In microbiology, colony-forming units (CFUs) are used to measure the number of microorganisms present in a sample. To determine the number of CFUs, the sample is prepared, spread uniformly on an agar plate, and then incubated at some suitable temperature. Suppose that the number of CFUs that appear after incubation follows a Poisson distribution with μ = 15.
(a) If the area of the agar plate is 75 square centimeters (cm2), what is the probability of observing fewer than 4 CFUs in a 25 cm2 area of the plate? (Round your answer to four decimal places.)
(b) If you were to count the total number of CFUs in 5 plates, what is the probability you would observe more than 95 CFUs? Use the Poisson distribution to obtain this probability. (Round your answer to four decimal places.)
(c) Repeat the probability calculation in part (b) but now use the normal approximation. (Round your answer to four decimal ​)
(d) Find the difference between this value and your answer in part (b). (Round your answer to four decimal places.)

Answer:

3x^2 + 9x + 8

Step-by-step explanation:

2x+5+3x^2+7x+3

2x+5+3x^2+7x+3

(3x^2)+(2x+7x)+ (5+3)

3x^2+9x+8

Answer:

Hypotenuse = 5√2 units

Step-by-step explanation:

Triangle ABC:

The legs are 5 units each

Opposite = 5unit

Adjacent = 5unit

Triangle ACB:

lengths of sides A C and C B are 5

The legs are 5 units each

Leg =AC = Opposite = 5unit

Leg = CB = Adjacent = 5unit

The hypotenuse for both ∆ACB is unknown. Since ∆ACB is a right angled triangle, we would apply Pythagoras theorem to find the hypotenuse.

Using Pythagoras theorem:

Hypotenuse ² = opposite ² + adjacent ²

Hypotenuse ² = leg² + leg²

AB = hypotenuse in ∆ACB

AB² = 5² + 5²

AB² = 25+25 = 50

AB = √50 = √(25×2)

AB = 5√2

Hypotenuse = 5√2 units

Answer:

The answer is B! Person above me is right!

Step-by-step explanation:

1000ML = 1 L

78ML ?

78*1/1000 = 0.078 L

Answer:

Tangent

Step-by-step explanation:

Tangent intersects a circle at exactly one point

Answer:

30.7

Step-by-step explanation:

add  the 15,3.7 ,and the 12

Answer:

number of minutes to drain the entire tower = 241 minutes(nearest minutes)

Step-by-step explanation:

The water tower has the shape of  a cylinder with a cone on top . The volume of the water tower can be find when you find the sum of the volume of the cylinder and the cone.

Therefore,

volume of the cylinder = πr²h

where

r = 12/2 = 6 ft

h = 15 ft

volume = π × 6² × 15

volume = π × 36 × 15

volume of the cylinder = 540π

Volume of the cone = 1/3πr²h

r = 6 ft

Using tangential ratio we can find the height which is the opposite side of the triangle

tan 25° = opposite/adjacent

tan 25° = h/6

cross multiply

h = 6 tan 25°

h = 6 × 0.46630765815

h = 2.79784594893

h = 2.8 ft

volume of the cone  =  1/3πr²h

volume = 1/3 × π × 36 × 2.8

volume = 100.8π/3

volume = 33.6π

Volume of the tower system = 540π + 33.6π =  573.6π

volume of the tower system = 573.6 × 3.14 = 1801.104 ft³

1 cubic ft  = 7.48 gallons

1801.104 cubic fit = ? gallons

cross multiply

gallons = 1801.104 × 7.48

gallons = 13472.25792  gallons

The residents drains the water at the rate of 56 gallons per minute. Therefore,

56 gallons = 1 minutes

13472.25792  gallons = ? minutes

number of minutes = 13472.25792  /56

number of minutes = 240.576034286

number of minutes to drain the entire tower = 241 minutes(nearest minutes)

Answer:

See below.

Step-by-step explanation:

For the first one:

[tex]f(x)=\frac{4x+3}{5x+2}[/tex]        

[tex]f(\frac{1}{x})= \frac{4(\frac{1}{x})+3}{5(\frac{1}{x})+2 }[/tex]

First, multiply both top and bottom by [tex]x[/tex].

Thus:

[tex](\frac{4(\frac{1}{x})+3}{5(\frac{1}{x})+2 } )\cdot \frac{x}{x}[/tex][tex]=\frac{4+3x}{5+2x}[/tex]

It cannot be simplified further.

For the second one:

[tex]g(x)=\sqrt{x^2-8x}[/tex]

[tex]g(x-2)=\sqrt{(x-2)^2-8(x-2)}[/tex]

[tex]\sqrt{(x^2-4x+4)-8x+16}[/tex]

[tex]\sqrt{x^2-12x+20}[/tex]

And that cannot be simplified further.

Answer:

C. [tex](f+g)(x)=-5^x-3x-6[/tex]

Step-by-step explanation:

→Set it up, like so:

[tex](-5^x-4)+(-3x-2)[/tex]

[tex]-5^x-4-3x-2[/tex]

→Add like terms (-4 and -2):

[tex]-5^x-3x-6[/tex]

Answer:

5

Step-by-step explanation:

Take the number of markers and divide by the number in each package

70/15

4.6666repeating

Round to the nearest whole number to determine the number of packages

5

They will need to buy 5 packages

Answer:

(1)19°

Step-by-step explanation:

The diagram is drawn and attached below.

Let x=mAC = 72°; and

y=mBD = 34°

By the Angle-Arc relationship, the external angle is half the difference.

[tex]\angle P=\frac{1}{2}(x^\circ-y ^\circ)\\$Therefore:\\m\angle P=\frac{1}{2}(72^\circ-34 ^\circ)\\m\angle P=19^\circ[/tex]

Using the cosine ratio, the length of BC to the nearest hundredth is: 4.91.

Cosine ratio is: cos ∅ = adjacent side/hypotenuse

Given the right triangle in the diagram above, thus:

Thus:

cos 35 = BC/6

BC = cos 35 × 6

BC = 4.91

Thus, using the cosine ratio, the length of BC to the nearest hundredth is: 4.91.

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Answer:

C.

Step-by-step explanation:

It is the complement of the circle in the square

Okay,

Let the square be Universal set(U) and the circle be A

So

A complement = A' = U-A So

The shaded area is the complement of the circle

Answer:

-72 y^4

Step-by-step explanation:

(8y^2)(-9y^2)​

Multiply the coefficients

8*-9 = -72

Add the exponents since the bases are the same

y^2 * y^2 = y^(2+2) = y^4

(8y^2)(-9y^2)​ = -72 y^4

Answer:

[tex]11\dfrac{3}{8}\text{cm}[/tex]

Step-by-step explanation:

[tex]1\dfrac{5}{8}+2\dfrac{9}{16}+2\dfrac{9}{16}+4\dfrac{1}{8}=11\dfrac{3}{8}[/tex]

Hope this helps!

Answer:

OB

Step-by-step explanation:

When you deduct something it means an intelligent reasoning based on given information for prediction.

In the above case we have a given formula from which we can deduct the facts .

We see a general statement is given from there we get a specific value.

By the way the formula given meant n(n+2)/ 2

The correct option is B. This is deductive reasoning because a specific conclusion is being proved from a general statement. This is obtained by checking the requirements of deductive reasoning.

Hence this is deductive reasoning because a specific conclusion is being proved from a general statement.

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Answer:

c+r+d= 200

1.50c+5.75r+2.60d= 589.50

r=d-20

Step-by-step explanation:

From the information given you have that Billy's restaurant ordered roses, daisies and carnations that total 200 flowers. The first equation is:

c+r+d= 200

c= number of carnations

r= number of roses

d= number of daisies

Also, you can say that the sum of the results of multiplying the price of each flower for its quantity is equal to $589.50. The second equation is:

1.50c+5.75r+2.60d= 589.50

Besides, from the statement you know there are 20 fewer roses than daisies and from that you can write the third equation:

r= d-20

The system of linear equations that can be used to find c, the number of carnations, r,  the number of roses, and d, the number of daisies is:

c+r+d= 200

1.50c+5.75r+2.60d= 589.50

r=d-20

Answer:

As angel WVU = angel WVF + angel FVU

Therefore angel WVF =152 - 70

so, angel WVF = 82

Answer:

17 weeks

Step-by-step explanation:

Please refer to the picture attached.

At the end of each week, she will be able to save 13 dollars. I'm the 17th week, whe will save more than 218 dollars and will be able to afford to buy the computer.

However, in 16th week, she will only save 208 dollars which is insufficient to buy the laptop.

Hence, u round up the value of x in order to get the answer.

Answer:

The integers are 11 and 12

Step-by-step explanation:

11 and 12 are consecutive positive integers, and 11 x 12 = 132.

Answer:

Step-by-step explanation:

Hello!

The variable of interest is

Y: number of new leaves of Bromeliads grown under different types of fertilization.

Factor: Type of fertilizer

Treatments: 1. Nitrogen, 2. Phosphorus, 3. Both, 4. Neither (control group)

To compare these four groups you have to conduct an ANOVA

The hypotheses are:

H₀: μ₁= μ₂= μ₃= μ₄

H₁: At least one population mean is different from the others.

α: 0.05

a)

The degrees of freedom of the F-statistic are:

[tex]F_{I-1;N-I}= F_{4-1;31-4}= F_{3;27}[/tex]

I= number of treatments

N= total number of experimental units (in all groups)

b)

SSTreatments= 39.37

SSError= 72.18

MSTreatments= SStreatments/DfTreatments= 39.37/3= 13.12

MSError=SSError/DfError= 72.18/27= 2.67

[tex]F= \frac{MS_{Treatments}}{MS_{Error}} = \frac{13.12}{2.67} = 4.91[/tex]

c)

This test is one-tailed to the right and so is the p-value:

P(F₃;₂₇≥4.91)= 1 - P(F₃;₂₇<4.91)= 1 - 0.9925= 0.0075

d)

The decision rule using the p-value is:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

The p-value is less than α, the test is significant at 5% significance level.

"We have significant evidence at the 5% level that the means are not all the same."

I hope this helps!

Answer:

[tex] x^{12} w^{-10}[/tex]

And we can find this rewriting the expression in terms of the info given and we got:

[tex]x^{12} w^{-10} = (x^6)^2 (w^{10})^{-1}[/tex]

And replacing we got:

[tex]x^{12} w^{-10} = (60)^2 (20)^{-1}= \frac{60^2}{20}= 180[/tex]

And the best option would be:

C. 180

Step-by-step explanation:

For this case we know that:

[tex] x^6, w^{10} = 20[/tex]

And we want to find the value for:

[tex] x^{12} w^{-10}[/tex]

And we can find this rewriting the expression in terms of the info given and we got:

[tex]x^{12} w^{-10} = (x^6)^2 (w^{10})^{-1}[/tex]

And replacing we got:

[tex]x^{12} w^{-10} = (60)^2 (20)^{-1}= \frac{60^2}{20}= 180[/tex]

And the best option would be:

C. 180

Answer:

Let's solve for m.

3m + 4n = 625

Step 1: Add -4n to both sides.

3m + 4n + −4n = 625 + −4n

3m = −4n + 625

Step 2: Divide both sides by 3.

3m/3 = 4n + 625/3

m = -4/3 n + 625/3

C) The variable m in the equation represents the number of hours Amy traveled on the

first train.

D) The variable n in the equation represents the number of hours Amy traveled on the

second train.

Answer:

Subtract

31

31

from both sides of the equation.

x

2

+

y

2

−

4

x

−

12

y

=

−

31

x2+y2-4x-12y=-31

Complete the square for

x

2

−

4

x

x2-4x

.

Tap for more steps...

(

x

−

2

)

2

−

4

(x-2)2-4

Substitute

(

x

−

2

)

2

−

4

(x-2)2-4

for

x

2

−

4

x

x2-4x

in the equation

x

2

+

y

2

−

4

x

−

12

y

=

−

31

x2+y2-4x-12y=-31

.

(

x

−

2

)

2

−

4

+

y

2

−

12

y

=

−

31

(x-2)2-4+y2-12y=-31

Move

−

4

-4

to the right side of the equation by adding

4

4

to both sides.

(

x

−

2

)

2

+

y

2

−

12

y

=

−

31

+

4

(x-2)2+y2-12y=-31+4

Complete the square for

y

2

−

12

y

y2-12y

.

Tap for more steps...

(

y

−

6

)

2

−

36

(y-6)2-36

Substitute

(

y

−

6

)

2

−

36

(y-6)2-36

for

y

2

−

12

y

y2-12y

in the equation

x

2

+

y

2

−

4

x

−

12

y

=

−

31

x2+y2-4x-12y=-31

.

(

x

−

2

)

2

+

(

y

−

6

)

2

−

36

=

−

31

+

4

(x-2)2+(y-6)2-36=-31+4

Move

−

36

-36

to the right side of the equation by adding

36

36

to both sides.

(

x

−

2

)

2

+

(

y

−

6

)

2

=

−

31

+

4

+

36

(x-2)2+(y-6)2=-31+4+36

Simplify

−

31

+

4

+

36

-31+4+36

.

(

x

−

2

)

2

+

(

y

−

6

)

2

=

9

(x-2)2+(y-6)2=9

This is the form of a circle. Use this form to determine the center and radius of the circle.

(

x

−

h

)

2

+

(

y

−

k

)

2

=

r

2

(x-h)2+(y-k)2=r2

Match the values in this circle to those of the standard form. The variable

r

r

represents the radius of the circle,

h

h

represents the x-offset from the origin, and

k

k

represents the y-offset from origin.

r

=

3

r=3

h

=

2

h=2

k

=

6

k=6

The center of the circle is found at

(

h

,

k

)

(h,k)

.

Center:

(

2

,

6

)

(2,6)

These values represent the important values for graphing and analyzing a circle.

Center:

(

2

,

6

)

(2,6)

Radius:

3

3

Answer:

center: (2,-6)

radius: 8

Step-by-step explanation:

trust me i checked khan academy

Answer:

Height = 47.77 inches

Step-by-step explanation:

We are given;

Mean = 49.9 in

Standard deviation;SD = 3.15 in

The first quartile is the 25th percentile, which means it's where 25% of the data falls.

Now from the normal distribution table attached, we can see that the z-value for 25% or 0.25 is approximately

-0.675.

To find the height that represents the first quartile of these students, we will use the formula;

z = (height - mean)/(SD)

Making height the subject ;

height = (z × SD) + mean

Plugging in the relevant values to obtain;

Height = (-0.675 × 3.15) + 49.9

Height ≈ 47.77 inches

Answer:

[tex]3(-4a-3)(2a-1)[/tex]

Step-by-step explanation:

[tex]-24a^2-6a+9[/tex]

[tex](-12a-9)(2a-1)[/tex]

[tex]3(-4a-3)(2a-1)[/tex]

Answer:

−3(2a−1)(4a+3)

Step-by-step explanation:

9 - 6a - 24a^2

24a²-6a-9=

−3(2a−1)(4a+3)

We get this because −3(2a−1)(4a+3) equals out to 24a²-6a-9. If you need more explanation, reply to this answer.

Answer: C.

Step-by-step explanation:

To find the discounted value off of a full price, you can multiply the full price by the discount percentage to find the discount:

250 * 0.20 = 50

The discount is 50 dollars.

The laptop costs $250, but with the discount of $50, it is now for sale for $200.

The correct answer is C.

The answer is [-1/2-1/2]

The range of the function f(x) is [-1/2, 1/2].

The range is the set of possible output values, which are shown on the y-axis. The range of a function, f is the set of all values f(x) , such that x is in the domain of f. Graphically speaking, the range is the set of all y such that (x,y) is a point on the graph of f.

For the given situation,

The function f(x) = 1/2sin(2x-π)

The graph below shows the range of the function f(x) = 1/2sin(2x-π) graphically.

As the range of sinx function is [-1, 1], the range of sin2x is also [-1, 1].

Let us consider [tex]\theta = 2x-\pi[/tex]

⇒ Then, [tex]sin \theta[/tex] lies in the range [tex][-1,1][/tex]

⇒ [tex]-1\leq sin(2x-\pi )\leq 1[/tex]

⇒ [tex](\frac{1}{2} )(-1)\leq sin(2x-\pi )\leq( 1)(\frac{1}{2} )[/tex]

⇒ [tex]\frac{-1}{2} \leq sin(2x-\pi )\leq\frac{1}{2}[/tex]

Hence we can conclude that the range of the function f(x) is [-1/2, 1/2].

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Answer:

Range : { -3,0,4,6}

Step-by-step explanation:

The range of the function is the output values

Range : { -3,0,4,6}

Answer:

C. {-3, 0 ,4, 6}

Step-by-step explanation:

→The range is the total of y-intercepts/outputs. In this case, looking at the function, you can see that the y-intercepts/outputs are 0, -3, 4, and 6.

→The others numbers are the x-intercepts/inputs, which would be the domain of the function.

Answer:

39.17% probability that a woman in her 60s who has a positive test actually has breast cancer

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Positive test.

Event B: Having breast cancer.

3.65% of women in their 60s get breast cancer

This means that [tex]P(B) = 0.0365[/tex]

A mammogram can typically identify correctly 85% of cancer cases

This means that [tex]P(A|B) = 0.85[/tex]

Probability of a positive test.

85% of 3.65% and 100-95 = 5% of 100-3.65 = 96.35%. So

[tex]P(A) = 0.85*0.0365 + 0.05*0.9635 = 0.0792[/tex]

What is the probability that a woman in her 60s who has a positive test actually has breast cancer?

[tex]P(B|A) = \frac{0.0365*0.85}{0.0792} = 0.3917[/tex]

39.17% probability that a woman in her 60s who has a positive test actually has breast cancer