.

The same thing applies to [tex]\pm2,\pm \frac{5}{2}[/tex] also.

As for

[tex]\pm \frac{2}{5}[/tex], 2 is a factor of 10 but 5 is not a factor of 2, hence it is not a possible rational root.

The values of the possible rational roots of 4x³ + 9x² - x + 10 = 0 among the options are;

±½, ±2, ±5/2

          The rational root theorem states that if a polynomial has any rational roots, then the rational roots must be of the form;

±(factors of the coefficient of the constant term/factors of coefficient of the term with the highest degree)

4x³ + 9x² - x + 10 = 0

Thus, the rational roots could be;

±(½, 2, 5/2, 5)

        Looking at the options, the only correct possible rational roots are;

±½, ±2, ±5/2

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To round 4.975 to the nearest tenth, since the hundredths place has a 7, you round up, leading the tenths place (9) to increase by 1, turning into a 0, and the ones place (4) to also increase by 1, resulting in 5.0 as the answer.

When you round 4.975 to the nearest tenth, since there is a '7' in the hundredths place, the number in the tenths place will be affected by rounding rules. According to the standard rules for rounding numbers, if the first dropped digit is 5 or higher, you round up. Since 7 is greater than 5, you add 1 to the tenths place. Therefore, 9 in the tenths place plus 1 equals 10, which means a '0' will go in the tenths place and an additional '1' will be added to the 4 in the ones place, making the rounded number 5.0.

Answer:

y+2 = (-1/2)(x-3)

Step-by-step explanation:

Note that as we move from (-17,8) to (3,-2), x increases by 20 and y decreases by 10.  Thus, the slope of this line is m = -10/20, or m = -1/2.

The standard equation in point-slope form is y - k = m(x - h), where (h, k) is a point on the line and m is the slope of the line.  Then, taking data from the point (3, -2), we have

y+2 = (-1/2)(x-3).

Check:  Does the point (-17,8) satisfy this equation?  Is 8+2 = (-1/2)(-17-3) true?

Is 10 = 10 true?  Yes.

Answer:

y+2 = (-1/2)(x-3)

Step-by-step explanation:

We are given that initially there were 40 people in the audience.

And an up-and-coming band has seen a 50% monthly increase in the the number of audience members at their concerts.

The number of audience members is represented by y variable and

Number of months is represented by x variable.

So, the exponential function would be

y= a(b)^x

Where a is the initial value, b is the growth factors.

a= 40 and b= 1+ 0.50 = 1.50.

Therefore,

y= 40(1.50)^x is the exponential function situation.

Let us check some point on the graph.

If we plug x=0, we get initial value 40.

If we pug x=2, we get

y=40(1.50)^2 = 40(2.25) = 90.

Graph C represents y=40 at x=0 and y=90 at x=2.

If you're on Plato the answer would be C

Answer:

Option B.

B. 5/2 cups of sugar, 19/6 cups of flour

Step-by-step explanation:

Given that Imogen is baking a cake.

The cake  requires two and one-half cups of sugar and three and one-sixth cups of flour.

Sugar required = 2 1/2

To make it improper fraction, we make the integer as a fraction with denominator 2

i.e. 2 1/2 = 2+1/2 =4/2 +1/2

Now we can add these

= 5/2

So 5/2 cups of sugar is required.

Similarly flour required=3 1/6

To make it improper we convert 3 into a fraction with denominator 6.

3=18/6

3 1/6 = 3+1/6 =18/6+1/6 = 19/6

Hence 19/6 cups of flour required.

[tex]a_n=2^n\\\\a_1=2^1=2\\\\a_2=2^2=4\\\\a_3=2^3=8\\\\a_4=2^4=16\\\\Answer:\ C.\ \{2,\ 4,\ 8,\ 16\}[/tex]

The collinear points with A and B are:

- A, B, R

- B, D, T

- C, D, U

- B, S, G (where G is the centroid of AEDC).

In the given pyramid BAEDC, the collinear points with points A and B are determined by the midpoints and the line coming from B.

1. Midpoint of BA is R:

  - Points A, B, and R are collinear.

2. Midpoint of BD is T:

  - Points B, D, and T are collinear.

3. Midpoint of CD is U:

  - Points C, D, and U are collinear.

4. Line coming from B meets at S, the midpoint of AEDC:

  - Points A, E, D, C, and B are vertices of the pyramid, and S is the midpoint of the line segment connecting B to the centroid of the base AEDC.

  - Therefore, points B, S, and the centroid (G) of AEDC are collinear.

In summary, the collinear points with A and B are:

- A, B, R

- B, D, T

- C, D, U

- B, S, G (where G is the centroid of AEDC).

Total number of baseball cards Jessica has = 1368 cards.

Total number of baseball cards Thomas has = 1633 cards.

We need to find who has more baseball cards.

We can see 1633 is greater than 1368, because we have hundreds digit in 1633 is 6 and hundreds digit in 1368 is 3.

6 is greater than 3.  Therefore 1633 is greater than 1368.

Answer:Thomas

Step-by-step explanation:

1633 > 1368

The answer is D because it passes the horizontal line test.  

629g < box + cereal < 633g

629g - 5g = 624g

633g - 5g = 628g

Answer: a. 624 < x < 628

18x8 is 144

The answer is 144 units^Squared

[tex]\left\{\begin{array}{ccc}-\dfrac{1}{4}x+y=-2&|\cdot4\\-x+4y=-8\end{array}\right\\\\\left\{\begin{array}{ccc}-x+4y=-8\\-x+4y=-8\end{array}\right\\\\-x+4y=-8\ \ \ \ |+x\\4y=x-8\ \ \ \ |:4\\y=\dfrac{1}{4}x+2\\\\\left\{\begin{array}{ccc}x\in\mathbb{R}\\\\y=\dfrac{1}{4}x+2\end{array}\right[/tex]

Answer:

He used 12.944... yards of pipe for the repiping job.

Step-by-step explanation:

We know that,  1 yard = 3 feet  and  1 feet = 12 inches.

That means,  1 yard = (3×12) inches = 36 inches.

So, 1 feet = [tex]\frac{1}{3}[/tex] yard and  1 inch = [tex]\frac{1}{36}[/tex] yard.

Thus,  26 yards, 2 feet and 5 inches [tex]=(26+\frac{2}{3}+\frac{5}{36}) yards = 26.805... yards[/tex]

and  13 yards, 2 feet and 7 inches [tex]=(13+\frac{2}{3}+\frac{7}{36}) yards = 13.861... yards[/tex]

So Austin began a repiping job with 26.805... yards of pipe and when he finshed the job, he had 13.861... yards.

So, the length of the pipe he used for the repiping job will be: [tex](26.805...-13.861...) yards = 12.944... yards[/tex]

12 yards, 2 feet, 10 inches

30/12=in 1 min you drive 2.5lap

120/48=in 1 min you drive 2.5lap

yes they are equivalant

If they are equivalent, you should be able to cross multiply and get a true statement.

12/30 = 48/120

12(120) = 30(48)

1440 = 1440

This is a true statement, therefore they ARE equivalent.

The median is 6. I hope this helps you out.

The Answer would be 5.5 because it splits between 6 and 5 and the median would be 5.5.

The length of the fabric is 4 cm.

To find the length of the piece of fabric, we need to divide the area by the width. The area of the fabric is given as 20 cm squared and the width is given as 5 cm. So, to find the length, we divide 20 cm squared by 5 cm:

Length = Area / Width

Length = 20 cm2 / 5 cm

Length = 4 cm

Therefore, the length of the piece of fabric is 4 cm.

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If (3,5) is a point on the graph of the function f, then (-1, 5) must be on the graph of the inverse function f-1.

To find the point that must be on the graph of the inverse function, we need to find the inverse of the given function first. Let's assume the given function is f(x) = y.

To find the inverse of f(x), we swap the x and y variables and solve for y. In this case, we have x = 3 and y = 5, so the inverse function is f-1(x) = (5, 3).

Therefore, the point (-1, 5) must be on the graph of the inverse function f-1.

Learn more about Inverse Functions here:

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<PTS = <RTQ (vertical angles are equal)

11(y - 10) = 4y - 5

11y - 110 = 4y - 5

7y = 105

y = 15

so

<PTS = 11(15 - 10) = 11(5) = 55

Answer

<PTS = 55°

Answer:

4 tickets were sold

Step-by-step explanation:if you have 100 of anything. 5 sets of 20=100

Answer:

Answer: x = 100

Step-by-step explanation:

(20)(x) = (5)(x) = 20/5 = 5x/5 = 100

I just answered and got it correct.

I'm confused too and I'm supposed to be an expert.  I'm not entirely sure what frequency density is.  We'll just treat this as a histogram.

Let's assume each five minute interval gives a value equal to or proportional to the number of people that finished in that interval.

From 0 to 50 we have 10 intervals; let's just make this into a table

0-5  0

5-10 40

10-15 40

15-20 30

20-25 30

25-30 25

30-35 25

35-40 25

40-45 25  

45-50 15

From 0 to 40 that adds up to

0+40+40+30+30+25+25+25 = 215

From 0 to 50 that's

215+25+15 = 255

The fraction less than 40 is 215/255 = 43/51 ≈ .843

Answer: 84.3%

Answer:

84.3%

Step-by-step explanation:

Total frequency is the total area:

Add all the areas

To find each area:

Frequency density × class width

Total frequency:

40×10 + 30×10 + 25×20 + 15×5

= 1275

Less than 40:

Bar 1 + Bar 2 + some part of Bar 3

40×10 + 30×10 + 25×15

= 1075

Percentage (<40) = 1075/1275 × 100

= 4300/51

= 84.31372549%

Answer:

y = 5cos(πx/4) +11

Step-by-step explanation:

The radius is 5 ft, so that will be the multiplier of the trig function.

The car starts at the top of the wheel, so the appropriate trig function is cosine, which is 1 (its maximum value) when its argument is zero.

The period is 8 seconds, so the argument of the cosine function will be 2π(x/8) = πx/4. This changes by 2π when x changes by 8.

The centerline of the wheel is the sum of the minimum and the radius, so is 6+5 = 11 ft. This is the offset of the scaled cosine function.

Putting that all together, you get

... y = 5cos(π/4x) + 11

_____

The answer selections don't seem to consistently identify the argument of the trig function properly. We assume that π/4(x) means (πx/4), where this product is the argument of the trig function.

Answer:

Step-by-step explanation:

You have to start by making a small chart of what  is happening at what time.

x    0        4        8

y    16       6       16

Essentially this is a cosine function.

Now you need to fill in some of the details. The key is what is happening at x = 4 seconds? At that time, you must add a minus amount in the cosine function to the amplitude to get 6. The only way to do that is if you have

y = 5* cos( (x/4)*pi) + 11

y = 5*cos( (4/4)*pi) + 11

y = 5 * cos(pi) + 11

y = 5 * (-1) + 11

y = -5 + 11 = 6

==================

x = 0

y = 5* cos( (pi/4)*0 ) + 11

y = 5 * cos(0) + 11

y = 5 (1) + 11

y = 16

===================

x = 8 seconds

y = 5*cos(8/4)*pi) + 11

y = 5*cos(2*pi) + 11

y = 5 * (1) + 11

y = 16

==================

The question is where did the 11 come from?

The Ferris wheel has a diameter of 10 feet and a radius of 5

The high and low points are 16 and 6.

The center of the Ferris wheel is between 16 and 6. Between in this case means average.

(16 + 6)/2 = 22/2 = 11

Answer:

Height of cylinder = 2 inches

Explanation:

 If a cylinder has a base radius r and height h, the volume of cylinder is given by the expression, Volume V = πr²h.

Here given that volume of cylinder = 628 cubic inches = 628 inch³

 Radius of base circle = 10 inch.

 Substituting in the volume of cylinder equation

           628 = π x 10² x h

           [tex]h= \frac{628}{\pi *10^2} \\ \\ h=2.00 inches[/tex]

So , height of cylinder = 2 inches

First take note he only has $20 and the bag he must buy is $12.55. Also the loose seeds are $1.49 per pound.

To solve subtract 12.55 from 20

20-12.55=7.45

So after buying the 10 lb bag he has $7.45 left now divide that by 1.49

7.45/1.49=5

So after buying the 10 lb bag he can also buy 5 lb of the loose seeds!

For this case, we have the expression given by:

[tex]a + b = c\\[/tex]

This expression turns out to be generic.

The commutative property of the addition states that the order of the addends does not alter the sum. Thus it is concluded that the previous expression above can be written as:

[tex]b + a = c\\[/tex]

In this way [tex]7 + 4 = 11[/tex], applying the commutative property of the addition, it can be written as:

[tex]4 + 7 = 11\\[/tex]

Answer:

Option A