Flow meters are installed in urban sewer systems to measure the flows through the pipes. In dry weatherconditions (no rain) the flows are generated by waste-water from households and industries, together withsome possible drainage from water stored in the topsoil from previous rainfalls. In a study of an urbansewer system, the following values were obtained for flowrates during dry weather conditions:

423.6, 487.3, 453.2, 402.9, 483.0, 477.7, 442.3, 418.4, 459.0

Assume that the flow rates are normally distributed.

a. Construct a 98% two-sided confidence interval for the standard deviation of the flow rate under dry weather conditions.
b. Explain, only using words, the meaning of the CI you determined in (a).

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

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:

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

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.

Learn more about cosine ratio on:

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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:

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: 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.

Answer:

6.28 inches

Step-by-step explanation:

Given that the diameter of the pie=8 inch

Radius=Diameter/2

Therefore: Radius of the pie=8/2=4 Inch

Circumference of a circle [tex]=2\pi r[/tex]

Since the pie is sliced into 4 equal parts:

Length of the Pie crust of one slice[tex]=\dfrac{2\pi r}{4}[/tex]

Substituting the value of r, we obtain:

Length of the Pie crust of one slice[tex]=\dfrac{2*\pi *4}{4}\\=2\pi $ inches\\=6.28 inches (correct to 2 decimal places)[/tex]

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:

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:

(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]

Answer:

X=96

Step-by-step explanation:

180-134=46

180-130=50

SUM OF TWO INTERIOR ANGLES = EXTERIOR ANGLE

50 + 46=96

Complete Question

The complete question is shown on the first uploaded image

Answer:

  Value  x of X     -3    -7     -15

          [tex]P_X (x)[/tex]          [tex]\frac{1}{2}[/tex]      [tex]\frac{3}{8}[/tex]       [tex]\frac{1}{8}[/tex]

Step-by-step explanation:

From the question we are told that  

     The values of X are  [tex]X = -3 , -7 , -15[/tex]

     The total number of outcomes is  n =  8

The probability distribution function of X is evaluated as follow

   [tex]p(X = -3 ) = \frac{N_{-3}}{n}[/tex]

Where  [tex]N{-3}[/tex] is the number of time  X = -3  occurred and from the table the value is  [tex]N _{-3} = 4[/tex]

     Therefore

       [tex]p(X = -3 ) = \frac{4}{8}[/tex]

        [tex]p(X = -3 ) = \frac{1}{2}[/tex]

Now  

    [tex]p(X = -7 ) = \frac{N_{-7}}{n}[/tex]

Where [tex]N_{-7} = 3[/tex] from table  

So  

     [tex]p(X = -7 ) = \frac{3}{8}[/tex]

Also  

    [tex]p(X = -15 ) = \frac{N_{-15}}{n}[/tex]

    [tex]p(X = -15 ) = \frac{1}{8}[/tex]

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:

G = 53 degrees

Step-by-step explanation:

Since this is  a right triangle, we can use trig functions

sin theta = opp/ hyp

sin G = 24/30

Take the inverse sin of each side

sin ^-1 sin G =  sin ^-1 (24/30)

G =53.13010235

To the nearest degree

G = 53 degrees

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:

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:

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:

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:

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.

Learn more about reasoning process here:

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#SPJ2

Answer:

30.7

Step-by-step explanation:

add  the 15,3.7 ,and the 12

Answer:

The integers are 11 and 12

Step-by-step explanation:

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

Answer:

Tangent

Step-by-step explanation:

Tangent intersects a circle at exactly one point

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:

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:

As angel WVU = angel WVF + angel FVU

Therefore angel WVF =152 - 70

so, angel WVF = 82

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

If I'm understanding the problem correctly, the vendor sells water in exactly 8 oz increments, but only has glasses that can hold 6 oz or 10 oz.

Fill up the 10 oz glass, then (carefully) pour its contents into a 6 oz glass until it it is full. Then the 10 oz glass should contain 4 oz of water. Drink the 4 oz, repeat this process to get your 8 oz, and pay the man.

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