Determine the domain of the following graph:

a. When p is very small or very large in the binomial distribution, it is feasible to estimate the binomial probabilities with normal probabilities.

b.  If two variables are independent, they do not rely on one another.

c. combining two decks has little effect on the likelihood of obtaining exactly two aces in 13 draws.

a. When p is very small or very large in the binomial distribution, it is feasible to estimate the binomial probabilities with normal probabilities. If np ≥ 5 and nq ≥ 5, where q = 1 − p, the binomial distribution can be estimated with a normal distribution with a mean of μ = np and a standard deviation of σ = npq.

b. If two variables are independent, they do not rely on one another. If X and Y are independent, the covariance of the variables will be 0, which means Cov(X,Y) = 0. This is because if the variables are uncorrelated, the covariance will be 0, since Cov(X,Y) = E(XY) - E(X)E(Y).

c. The likelihood of drawing exactly two aces from 13 draws would not change if two decks were combined (so 8 out of 104 cards would be aces). The original probability of getting an ace when drawing from a single deck is: 4/52. The probability of not drawing an ace is therefore: 48/52.

We can use the binomial distribution to calculate the probability of getting exactly 2 aces in 13 draws: P(X=2) = (13 C 2) * (4/52)^2 * (48/52)^11 = 0.3182.

If we use the same approach with two decks, we get: P(X=2) = (13 C 2) * (8/104)^2 * (96/104)^11 = 0.3183.

As a result, combining two decks has little effect on the likelihood of obtaining exactly two aces in 13 draws.

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Step-by-step explanation:

using SOH CAH TOA

0=30°, hyp =x,adj=y,opp=4

sin0=opp/hyp

sin 30=4/x

0.5=4/x

0.5x=4

divide both sides by 0.5

x=8

using c²=a²+b²

where c=Hypotenuse=8

a=opposite=4

b=Adjacent=y

making b the subject of formula

b²=c²-a²

b²=8²-4

b²=64-16

b²=48

b=√48

b=4√3

Answer:

Step-by-step explanation:

To convert square meters to square centimeters, we need to multiply by the conversion factor (100 cm / 1 m)^2.

So,

3.9 m² = 3.9 × (100 cm / 1 m)²

3.9 m² = 3.9 × 10,000 cm²

3.9 m² = 39,000 cm²

Therefore, 3.9 square meters is equal to 39,000 square centimeters.

Answer:

40

Step-by-step explanation:

so (48/120)× 100%=40%

Answer:

28

Step-by-step explanation:

28 times 2 = 56

28 times 1 = 28

56 + 28 = 84

Answer:

3+x=11

Step-by-step explanation:

Answer is $8 for an children and $15 for adult

1 ticket would be $8

Answer:

The children ticket cost is 8$

Step-by-step explanation:

I. Given a = adult and c = children

10a + 10c = 200  => 1st day

13a + 2c = 172     => 2nd day

II. Multiply 2nd day with 5

65a + 10c = 860  => simulate

III. Eliminate c value by simulate - 1st day

55a + 0 = 660

a = 660/55

a = 12 or adult ticket cost is 12$

IV. Find children ticket cost by replace a value in 2nd day

13(12) + 2c = 172

156 + 2c = 172

2c = 172 - 156

c = 8 or children ticket cost is 8$

Hope that help :)

Given:

The function is

\(f(x)=7x+11\)

To find:

The domain, range, and intercepts of the function.

Solution:

We have,

\(f(x)=7x+11\)

It is a linear function, and domain and range of these types of functions  are all real numbers.

\(Domain:(-\infty,\infty)\)

\(Range:(-\infty,\infty)\)

Put x=0 in f(x), to find the y-intercept.

\(f(0)=7(0)+11\)

\(f(0)=0+11\)

\(f(0)=11\)

So, the y-intercept is 11.

Put f(x)=0 in f(x), to find the x-intercept.

\(0=7x+11\)

\(0-11=7x\)

\(-11=7x\)

Divide both sides by 7.

\(\dfrac{-11}{7}=x\)

So, the x-intercept is \(\dfrac{-11}{7}\).

Therefore, \(Domain:(-\infty,\infty), Range:(-\infty,\infty), x-intercept : (\dfrac{-11}{7},0),\) \(y-intercept :11\).

Answer:

182

Step-by-step explanation:

The given statement "the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring." is False.

The union of two events A and B represents the event that at least one of the events A or B occurs. The probability of the union of two events can be calculated using the formula:

P(A or B) = P(A) + P(B) - P(A and B)

On the other hand, the intersection of two events A and B represents the event that both events A and B occur. The probability of the intersection of two events can be calculated using the formula:

P(A and B) = P(A) * P(B|A)

where P(B|A) is the conditional probability of B given that A has occurred.

It is possible for the probability of the union of two events to be greater than the probability of the intersection of two events if the two events are not mutually exclusive.

In this case, the probability of both events occurring together (the intersection) may be relatively small, while the probability of at least one of the events occurring (the union) may be relatively high.

In summary, the probability of the union of two events occurring can sometimes be greater than the probability of the intersection of two events occurring, depending on the relationship between the events.

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Step-by-step explanation:

24 ÷ 3:4

= 24 / 3 / 4

Basics

a / b / c = a / b / c / 1

....1 is normally invisible since a number

divided by 1 is itself. i wrote 1 down to show the reciprocal property.

a/b/c/1 = a/b × 1/c = a/bc ...Flip the number you're dividing with.

24/3/4 = 1/24 × 3/4 = 3 / 96 = 3 × 1 / 3 × 32 ...cancel the 3s'

= 1 / 32.

Answer:

a) The sum of numbers p and 4 is 15.

Step-by-step explanation:

I'm not sure but hope it helps.

Answer:

C-D = 6

A-B = 3.25

D = 118

Step-by-step explanation:

C-D = 6 because the line is the same as B-C

A-B = 3.25 because the line is the same as A-D

D = 118 because the angle of B is vertically opposite to D

The major problem with point estimation is that it provides only a single point in its estimate. This means that it does not take into account the possible variability or uncertainty that comes from sampling error when estimating population parameters.

The major problem with point estimation is that it provides only a single point in its estimate, which may not accurately represent the true population parameter. This is because point estimation relies on a single sample to estimate the parameter, and does not take into account the variability that could result from different samples.

Additionally, point estimation cannot be utilized to estimate population parameters directly, as it only provides an estimate for the specific sample used. However, point estimation can still be useful for obtaining rough estimates of parameters, particularly when more precise methods are not available or feasible. It is important to keep in mind that point estimation is subject to sampling error, which can affect the accuracy of the estimate. To minimize this error, it is often necessary to use larger sample sizes or employ other sampling techniques such as stratified sampling or random sampling.

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a) a minimum of 3 doctors required so that at least 70% of the arriving patients.

b) a minimum of 7 doctors are required so that the average time a patient waits for treatment is no more than 30 minutes

a) Minimum number of doctors required so that at least 70% of the arriving patients can receive treatment immediately

Formula used:

The number of patients arriving in an hour: λ = 9

Treatment time: μ = 6 minutes

Per the Little’s law, the waiting time is proportional to the average number of patients present at any given time.

λ/μ is the average number of patients present at any given time.

If there are k servers present in the ER, the number of patients they can serve is given by kμ.

Hence, the percentage of patients who have to wait is given by:

Percentage of patients waiting = λ / (kμ + λ)

Percentage of patients receiving treatment immediately = kμ / (kμ + λ)

Thus, we can now form an equation as:

kμ / (kμ + λ) ≥ 0.7

=> kμ / (kμ + 9) ≥ 0.7

=> k ≥ 3 doctors (Approximately)

Therefore, a minimum of 3 doctors required so that at least 70% of the arriving patients can receive treatment immediately.

b) Minimum number of doctors required so that the average time a patient waits for treatment is no more than 30 minutes as advertised

The percentage of patients who have to wait = λ / (kμ + λ)

Again, let us use the Little's law to find the average time patients spend waiting in the queue, which is equal to

λ / (k(μ - λ/k)).

We are given that the waiting time should not be more than 30 minutes, which can be converted to 0.5 hours.

Thus:

λ / (k(μ - λ/k)) ≤ 0.5

=> 9 / (k(0.1 - 1/k)) ≤ 0.5

=> 18 ≤ k(0.1 - 1/k)

=> 0.1k - 1 ≤ 18/k

=> 0.1k² - k - 18 ≥ 0

Using the quadratic formula, the solution is k = 6.66, which is rounded up to 7, and k = 2.5, which is rounded up to 3.

Therefore, a minimum of 7 doctors are required so that the average time a patient waits for treatment is no more than 30 minutes as advertised and a minimum of 3 doctors are required so that the average time a patient waits for treatment is no more than 15 minutes.

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Answer:

slope

Step-by-step explanation:

y = mx + c

where m is the slope of the line

Answer: Your answer should be  294 cm2.

Answer:

294 cm²

Step-by-step explanation:

A cube has 6 congruent square faces. The surface area is the sum of the area of the 6 faces.

area of one face = 7 × 7 = 49 cm²

surface area = 6 × 49 = 294 cm²

Answer:

Top left because its 3:15-4:45

Step-by-step explanation:

Answer:

the top left one

Step-by-step explanation:

each line represents 15 minutes

it starts at 3:15 and end at 4:45 and there is a 1 and a half hour difference between these two times

Answer:

Multiply the 3*5

Step-by-step explanation:

x+3x -4.2

Substitute x=5

5 + 3*5 -4.2

PEMDAS states multiply first

Multiply the 3*5

5 + 15 -4.2

Answer:

a!

Step-by-step explanation:

yw

Complete Question

In triangle ABC: AC=10 , AB=5., Angle C = 30 degrees.  

In Triangle DEF: ED= 7.5 , DF=15, Angle F =30 degrees , Angle E = 90 degrees.  

Answer:

A, D and E

Step-by-step explanation:

The diagram is drawn and attached below.

Writing it backwards:

Also,

Therefore, A, D and E are the similarity statements that describe the relationship between the two triangles.

Answer:

A, D and E

Step-by-step explanation:

Answer:

Just give Levi brainliest I just need points ;-;

Step-by-step explanation:

Answer is C

Answer:

Answer is C

Step-by-step explanation:

Just did the question. Got it correct.

i) The multiplication of (3.1x\(10^0\)) and (1.5x10) results in 4.65x\(10^1\).

j) The division of (3.1x10) by (1.5x\(10^{-1\)) equals 2.07x\(10^1\).

i) To multiply numbers in scientific notation, we multiply the coefficients (3.1 and 1.5) and add the exponents (0 and 1) together. In this case, 3.1 multiplied by 1.5 gives us 4.65. Adding the exponents, \(10^0\) multiplied by \(10^1\) results in \(10^1\). Therefore, the final result is 4.65x\(10^1\).

j) When dividing numbers in scientific notation, we divide the coefficients (3.1 and 1.5) and subtract the exponents (1 and -1) from each other. Dividing 3.1 by 1.5 gives us approximately 2.07. Subtracting the exponents, \(10^1\)divided by \(10^{-1\) is equivalent to \(10^{(1-(-1))}\) which simplifies to 10^2. Hence, the result is 2.07x\(10^1\).

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Lower class limits are 15, 25, 35, 45, 55, 65, 75, Upper class limits are 24, 34, 44, 54, 64, 74, 84, Class width are 10 (all classes have a width of 10), Class midpoints are 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5, Class boundaries are [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) and Number of individuals included in the summary is 76.

Here are the details for the given frequency distribution:

Lower class limits are the least number among the pair

Here, Lower class limits are 15, 25, 35, 45, 55, 65, 75 respectively.

Upper class limits are the greater number among the pair

Here, upper limit class are 24, 34, 44, 54, 64, 74, 84 respectively.

Class width is the difference between the Lower class limits and Upper class limits which is 10 (all classes have a width of 10).

Class midpoints is the middle point of the lower class limits and Upper class limits which is 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5 respectively.

Class boundaries are the extreme points of the classes which are  [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) respectively.

Number of individuals = 27 + 33 + 14 + 4 + 6 + 1 + 1

                                     = 76

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Answer:

120 in³

Step-by-step explanation:

10 x 4 x 3 = 120

Answer:

-2.25

Step-by-step explanation:

9(1-x) = 27Y

9-9x =27y

-9x -27y = -9  multiply all terms by -1

9x +27y =9   equation (1)

x-y= -11/2 equation (2)

by solving 2 equations

x= -3.875

y= 1.625

∴ x+ y = 1.625 +(-3.875) = -2.25

Answer:

given radius =6

Area of triangle =1/2*base*height

=1/2*6*6=18

area of quadrant =1/4πr^2

=1/4*22/7*6*6=22/7*9=198/7=28.2

area of shaded region =area of quadrant -area of triangle

=28.2-18=10.2

Answer:

49 hot dogs, 77 sodas

Step-by-step explanation:

2.25h + 1.5s = 225.75

h + s = 126, so s = 126 - h. Substitute that into the first equation.

2.25h + 1.5(126 - h) = 225.75

Solve for h

2.25h + 189 - 1.5h = 225.75

0.75h = 36.75

h = 49  So they sold 49 hot dogs

h + s = 126, so 49 + s = 126, s = 77

The area of the square is 25ft² and the perimeter is 20ft.

It's important to note that the area of a square is calculated as:

= Side ²

The perimeter is calculated as:

= 4 × Side

From the information given, the side is 5ft. The area will be:.

= 5 × 5

= 25ft²

The perimeter will be:

= 4 × Sode

= 4 × 5ft.

= 20 feet

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