A farmer wishes to construct a fence around his rectangular field. The farmer has 150 feet of fence and
wishes to have the length be three more than the width. What is the width of the field. Make sure and
include feet in your answer.
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Answer:

The probability that the diagnosis is correct is 0.95249.

Step-by-step explanation:

We are given that the American Diabetes Association estimates that 8.3% of people in the United States have diabetes.

Suppose that a medical lab has developed a simple diagnostic test for diabetes that is 98% accurate for people who have the disease and 95% accurate for people who do not have it.

Let the probability that people in the United States have diabetes = P(D) = 0.083.

So, the probability that people in the United States do not have diabetes = P(D') = 1 - P(D) = 1 - 0.083 = 0.917

Also, let A = event that the diagnostic test is accurate

So, the probability that a simple diagnostic test for diabetes is accurate for people who have the disease = P(A/D) = 0.98

And the probability that a simple diagnostic test for diabetes is accurate for people who do not have the disease = P(A/D') = 0.95

Now, the probability that the diagnosis is correct is given by;

    Probability = P(D) [tex]\times[/tex] P(A/D) + P(D') [tex]\times[/tex] P(A/D')

                      = (0.083 [tex]\times[/tex] 0.98) + (0.917 [tex]\times[/tex]0.95)

                      = 0.08134 + 0.87115

                      = 0.95249

Hence, the probability that the diagnosis is correct is 0.95249.

Answer: 20 ft³

Step-by-step explanation:

volume of triangular pyramid = [tex]\frac{1}{3} bh[/tex]

Therefore, the volume is:

[tex]\frac{1}{3} *10*6=\frac{1}{3}*60=\frac{60}{3}=20[/tex]

Answer:

Option a is the correct answer

Answer:

C. 50 degrees

Step-by-step explanation:

Because 6x + 5x = 110° and x = 10

5×10 = FEG 50°

The phrasing "nine times out of ten" means 9/10 = 0.90 = 90% is the confidence level. We're confident 90% of the time that the confidence interval captures the population parameter we're after (in this case mu = population mean)

The portion "have an average score within 5% of 75%" means that 75% = 0.75 is the center of the confidence interval, and it goes as low as 0.75 - 0.05 = 0.70 and as high as 0.75 + 0.05 = 0.80

This confidence interval is from 70% to 80%, meaning that nine times out of ten, we're confident that the average score is between 70% and 80%

We write the confidence interval as (0.70, 0.80). It's common to use the notation (L, U) to indicate the lower (L) and upper (U) boundaries. You might see the notation in the form L < mu < U. If so, then it would be 0.70 < mu < 0.80; either way they mean the same thing.

The margin of error is 0.05 as its the 5% radius of the interval. It tells us how far the most distant score is from the center (75%)

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

In summary, we have these answers

Answer:

(-1,0,1,2)

Step-by-step explanation:

in listing the values of z it will now be (z:z= -1,0,1,2)

Answer:

The first option is not the same point in polar coordinates as (-3, 1.236). This proves that inverting the signs of r and θ does not generally give the same point in polar coordinates.

Step-by-step explanation:

Let's think about the position of this point. As you can tell it lies in the 4th quadrant, on the 3rd circle of this polar graph.

Remember that polar coordinates is expressed as (r,θ) where r = distance from the positive x - axis, and theta = angle from the terminal side of the positive x - axis. Now there are two cases you can consider here when r > 0.

Given : (- 3, 1.236), (3,5.047), (3, - 7.518), (- 3, 1.906)

We know that :

7.518 - 1.236 = 6.282 = ( About ) 2π

5.047 + 1.236 = 6.283 = ( About ) 2π

1.236 + 1.906 = 3.142 = ( About ) 2π

Remember that sin and cos have a uniform period of 2π. All of the points are equivalent but the first option, as all of them ( but the first ) differ by 2π compared to the given point (3, - 1.236).

Answer:

  2700 years

Step-by-step explanation:

The exponential function for the fraction remaining is ...

  r(t) = (1/2)^(t/5730)

where r is the remaining fraction and t is the time in years. We can solve for t to get ...

  log(r) = (t/5730)log(1/2)

  t = 5730·log(r)/log(1/2)

For the given r=0.72, the age of the artifact is estimated to be ...

  t = 5730·log(0.72)/log(0.5) ≈ 2700 . . . years

Answer:

(3x+2)^2

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Here, we want to check the validity of the given statement. The statement is false.

Under the empirical rule, following a normal distribution, 99.7% of observed data lies within 3 standard deviations from the mean while 95% of observed data lies within 2 standard deviation from the mean and 68% of observed data lies within 1 standard deviation of the mean.

Please check attachment for diagrammatic representation of the empirical rule.

Answer:

173 MRI machines

Step-by-step explanation:

Margin of error E = 0.5

Confidence interval 90% = 1-0.9 = 0.1

Standard deviation = 4 hours

Number of MRI machines needed per day n, = [(z alpha/2 * SD)/E]²

Z alpha/2 = 1.645 at alpha = 0.1

Inputting these values into n we have that

[(1.645*4)/0.5]²

= 13.16²

= 173.18 is approximately equal to 173

The company has to study 173 machines.

Answer:

46.2÷m=x

Step-by-step explanation:

u divide the amount of water by the time it takes to fill up(m). Witch will equal the amount per minute (x).

16.5/min

time = m

gallons / minutes = rate

46.2  = 16.5 (m)

46.2 / 16.5 = 16.5 (m) / 16.5

2.8 = minutes

Answer:

22

Step-by-step explanation:

This is a right angle so the sum of those would be equal to 90 degrees

x + 7 + 3x - 5 = 90 add like terms

4x + 2 = 90 subtract 2 from both sides

4x = 88 divide both sides by 4

x = 22

Answer:

Step-by-step explanation:

Semester Costs = 8*2858 =                     22864

Books / semester= 8 * 391 =                        3128

Total                                                            25992

If he wants to repay all this in six years the answer would be

45000 + 25992/6 = 45000 + 4332 = 49332

Answer:

49332

Step-by-step explanation:

Answer:

the probability of no defects in 10 feet of steel = 0.1353

Step-by-step explanation:

GIven that:

A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two.

Let consider β to be the average value for defecting

So;

β = 2

Assuming Y to be the random variable which signifies the anticipated number of defects in a 10-foot segment of this roll.

Thus, y follows a poisson distribution as number of defect is infinite with the average value of β = 2

i.e

[tex]Y \sim P( \beta = 2)[/tex]

the probability mass function can be represented as follows:

[tex]\mathtt{P(y) = \dfrac{e^{- \beta} \ \beta^ \ y}{y!}}[/tex]

where;

y =  0,1,2,3 ...

Hence,  the probability of no defects in 10 feet of steel

y = 0

[tex]\mathtt{P(y =0) = \dfrac{e^{- 2} \ 2^ \ 0}{0!}}[/tex]

[tex]\mathtt{P(y =0) = \dfrac{0.1353 \times 1}{1}}[/tex]

P(y =0) = 0.1353

Answer:

A

The null hypothesis is  [tex]H_o : \mu \ge 8300[/tex]

The  alternative hypothesis is  [tex]H_a : \mu < 8300[/tex]

B

  [tex]t = -3.34[/tex]

C

 [tex]p-value = P(t< -3.34) = 0.00041889[/tex]

D

 reject the null hypothesis  

Step-by-step explanation:

From the question we are told that

    The population mean is  [tex]\mu = 8300[/tex]

    The sample mean is [tex]\ = x = 8000[/tex]

     The  standard deviation is [tex]s = 440[/tex]

      The sample size is  [tex]n = 24[/tex]

       The  level of significance is  [tex]\alpha = 0.01[/tex]

The null hypothesis is  [tex]H_o : \mu \ge 8300[/tex]

The  alternative hypothesis is  [tex]H_a : \mu < 8300[/tex]

 The  test statistic is mathematically evaluated as

                     [tex]t = \frac{\= x - \mu }{ \frac{s}{\sqrt{n} } }[/tex]

=>                  [tex]t = \frac{8000- 8300 }{ \frac{440}{\sqrt{24} } }[/tex]

=>                    [tex]t = -3.34[/tex]

The p-value is obtained from the z -table ( reference calculator dot net ) , the value is

         [tex]p-value = P(t< -3.34) = 0.00041889[/tex]

Looking at the values of  [tex]p-value and \ \alpha[/tex] we see that  [tex]p-value < \alpha[/tex] Hence we reject the null hypothesis  

Answer:  $9,000

Step-by-step explanation:

Step 1

Calculate the amount of dividends the company will pay to all its shareholders.

= 15% of profits

= 15% * 6,000,000

= $900,000

Step 2

Calculate how much dividends each share will get;

$900,000 to 2 million shares of Company Y.

= 900,000/2,000,000

= $0.45

Step 3

Calculate how much the Mutual fund will get for its 20,000 shares

= 20,000 * 0.45

= $9,000

Answer: 0.0215 .

Step-by-step explanation:

Let X denotes the weekly wages at a certain factory .

It is normally distributed , such that

[tex]X\sim N(\mu=400,\ \sigma= 50)[/tex]

Then, the probability that a worker  selected at random makes between

$250 and $300:

[tex]P(250<X<300)=P(\dfrac{250-400}{50}<\dfrac{x-\mu}{\sigma}<\dfrac{300-400}{50})\\\\=P(\dfrac{-150}{50}<z<\dfrac{-100}{50})\ \ [z=\dfrac{x-\mu}{\sigma}]\\\\=P(-3<z<-2)\\\\=P(z<-2)-P(z<-3)\\\\=1-P(z<2)-(1-P(z<3))\\\\=P(z<3)-P(z<2)\\\\=0.9987-0.9772\\\\=0.0215[/tex]

Hence,the required probability = 0.0215 .

Answer:

-6

Step-by-step explanation:

Answer:

[tex]24 + x = 13 \\ x = 13 - 24 \\ x = - 11 \\ thank \: you[/tex]

Answer:

B. The vectors v and w are orthogonal because their dot product is 0

Step-by-step explanation:

Given that :

v=  - i - j  

w= - i + j

Therefore;

vw = ( - i - j )  ( - i + j )

Taking each  set of integer of the vector into consideration:

vw = ( -1 × - 1) ( -1 × 1)

vw = 1 - 1

vw = 0

Hence, we can conclude that :

The vectors v and w are orthogonal because their dot product is 0  

Answer:

[tex]\huge\boxed{\$ (4 b + 0.60 a)}[/tex]

Step-by-step explanation:

Bananas represented by b

1 banana costs $4 so b bananas will cost $ 4 b

Apples represented  by a

1 apples costs 0.60 $ so a apples will cost $ 0.60 a

Totally, they will cost:

=> $ (4 b + 0.60 a)

Answer:

hiiiiiiiiiiiiiiiiiiii

Step-by-step explanation:

Answer: A,C, and D

Step-by-step explanation:

Answer:

the answer to this question may be option B, C and D

Answer:

Step-by-step explanation:

Given that:

Mean = 3.34

sample size = 26

sample mean = 2.7

standard deviation = 1.17

level of significance = 0.10

The null hypothesis and the alternative hypothesis can be computed as follows:

[tex]\mathtt{H_o: \mu \geq 3.34} \\ \\ \mathtt{H_1: \mu < 3.34}[/tex]

degree of freedom = n - 1

degree of freedom = 26 -1

degree of freedom =  25

level of significance = 0.10

Since the alternative hypothesis contains <, then the test is left tailed

[tex]\mathtt{t_{\alpha, df} = t_{0.10, 25}}[/tex]

[tex]\mathtt{t_{0.10, 25}}[/tex] = - 1.316

The rejection region therefore consist of all values smaller than - 1.316, therefore ; reject [tex]H_o[/tex] if t < -1.316

The test statistics can be computed as follows:

[tex]t = \dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]t = \dfrac{2.7 - 3.34}{\dfrac{1.17}{\sqrt{26}}}[/tex]

[tex]t = \dfrac{-0.64}{\dfrac{1.17}{5.099}}[/tex]

t = - 2.789

Decision Rule:  To reject the null hypothesis if the t test lies in the rejection region or less than the rejection region.

Conclusion: We  reject the null hypothesis since t = (- 2.789) < -1.316. Then we conclude that  the mean number of residents in the retirement community household is less than 3.34 persons.

Answer:

15 squares

Step-by-step explanation:

60/100 * 25 = 15

Answer:

The p-value of the test is 0.0301 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the company's claim.

Step-by-step explanation:

The company's promotional literature claimed that under 64% fail in the first 1000 hours of their use.

At the null hypothesis, we test if the proportion is of at least 64%, that is:

[tex]H_0: p \geq 0.64[/tex]

At the alternative hypothesis, we test if the proportion is of less than 64%, that is:

[tex]H_1: p < 0.64[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

64% is tested at the null hypothesis:

This means that [tex]\mu = 0.64, \sigma = \sqrt{0.64*0.36}[/tex]

A sample of 900 computer chips revealed that 61% of the chips fail in the first 1000 hours of their use.

This means that [tex]n = 900, X = 0.61[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.61 - 0.64}{\frac{\sqrt{0.64*0.36}}{\sqrt{900}}}[/tex]

[tex]z = -1.88[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion below 0.61, which is the p-value of z = -1.88.

Looking at the z-table, z = -1.88 has a p-value of 0.0301.

The p-value of the test is 0.0301 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the company's claim.

Answer:

P [ X < 67 ] =  0,66,81      or    66,81 %

Step-by-step explanation:

We assume Normal Distribution  N ( μ ; σ )    N ( 76 ; 6 )

z score for 67 is :

z(s) =  (  X - μ  ) /σ

z(s) =  (  67 - 76 ) / 6

z(s) =  - 9 / 6

z(s) = - 1,5

with 1,5 we fnd n z-table area undr the curve  α = 0,6681

Then  P [ X < 67 ] =  0,66,81      or    66,81 %

Answer:

y=-1/7x + 12/7

Step-by-step explanation:

Start by finding the slope

m=(1-0)/(-5-2)

m=-1/7

next plug the slope and the point (-5,1) into point slope formula

y-y1=m(x-x1)

y1=1

x1= -5

m=-1/7

y- 1 = -1/7(x - -5)

y-1=-1/7(x+5)

Distribute -1/7 first

y- 1=-1/7x + 5/7

Add 1 on both sides, but since its a fraction add 7/7

y=-1/7x + (5/7+7/7)

y=-1/7x+12/7

Answer:

After 7 days the crystals will be 57.57 grams.

Step-by-step explanation:

In this the continuous exponential growth formula will be used.

y = A e ^rt

Where A = original amount = 10 grams

y is the growth after 7 days

e is Euler's number= 2.719

t is the time in hours , weeks, years etc.= 7 days

r  is the rate in decimals = 25% = 0.25

Putting the values in the formula:

y = A e ^rt

y = 10 e ^0.25 (7)

Calculating with the calculator

y = 10* 2.719^1.75

y= 57.57 grams.

After 7 days the crystals will be 57.57 grams.

Answer:

57.55g

Step-by-step explanation:

Use the formula f(t) = aert, where a = 10, r = 0.25, and t = 7. This gives f(7) = 10e(0.25)(7) = 10e1.75 ≈ 10(5.755) ≈ 57.55.

5400 dollars

540x10= 5400

Answer:

232.045

Step-by-step explanation:

217 + 253 + 214 + 247 + 217 + 253 + 232 + 246 + 223 + 227 + 229 + 247 + 206 + 241 + 239 + 223 + 222 + 216 + 252 + 209 + 236 + 256 = 5105

5105 / 22 = 232.045454545