Question 20 plz show ALL STEPS and hurry PLEASE

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:

[tex]3n + 3[/tex]

[tex]3(n+1)[/tex]

Step-by-step explanation:

Given

[tex]7n - (4n - 3)[/tex]

Required

Simplify

To simplify the given expression, you start by opening  the bracket

[tex]7n - (4n - 3)[/tex]

[tex]7n - 4n + 3[/tex]

Next, you perform arithmetic operations on like terms

[tex]3n + 3[/tex]

The answer can be further simplified;

Factorize [tex]3n + 3[/tex]

[tex]3(n+1)[/tex]

Hence;

[tex]7n - (4n - 3)[/tex] when simplified is equivalent to [tex]3n + 3[/tex] or [tex]3(n+1)[/tex]

Answer:

3n+n

Step-by-step explanation:

Answer:

Option a is the correct answer

Answer:

1 = C

2 = A

3= B

4 = B

Step-by-step explanation:

Step-by-step explanation:

I assume the length that got cut off is 18.

Use Pythagorean theorem:

x² + 36² = (x + 18)²

x² + 1296 = x² + 36x + 324

972 = 36x

x = 27

[tex]\\ \sf\longmapsto \frac{5}{ \sqrt{7} - \sqrt{3} } + \frac{1}{ \sqrt{7} + \sqrt{3} } \\ \\ \sf\longmapsto \frac{5( \sqrt{7} + \sqrt{3} ) + 1 (\sqrt{7} - \sqrt{3} )}{( \sqrt{7} - \sqrt{3} )( \sqrt{7} + \sqrt{3} )} \\ \\ \sf\longmapsto \frac{5 \sqrt{7} + 5 \sqrt{3} + \sqrt{7} - \sqrt{3} }{( { \sqrt{7} )}^{2} - ( \sqrt{3}) {}^{2} } \\ \\ \sf\longmapsto \frac{5 \sqrt{7} + \sqrt{7} + 5 \sqrt{3} - \sqrt{3} }{7 - 3} \\ \\ \sf\longmapsto \frac{6 \sqrt{7} + 4 \sqrt{3} }{4} [/tex]

Answer:

15 squares

Step-by-step explanation:

60/100 * 25 = 15

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.

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:

[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:

-6

Step-by-step explanation:

Answer:

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

Answer:

y<(x-2)^2

Step-by-step explanation:

To graph this inequality, we first identify the function.

This is a quadratic function y=x^2

The function is translated horizontally to the right two. (x-2)^2

It is also a dotted line, <.

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:

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:

>

Step-by-step explanation:

the less negative the greater the number

Answer:

The p-value of the test is 0.0023 < 0.02, which means that there is sufficient evidence at the 0.02 level to dispute the company's claim.

Step-by-step explanation:

The company's promotional literature claimed that 28% do not fail in the first 1000 hours of their use.

At the null hypothesis, we test that at least 28% do not fail, that is:

[tex]H_0: p \geq 0.28[/tex]

At the alternative hypothesis, we test if the proportion is of less than 28%, that is:

[tex]H_1: p < 0.28[/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.

0.28 is tested at the null hypothesis:

This means that [tex]\mu = 0.28, \sigma = \sqrt{0.28*0.72}[/tex]

Sample of 1800 computer chips revealed that 25% of the chips do not fail in the first 1000 hours of their use.

This means that [tex]n = 1800, X = 0.25[/tex]

Value of the test statistic:

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

[tex]z = \frac{0.25 - 0.28}{\frac{\sqrt{0.28*0.72}}{\sqrt{1800}}}[/tex]

[tex]z = -2.83[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion below 0.25, which is the p-value of Z = -2.83.

Looking at the z-table, z = -2.83 has a p-value of 0.0023.

The p-value of the test is 0.0023 < 0.02, which means that there is sufficient evidence at the 0.02 level to dispute the company's claim.

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.

5400 dollars

540x10= 5400

Answer:

d. all of the above

Step-by-step explanation:

A one sample z test measures whether the mean of a population is greater, less or equal to a specific value. It is called one sampl z test since the standard normal distribution is used in calculation of critical values. It makes use of the null hypothesis and alternative hypothesis in determining if the mean is greater than or equal or less than the reference value. Variance and standard deviation is assumed to be known and at least one population is used

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:

[tex]thank \: you[/tex]

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:

60.36 steps West from centre

85.36 steps North from centre

Step-by-step explanation:

Refer to attached

Musah start point and movement is captured in the picture.

or 360°, so bearing of 315° is same as North-West 45°.

Note. According to Pythagorean theorem, 45° right triangle with hypotenuse of a has legs equal to a/√2.

How far West Is Musah's final point from the centre?

How far North Is Musah's final point from the centre?

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:

[tex]-[ln(x^2-yx-y^2)] = K\\[/tex]

Step-by-step explanation:

Given the differential equation [tex](x+2y)y'=2x-y[/tex], this can also be written as;

[tex](x+2y)\frac{dy}{dx} =2x-y[/tex]

On simplification

[tex](x+2y)\frac{dy}{dx} =2x-y\\\\\frac{dy}{dx} = \frac{2x-y}{x+2y} \\\\let \ y = vx\\\frac{dy}{dx} = v+x\frac{dv}{dx}[/tex]

The differential equation becomes;

[tex]v+x\frac{dv}{dx} =\frac{ 2x-vx}{x+2vx}\\\\v+x\frac{dv}{dx} = \frac{ x(2-v)}{x(1+2v)}\\\\v+x\frac{dv}{dx} = \frac{2-v}{1+2v}\\\\x\frac{dv}{dx} = \frac{2-v}{1+2v} - v\\\\x\frac{dv}{dx} = \frac{(2-v)-v(1+2v)}{1+2v}\\\\x\frac{dv}{dx} = \frac{2-v-v-2v^2}{1+2v}\\\\x\frac{dv}{dx} = \frac{2-2v-2v^2}{1+2v}[/tex]

[tex]\frac{dx}{x} = \frac{1+2v}{2-2v-2v^2}dv\\\\integrating\ both \ sides\\\\[/tex]

[tex]\int\limits \frac{dx}{x} = \int\limits \frac{1+2v}{2-2v-2v^2}dv\\\\lnx = \frac{1}{2} \int\limits \frac{1+2v}{1-v-v^2}dv\\\\lnx + C = -\frac{1}{2}ln(1-v-v^2)[/tex]

[tex]C = -\frac{1}{2}ln(1-v-v^2) - lnx \\\\ -ln(1-v-v^2) - 2lnx = 2C\\\\-[ln(1-v-v^2) + lnx^2] = 2C\\\\-[ln(1-v-v^2)x^2] = 2C\\since\ v = y/x\\\\- [ln(1-y/x-y^2/x^2)x^2] = K\\\\-[ln(x^2-yx-y^2)] = K\\[/tex]

Hence the solution to the differential equation is [tex]-[ln(x^2-yx-y^2)] = K\\[/tex]

Answer:

Length:8

Width:5.5

Step-by-step explanation:

We're given area = 44m^2, and the formula for the area of a rectangle is the length multiplied by the width. So,

A = L * w = 44

We're given that the length is 3m shorter than 2 times the width, which is 2w - 3. "2w" is the same as "2 times the width", and the 3 is subtracted because it says 3m shorter than 2 times the width. So L = 2w - 3, and we can substitute that into our equation above.

(2w - 3)(w) = 44

2w^2 - 3w - 44 = 0

Use the quadratic formula here.

x = {3 ± √(-3)^2 - 4(-44)(2)}/2(2)

= {3 ± √9 + 352}/4

= (3 ± 19)/4

You'll get two answers, but remember, we're measuring the length of the sides of shapes, so it has to be positive. It's impossible to have negative lengths, so we're going to stick with the (3 + 19)/4 answer, which is 22/4, which is 5.5. However, we are not finished yet. This is just the width. Now we need to plug it into the equation for length, which was 2w - 3

2(5.5) - 3 = 11 - 3 = 8

The length is 8m and the width is 5.5m.

Answer:

1023.75

Step-by-step explanation:

The sum of a geometric sequence is

sum = a( 1 - r^n) / (1-r)

where a is the first term  r is the common ratio and  r^n is the nth term

We need to find the common ratio

r = 256/512 = 1/2

sum = 512 ( 1 - 1/2^12) / ( 1-1/2)

       =512( 1-.000244141) / (.5)

       =512(.999755859) /.5

     =1023.75

Answer:

1023.75

Step-by-step explanation:

sum = a( 1 - r^n) / (1-r)

a1 = 512

n = 12

r = 256 / 512 = 1/2

                              512 (1 - 1/2¹²)

therefore.. sum =  ------------------ = 1023.75

                                   1 - 1/2

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.