Two cyclists, 112 miles apart, start riding toward each other at the same time. One cycles 3 times as fast as the other, and they meet after 4 hours of riding.

a. Write an equation using the information as it is given above that can be solved to answer this problem. Use the variable r to represent the speed of the slower cyclist.

b. What are the speeds of the two cyclists? Put both values in the answerbox, separated with a comma, and select the appropriate units.

Answer:

84.13.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

For this question:

[tex]\mu = 143, \sigma = 8[/tex]

What percentage of homes will have a monthly utility bill of more than $135?

This is 1 subtracted by the pvalue of Z when X = 135. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{135 - 143}{8}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587

1 - 0.1587 = 0.8413

84.13% of homes will have a monthly utility bill of more than $135. Excluding the percentage, the answer is 84.13.

Answer:

Step-by-step explanation:

If we assume the length and width are integer numbers of centimeters, we can look at the factors of 330:

  330 = 1×330 = 2×165 = 3×110 = 5×66 = 6×55 = 10×33 = 11×30 = 15×22

The factors in this last pair differ by 7, so represent the width and length of the rectangle.

The rectangle's length and width are 22 cm and 15 cm, respectively.

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer:

[tex]= 24 {x}^{4} + 32 {x}^{3} + 32 {x}^{2} + 16x + 10 \\ [/tex]

Step-by-step explanation:

[tex](4 {x}^{2} + 2)(6 {x}^{2} + 8x + 5) \\ 4 {x}^{2} (6 {x}^{2} + 8x + 5) + 2(6 {x}^{2} + 8x + 5) \\ 24 {x}^{4} + 32 {x}^{3} + 2 0{x}^{2} + 12 {x}^{2} + 16x + 10 \\ = 24 {x}^{4} + 32 {x}^{3} + 32{x}^{2} + 16x + 10 \\ [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

The complete question is;

Instructions:Select the correct answer from each drop-down menu.

The side length of the square in the figure is 8 cm.

The radius of the inscribed circle is [ (32)^(1/2), 16, 4, 32 ] cm, and the radius of the circumscribed circle is [ (32)^(1/2), 2(32)^(1/2), (128)^(1/2), 128 ] cm.

Image is attached.

Answer:

Radius of inscribed circle = 4 cm

Radius of circumscribed circle = 32^(1/2) cm

Step-by-step explanation:

The square has a side of 8cm.

Thus,the diameter of the inscribed circle would be same as a side of the square.

So, if diameter = 8cm, then, radius of inscribed = 8/2 = 4cm

Now, to the circumscribed circle, the diagonal of the square would be the diameter of the circumscribed circle. It can be calculated with Pythagoreas theorem.

So, d² = 8² + 8²

d² = 64 + 64

d² = 128

d = √128

Expressing it in surd form gives;

d = √32 x √4

d = 2√32 cm

So radius of circumscribed circle = (2√32)/2 = √32 cm or 32^(1/2) cm

Answer:

4 and 32^1/2

Step-by-step explanation:

i just did it on plato :))

Answer:

The percentage of hotels with rates between 120 and 144 euros is 84%.

Step-by-step explanation:

We know that the distribution of the nightly rate for a hotel in Rome is bell shaped with a mean of 138 euros and a standard deviation of 6 euros.

We want to know the proportion of hotels between 120 and 144 euros.

We can approximate the distribution to a normal distribution and calculate the z-score for both boundaries:

[tex]z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{120-138}{6}=\dfrac{-18}{6}=-3\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{144-138}{6}=\dfrac{6}{6}=1[/tex]

Then, we can calculate the proportion as the probability of having rates between 120 and 144:

[tex]P=P(120<X<144)=P(-3<z<1)\\\\P=P(z<1)-P(z<-3)\\\\P=0.8413-0.0013\\\\P=0.8400[/tex]

Then, we can conclude that the percentage of hotels with rates between 120 and 144 euros is 84%.

Step-by-step explanation:

[tex]7 \times \frac{3}{5} + 2 \times \frac{4}{5} \\ \frac{38}{5} + \frac{14}{5} \\ \frac{38 + 14}{5} \\ \frac{52}{5} \\ 10 \times \frac{2}{5} [/tex]

Answer:

Step-by-step explanation

7 [tex]\frac{3}{5}[/tex] + 2  [tex]\frac{4}{5}[/tex]

= 38/5 + 14/5

=52/5

Answer:

5) 8

6) True, a trapezium has at least 1 parallel side, and a parallelogram has 2.

7) I can't see where angle z is..., but x=42 and y= 96

Step-by-step explanation:

A rhombus has all sides of equal length, thus, if DC is 5, then all the other sides are also 5.

We see that AC is 6, and OC will be 3, or 6/2.

The pythagorean theorem shows that OD is 4, and BD is 8.

42+42=84

180-84=96

Answer:

5. BD = 8 cm

6. See explanation below.

7. x = 42; y = 96; z = 64

Step-by-step explanation:

5.

DC = 5 cm

The diagonals of a rhombus bisect each other, so since AC = 6 cm, OC = 3 cm.

The diagonals of a rhombus are perpendicular to each other, so triangle DOC is a right triangle with right angle DOC.

a^2 + b^2 = c^2

(DO)^2 + (OC)^2 = (DC)^2

(DO)^2 + (3 cm)^2 = (5 cm)^2

(DO)^2 + 9 cm^2 = 25 cm^2

(DO)^2 = 16 cm^2

DO = 4 cm

Since BD = 2DO,

BD = 2(4 cm) = 8 cm

Answer: BD = 8 cm

6.

There are different definitions of trapezium. In the U.S., trapezium is a quadrilateral, none of whose sides are parallel. According to the U.S. definition of trapezium, then, no parallelogram is a trapezium.

According to the UK definition of trapezium, a trapezium is a quadrilateral with at least 2 parallel sides. That means the other two sides may or may not be parallel. According to this definition, then a parallelogram is always a trapezium.

8.

Triangle ADB is isosceles with AD = AB. That meakes their opposite angles congruent.

x = m<ADB = 42

42 + 42 + y = 180

y = 96

In a kite, there are two pairs of congruent sides. DC = BC, so z = m<BDC

z + z + 52 = 180

2z = 128

z = 64

Answer:

volume = 36 cm³

Step-by-step explanation:

The volume of a rectangular prism = lwh

where

w = width

l = length

h = height

The base of a rectangular prism is a rectangle and the area of a rectangle is the product of length and width. Therefore,

base area of the rectangular prism = length × width

base area = lw

Base area of the rectangular prism =  12 cm²

Recall, the formula of the volume of a rectangular prism is the product of the length, width and height.

volume  = lwh

substitute lw value in the formula above

volume = 12 × 3

volume = 36 cm³

Answer:

The 95% confidence interval for the true proportion of all medical students who plan to work in a rural community is (0.0525, 0.1075).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 375, \pi = \frac{30}{375} = 0.08[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.08 - 1.96\sqrt{\frac{0.08*0.92}{375}} = 0.0525[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.08 + 1.96\sqrt{\frac{0.08*0.92}{375}} = 0.1075[/tex]

The 95% confidence interval for the true proportion of all medical students who plan to work in a rural community is (0.0525, 0.1075).

Step-by-step explanation:

2 hrs 45 min + 3 hrs 35 min

= 5 hrs 80 min

60 min = 1 hr

*80 min = 1 hr + 20 min

5hrs 80 min

= 5 hrs + 1 hr + 20 min

= 6 hrs 20 min

Answer:

6 hour 20 minutes

Step-by-step explanation:

Add the two time measurements separately.

2 hours  +  3 hours  =  5 hours

35 minutes  +  45 minutes  =  80 minutes

Now, simplify the measurements to the lowest terms.  You can simplify the minutes by subtracting 60 from the value.  60 minutes is 1 hour.  The number you get after subtracting is how many minutes there are.

80 - 60 = 20

80 minutes  =  1 hour 20 minutes

Now add the two measurements together.

5 hours  +  1 hour 20 minutes  =  6 hour 20 minutes

Answer:

The number of 7th graders exceed that of the number of 5th and 6th graders taken together by 5.88%.

Step-by-step explanation:

I am going to say that:

x is the proportion of 5th graders.

y is the proportion of 6th graders.

z is the proportion of 7th graders.

The number of 6th graders in RSM summer camp to that of 7th graders was 4 to 11

This means that:

[tex]\frac{y}{z} = \frac{4}{11}[/tex]

So

[tex]11y = 4z[/tex]

[tex]y = \frac{4z}{11}[/tex]

The number of 5th graders to that of the 6th graders was 13 to 9.

This means that:

[tex]\frac{x}{y} = \frac{13}{9}[/tex]

[tex]9x = 13y[/tex]

[tex]x = \frac{13y}{9}[/tex]

All of them is 100%

This means that:

[tex]x + y + z = 1[/tex]

We need to find z.

[tex]y = \frac{4z}{11}[/tex]

[tex]x = \frac{13y}{9} = \frac{13*4z}{9*11} = \frac{52z}{99}[/tex]

Then

[tex]x + y + z = 1[/tex]

[tex]\frac{52z}{99} + \frac{4z}{11} + z = 1[/tex]

The lcm(least common multiple) between 11 and 99 is 99. Then

[tex]\frac{52z + 9*4z + 99z}{99} = 1[/tex]

[tex]187z = 99[/tex]

[tex]z = \frac{99}{187}[/tex]

[tex]z = 0.5294[/tex]

By what percent did the number of 7th graders exceed that of the number of 5th and 6th graders taken together ?

z(7th graders) is 52.94%.

x + y(5th and 6th graders) is 100 - 52.94 = 47.06%

52.94 - 47.06 = 5.88

The number of 7th graders exceed that of the number of 5th and 6th graders taken together by 5.88%.

Answer:

Nancy can cut 6 full circles

Step-by-step explanation:

Length of aluminium strip = [tex]7 \frac{1}{7} cm[/tex]

Length of aluminium strip =[tex]\frac{50}{7} cm[/tex]

Breadth of aluminium strip =[tex]1 \frac{3}{7} cm[/tex]

Breadth of aluminium strip =[tex]\frac{10}{7} cm[/tex]

Area of strip = [tex]Length \times Breadth = \frac{50}{7} \times \frac{10}{7} =\frac{500}{49}[/tex]

Diameter of circle = [tex]1 \frac{3}{7} cm[/tex]

Diameter of circle = [tex]\frac{10}{7} cm[/tex]

Radius of circle =[tex]\frac{10}{ 7 \times 2}=\frac{10}{14} cm[/tex]

Area of circle =[tex]\pi r^2 = \frac{22}{7} \times (\frac{10}{14})^2=\frac{550}{343} cm^2[/tex]

No. of circles can be cut = [tex]\frac{\frac{500}{49}}{\frac{550}{343}}=6.3636[/tex]

So,Nancy can cut 6 full circles

Answer:

The new standard error is [tex]e_{new} = 23.4[/tex]

Step-by-step explanation:

 From the question we are told that

   The standard  error is  [tex]e = 52.4[/tex]

Generally the standard error is mathematically represented as

       [tex]e = \frac{6}{\sqrt{n} }[/tex]

Where n is the sample size

for the original standard error we have

          [tex]52.4 = \frac{6}{\sqrt{n} }[/tex]

Now sample size is quintuple

     [tex]e_{new} = \frac{6}{\sqrt{5 * n} }[/tex]

    [tex]but \ \ 52.4 = \frac{6}{\sqrt{n} }[/tex]

  So    [tex]e_{new} = \frac{52.4}{\sqrt{5} }[/tex]

          [tex]e_{new} = 23.4[/tex]

Answer:

P = 10z + 10 units.

Step-by-step explanation:

To find the perimeter of a rectangle, you can use the formula P = 2l + 2w.

If one side is '3z + 2' and the other is '2z + 3', we can plug these into the equation:

P = 2(3z + 2) + 2(2z + 3).

Distributing the 2's gives us:

P = 6z + 4 + 4z + 6

Combine like terms, resulting in the final answer:

P = 10z + 10 units.

Answer:

[tex] \bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}}) [/tex]

And the standard deviation for the sample mean would be given by:

[tex] \sigma_{\bar X}= \frac{1.5}{\sqrt{25}}= 0.3[/tex]

Step-by-step explanation:

For this case we know that the amount of cheese inserted into the ravioli is normally distributed. And we have the following info given;

[tex] \bar X =15[/tex] the sample mean

[tex]s= 1.5[/tex] the sample deviation

[tex] n=25[/tex] the sample size

And for this case we know that the sample size is large enough in order to apply the central limit theorem and the distribution for the sample mean would be given by:

[tex] \bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}}) [/tex]

And the standard deviation for the sample mean would be given by:

[tex] \sigma_{\bar X}= \frac{1.5}{\sqrt{25}}= 0.3[/tex]

Answer:

a) (iv) Poisson.

b) E(X)=V(X)=λ=4.8

c) E(Y)=24,000

V(Y)=120,000,000

Step-by-step explanation:

We can appropiately describe this random variable with a Poisson distribution, as the probability of having a pothole can be expressed as a constant rate per mile (0.16 potholes/mile) multiplied by the stretch that correspond to the county (30 miles).

The parameter of the Poisson distribution is then:

[tex]\lambda=0.16\cdot 30=4.8[/tex]

b) The expected value and variance of X are both equal to the parameter λ=4.8.

c) If we define Y as:

[tex]Y=5000X[/tex]

the expected value and variance of Y are:

[tex]E(Y)=E(5,000\cdot X)=5,000\cdot E(X)=5,000\cdot 4.8=24,000\\\\\\ V(Y)=V(5000\cdot X)=5000^2\cdot V(X)=25,000,000\cdot 4.8=120,000,000[/tex]

Answer:

[tex] \boxed{(f + g)(x) = {x}^{2} - x + 6} [/tex]

Given:

[tex]f(x) = {x}^{2} + 1 \\ \\ g(x) = 5 - x[/tex]

To Find:

[tex](f + g)(x) = f(x) + g(x)[/tex]

Step-by-step explanation:

[tex] = > f(x) + g(x) = ({x}^{2} + 1) + (5 - x) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} + 1 + 5 - x\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} + 6 - x\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} - x + 6[/tex]

Answer:

A.)359.2, B.)2.5 uf

Step-by-step explanation:

E / I = R

208 / 1.04 = 200 ohms

2*pi*f*L = Xl

6.28*400*.143 = 359.2 ohm

1 / (2*pi*f*Xc) = c

1 /(6.28*400*159.2) = 2.5 uf

Answer:

Step-by-step explanation:

Find the values of p for which the following integral converges:

∫[infinity]e 1/(x(ln(x))^p)dx

Input youranswer by writing it as an interval. Enter brackets or parentheses in the first and fourth blanks as appropriate, and enter the interval endpoints in the second and third blanks. Use INF and NINF (in upper-case letters) for positive and negative infinity if needed. If the improper integral diverges for all p, type an upper-case "D" in every blank.

​Values of p are in the interval ,

For the values of p at which the integral converges, evaluate it. Integral =

Recall that

[tex]\int\limits^{\infty}_1 \frac{1}{x^p} dx[/tex]

converge if p > 1  and converge to [tex]\frac{1}{p-1}[/tex] and divertgent if p ≤ 1

Now, let u = Inx ⇒ du = 1/x dx

: e ≤ x ≤ ∞ ⇒ 1 ≤ u < ∞

⇒ [tex]\int\limits^{\infty}_e \frac{dx}{x(Inx)^p} = \int\limits^{\infty}_1 {x} \frac{du}{u^p}[/tex]

converge if p > 1  and converge to [tex]\frac{1}{p-1}[/tex] and divertgent if p ≤ 1

[tex]\text {Integral}=\frac{1}{p-1}[/tex]

Answer:

the correct option is d. 0.02

Step-by-step explanation:

We have the following events:

x: A drought occurd

y: Water rationing.

Therefore, according to the plaster we have:

P [x] = 0.20

P [y | x] = 0.10

Now P [it is a drought and water rationing happens] =

P [x n y] = P [y | x] * P [x] = 0.10 * 0.20 = 0.02

Which means that the correct option is d. 0.02

Answer:

x=24.8

Step-by-step explanation:

Answer:

Jamal travels at a speed of 5 mph and Diego travels at a speed of 12 mph.

Step-by-step explanation:

Jamal's speed is of x mph.

Diego's speed is of (x + 7) mph.

Opposite directions.

This means that each hour, they will be x + x + 7 = 2x + 7 miles apart.

After 4 hours they are 68 miles apart, how fast is each traveling?

Using a rule of three.

1 hour - 2x + 7 miles apart.

4 hours - 68 miles apart.

[tex]4(2x + 7) = 68[/tex]

[tex]8x + 28 = 68[/tex]

[tex]8x = 40[/tex]

[tex]x = \frac{40}{8}[/tex]

[tex]x = 5[/tex]

Jamal travels at a speed of 5 mph and Diego travels at a speed of 12 mph.

Answer:

Nitrogen

Step-by-step explanation:

Nitrogen and oxygen are by far the most common; dry air is composed of about 78% nitrogen (N2) and about 21% oxygen (O2). Argon, carbon dioxide (CO2), and many other gases are also present in much lower amounts; each makes up less than 1% of the atmosphere's mixture of gases. Hope this helped!

Answer:

The sampling error =  0.06

Step-by-step explanation:

From the given information:

Let represent [tex]\beta[/tex] to  be the population proportion = 0.4

The sample proportion be P = 0.46   &

The sample size be n = 100

The population standard duration can be expressed by the relation:

Population standard duration [tex]\sigma = \sqrt{\dfrac{\beta(1- \beta)}{n}}[/tex]

[tex]\sigma = \sqrt{\dfrac{0.4(1-0.4)}{100}}[/tex]

[tex]\sigma = \sqrt{\dfrac{0.4(0.6)}{100}}[/tex]

[tex]\sigma = 0.049[/tex]

The sample proportion = 0.46

Then the sampling error  = P - [tex]\beta[/tex]

The sampling error  = 0.46 - 0.4

The sampling error =  0.06

Answer:

the expected value of the frocks​ (EV) is 2800

Step-by-step explanation:

the expected value of the frocks= (probability of stylish* worth)+(probability of passe* worth)

If the public view it as being the latest​ style, the frocks will be worth ​$10,000. ​

if the frocks are viewed as​ passe, they will be worth only ​$2,000.

If the probability that they are stylish is 10​%

probability of stylish = 10000

worth = 10%

probability of passe = 2000

[tex]=10 \%*10000+(1-10 \%)*2000\\\\=0.1\times 10000+(1-0.1)\times2000\\\\=1000+(0.9)\times2000\\\\=1000+1800\\\\=2800[/tex]

Therefore, the expected value of the frocks​ (EV) is 2800

Answer:

[tex] \boxed{Area \: of \: circle = 5538.96 {in}^{2}} [/tex]

Step-by-step explanation:

Radius (r) = 42 in.

Area of circle = πr²

= 3.14 × (42)²

= 3.14 × 1764

= 5538.96 in²

Answer:

6

Step-by-step explanation:

4-3x54÷9

How I'd do it is separate it:

4-3=1

Then 1x54=54

Then 54/9=6

Answer:

6

Step-by-step explanation:

[tex]4-3*54/9\\4-3 =1\\1*54 =54 \\54/9 =6[/tex]

x = # of CDs Walter has

3x - number of CDs Brian has

144 - total

x + 3x = 144

4x = 144

x = 144/4

x = 36

Answer: D. 36

Answer:

D.36

Step-by-step explanation:

X+3X=144

4X=144 (THEN DIVIDE BOTH SIDES B 4)

X=144/4=36

Answer:

a) 87.91% probability that at most three used the emergency room

b) 20.13% probability that exactly three used the emergency room.

c) 3.28% probability that at least five used the emergency room​

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they use the emergency room, or they do not. The probability of a person using the emergency room is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Sample of 10 people:

This means that [tex]n = 10[/tex]

20% of the people in a community use the emergency room at a hospital in one year

This means that [tex]p = 0.2[/tex]

a) At most three used the emergency room

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074[/tex]

[tex]P(X = 1) = C_{10,1}.(0.2)^{1}.(0.8)^{9} = 0.2684[/tex]

[tex]P(X = 2) = C_{10,2}.(0.2)^{2}.(0.8)^{8} = 0.3020[/tex]

[tex]P(X = 3) = C_{10,3}.(0.2)^{3}.(0.8)^{7} = 0.2013[/tex]

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.1074 + 0.2684 + 0.3020 + 0.2013 = 0.8791[/tex]

87.91% probability that at most three used the emergency room

b) Exactly three used the emergency room

[tex]P(X = 3) = C_{10,3}.(0.2)^{3}.(0.8)^{7} = 0.2013[/tex]

20.13% probability that exactly three used the emergency room.

c) At least five used the emergency room​

[tex]P(X \geq 5) = 1 - P(X < 5)[/tex]

In which

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

From 0 to 3, we already have in a).

[tex]P(X = 4) = C_{10,4}.(0.2)^{4}.(0.8)^{6} = 0.0881[/tex]

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.1074 + 0.2684 + 0.3020 + 0.2013 + 0.0881 = 0.9672[/tex]

[tex]P(X \geq 5) = 1 - P(X < 5) = 1 - 0.9672 = 0.0328[/tex]

3.28% probability that at least five used the emergency room​

Answer:

The minimum separation is  [tex]z = 1.0292 *10^{-4} \ m[/tex]

Step-by-step explanation:

    From the question we are told that

         The  reading randomized variable are [tex]D= 2.5 \ mm[/tex] and [tex]d = 38 \ cm[/tex]

          The diameter of the pupil is  [tex]d = 2.5 \ mm = \frac{2.5}{1000} = 0.0025 \ m[/tex]

            The distance from the paper is [tex]D = 38 \ cm = 0.38 \ m[/tex]

            The wavelength is  [tex]\lambda = 555 \ nm = 555 * 10 ^{-9} m[/tex]

Generally the Raleigh's equation for resolution is  

             [tex]\theta = 1.22 [\frac{\lambda}{D} ][/tex]

substituting values

               [tex]\theta = 1.22 * \frac{555*10^{-9}}{0.0025}[/tex]  

              [tex]\theta = 2.7084*10^{-4} \ rad[/tex]

The minimum separation of two dots is mathematically represented as

            [tex]z = \theta d[/tex]

substituting values

            [tex]z = 2.7084*10^{-4} * 0.38[/tex]

             [tex]z = 1.0292 *10^{-4} \ m[/tex]