Consider making an inference about pi-p2 , where there are x1 successes in ni binomial trials and χ2 successes in n, binomial trials. a. Describe the distributions ofx1 and x2 b. Explain why the Central Limit Theorem is important in finding an approximate distribution for (Pi-P2 a. Choose the correct distributions below. x1 has a distribution and x2 has a distribution.

The intersection of this sphere with the -plane is (y+6)²+(z-4)²=21

The equation of a sphere centered at (h,k,l) and radius r is given by:

(x−h)²+(y−k)²+(z−l)²=r²

where x,y, and z represent the coordinates of the points on the surface of the surface.

so if the center is (-3,2,5) and radius r=4 then we can plug the values in the above formula:

consider the points  h=-3 k=2 l=5 and r=4.

(x−(-3))²+(y−2)²+(z−5)²=4²

(x+3)²+(y−2)²+(z−5)²=16.

If the sphere intersects the yz-plane then x=0

The resulting equation is an equation of a circle with a radius r=√21

and at the center with (6,-4) on the yz-plane

with yx-plane:

⇒(x−2)²+(y+6)²+(z−4)²=25

⇒ (0−2)²+(y+6)²+(z−4)²=25

⇒4+(y+6)²+(z−4)²=25

⇒(y+6)²+(z−4)²=25-4

⇒(y+6)²+(z−4)²=21

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Answer:

A rational number: 5.4, which also can be written as 27/5

Irrational number:

sqroot 28

approx= 5.29

Step-by-step explanation:

5.4 is a rational number because it is a terminating decimal. That means it ends after the 4, there are no more numbers. Also it can be written as a ratio (looks like a fraction) 27/5.

Sqroot28 is irrational. Since 28 is not a perfect square, when you squareroot it you get a number with a neverending decimal

sqroot28 = 5.2915026221...

since the decimal does not repeat or end it cannot be written as a ratio, so it is not rational

sqroot28 ~= 5.29

Answer:

x= \(5\sqrt{5}\)

Step-by-step explanation:

To solve this problem we first observe the Pythagoras equation. If a= 10 and b =5 are the lengths of the legs of a right triangle and c= x is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

This relationship is represented by the formula:

\(a^{2} + b^{2} = c^{2}\) =>\(10^2 +5 ^2 = x^2\)

=> 100 + 25 = \(x^2\)

=> \(\sqrt{125}\) = x => \(\sqrt{25} \sqrt{5}\) = x

=> x= 5\(\sqrt{5}\)

The probability that Sam's first upgrade will occur after the third flight = 0.729

Let m represents the number of flights Sam must take in order to receive his first upgrade.

To find the probability that Sam's first upgrade will occur after the third flight.

i.e., to find P(m ≥ 4)

Here,  0.10 probability that a coach-class ticket holder who flies frequently will be upgraded to first class on any flight.

p = 0.10

q = 1 - p

q = 0.90

P(m ≥ 4) = 1 - P(m ≤ 3)

P(m ≥ 4) = 1 - [P(m = 1) + P(m = 2) + P(m = 3)]

P(m ≥ 4) = 1 - [0.1 + (0.9 × 0.1) + (0.9² × 0.1)]

P(m ≥ 4) = 1 - (0.1 + 0.09 + 0.081)

P(m ≥ 4) = 0.729

therefore, the required probability = 0.729

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The complete question is:

An airline claims that there is a 0.10

probability that a coach-class ticket holder who flies frequently will be upgraded to first class on any flight. This outcome is independent from flight to flight. Sam is a frequent flier who always purchases coach-class tickets.

What is the probability that Sam's first upgrade will occur after the third flight?

Hey there!☺

\(Answer:\boxed{-z-3}\)

\(Explanation:\)

\(-3-z\)

-3 + -z Add together

-z - 3

Hope this helps!

Answer:

No linear relationship between x and y

Step-by-step explanation:

change in y is constant, change in x is increasing not a constant. constant means it remains the same doesnt change.

Answer: (3/6) then (2/6)

Step-by-step explanation:

FRACTIONS: YOU TIMES IT SO THE DENOMINATOR IS THE SAME APPLY THE NUMBER YOU TIMED BY THE NUMERATOR.

Answer:

7,986

Step-by-step explanation:

Picture that shows steps and how to do it with formula!!

Hope this helped!!!

~ Kaitlyn

Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

To find out how much of each leftover paint Josh should mix to achieve a medium pink color (50% red), we can set up a system of equations based on the percentages of red in the paints.

Let's assume that Josh needs x gallons of dark pink paint and y gallons of light pink paint to achieve the desired color.

The total amount of paint needed is 3 gallons, so we have the equation:

x + y = 3

The percentage of red in the dark pink paint is 80%, which means 80% of x gallons is red. Similarly, the percentage of red in the light pink paint is 30%, which means 30% of y gallons is red. Since Josh wants a 50% red mixture, we have the equation:

(80/100)x + (30/100)y = (50/100)(x + y)

Simplifying this equation, we get:

0.8x + 0.3y = 0.5(x + y)

Now, we can solve this system of equations to find the values of x and y.

Let's multiply both sides of the first equation by 0.3 to eliminate decimals:

0.3x + 0.3y = 0.3(3)

0.3x + 0.3y = 0.9

Now we can subtract the second equation from this equation:

(0.3x + 0.3y) - (0.8x + 0.3y) = 0.9 - 0.5(x + y)

-0.5x = 0.9 - 0.5x - 0.5y

Simplifying further, we have:

-0.5x = 0.9 - 0.5x - 0.5y

Now, rearrange the equation to isolate y:

0.5x - 0.5y = 0.9 - 0.5x

Next, divide through by -0.5:

x - y = -1.8 + x

Canceling out the x terms, we get:

-y = -1.8

Finally, solve for y:

y = 1.8

Substitute this value of y back into the first equation to solve for x:

x + 1.8 = 3

x = 3 - 1.8

x = 1.2

Therefore, Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

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Answer:

$6.68

Step-by-step explanation:

83.50(0.08) = 6.68

First, we need to find the quantity demanded when the selling price is $10 by setting p = 10 in the demand curve: 10 = 420/(q + 9) Solving for q, we get: q = 39 So, when the selling price is $10, the quantity demanded is 39.

Next, we need to find the area of the triangle formed by the demand curve, the price axis, and the line p = 10. This area represents the consumer surplus. Using the formula for the area of a triangle, we have:

Consumer surplus = (1/2) x (10 - 420/(39 + 9)) x 39

Consumer surplus ≈ $85.38 Therefore, the consumer surplus when the selling price is $10 is approximately $85.38. This means that consumers are willing to pay $85.38 more than the selling price for the given quantity of goods. The consumer surplus represents the benefit that consumers receive from buying goods at a price lower than what they are willing to pay.

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The measure of angle 3 is equal to 114° by the corresponding angle property.

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

Now, According to the definition of corresponding angles, when two parallel lines cross the third one, the angles that are in the same relative position at each intersection are referred to as being corresponding angles to one another.

Hence, In the image, it is given that angle 7 is 114 degrees.

As in the image, the two parallel lines a and b are cut by the transversal line.

And, The given angle 7 is 114°.

Thus, From the correspondence angle property, the two angles on the same side of the transversal line will be equal to each other. The angle 3 will be calculated as:-

⇒ ∠7 = ∠3

⇒ 114° =  ∠3

Therefore, Value of angle 3 will be 114°.

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I think your work was right, except you mixed up or lost track of a sign.

7x+5 = 14x-16

subtract 7x and add 16 to both sides:

21 = 7x

divide by 7

3 = x

Now substitute that back into either of angle 1 or angle 2 to find the measure of those.  (They'll be the same.)

Then use the fact that angle 1 and angle 2 form a straight line and add up to 180º.

FALSE. The number of dots in a dotplot of a bootstrap distribution is equal to the size of the bootstrap sample, not the original sample.

In a bootstrap analysis, multiple samples of the same size are drawn from the original sample with replacement, creating a distribution of sample statistics. The dotplot of this distribution represents the frequency of the sample statistics and can help us understand the variability of the original sample.

The number of dots in the dotplot reflects the number of bootstrap samples, which can be much larger than the original sample size. Therefore, the number of dots in the bootstrap distribution can be different from the size of the original sample.

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Answer:

20 and -20

20^2 = 400

(-20)^2=400 since two negative is positive

On solving the provided question, we can say that - the each angle of pentagon is x = 108

A pentagon is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles. The polygon's exterior angle total is therefore equal to n(360°/n). There are five sides to a pentagon, therefore n must equal five. Consequently, 5(360°/5) = 360° is the sum of the pentagon's outer angles.

since all sum of pentagon is 540

so, 5x = 540

x = 108

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Answer:

32

Step-by-step explanation:

1) Simplify 32 ÷ 4 to 8.

48 - 8 × 2

2) Simplify 8 × 2 to 16.

48 - 16

3) Simplify.

32

Occupants are 10 times more likely to be killed in a crash when not buckled in. option c.

Wearing a seatbelt is one of the simplest ways to protect oneself while in a vehicle. When properly worn, it decreases the likelihood of being seriously injured or killed in a collision by as much as 50%. When an individual is not wearing a seatbelt, they are putting their lives at risk. Wearing a seatbelt should be a routine habit whenever an individual sits in a vehicle.

Buckling up is the easiest and most effective way to prevent injuries and fatalities on the road. If drivers, passengers, and children buckle up every time they travel in a vehicle, the likelihood of being killed or injured in a collision is greatly reduced. When occupants of a vehicle do not buckle up, they are 10 times more likely to be killed in a crash. This means that the likelihood of being killed is significantly higher when not wearing a seatbelt.

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(a)The optimal order quantity is  4609 units.

(b)The time between orders is  1.98 months.

To determine the optimal order quantity and the approximate time between orders, the Economic Order Quantity (EOQ) model. The EOQ model minimizes the total cost of inventory by balancing ordering costs and carrying costs.

Optimal Order Quantity:

The formula for the EOQ is given by:

EOQ = √[(2DS) / H]

Where:

D = Annual demand

S = Cost per order

H = Holding cost per unit per year

calculate the annual demand (D) using the 2020

sales numbers provided:

D = 651 + 808 + 514 + 174 + 435 + 426 + 687 + 582 + 662 + 1551 + 1295 + 1774

= 9559 units

To calculate the cost per order (S) and the holding cost per unit per year (H).

The cost per order (S) is given as $500.

The holding cost per unit per year (H)  calculated as follows:

H = Carrying cost percentage × Unit value

= 0.30 × $3

= $0.90

substitute these values into the EOQ formula:

EOQ = √[(2 × 9559 × $500) / $0.90]

= √[19118000 / $0.90]

≈ √21242222.22

≈ 4608.71

Approximate Time Between Orders:

To calculate the approximate time between orders, we'll divide the total number of working days in a year by the number of orders per year.

Assuming 360 days in a year and a lead time of 1 week (7 days) for shipping, we have:

Working days in a year = 360 - 7 = 353 days

Approximate time between orders = Working days in a year / Number of orders per year

= 353 / (9559 / 4609)

= 0.165 years

Converting this time to months:

Approximate time between orders (months) = 0.165 × 12

= 1.98 months

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The revenue function will be 98.96x.

From the information, the number of units that was sold was represented by x.

The product sells for $98.96.

Therefore, the revenue as s function of the units sold will be:

= $98.96 × x

= 98.96x

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Improved public health care, sanitation, nutrition, and medical technology are likely factors that have contributed to the 40% decrease in death rates in the United States from 1930 to 2015.

Improved access to health care and medical technology have allowed for more effective treatments of illnesses and diseases, while improved sanitation, nutrition, and access to clean water have reduced the prevalence of communicable diseases. Additionally, advances in public health awareness, such as the introduction of mandatory vaccinations, have also played a role in reducing death rates.

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Answer: A

Step-by-step explanation:

If 2sinθ = 6/5, then the value of cos (90 - θ) will be 3/5. Then the correct option is A.

We can use the fact that:

sinθ = cos(90 - θ)

to convert the sine to cosine (but the angles won't stay the same unless it's 45 degrees).

If 2sinθ = 6/5.

Then the value of cos (90 - θ) will be

cos (90 - θ) can be written as sin θ

Then we have

cos (90 - θ) = sin θ

cos (90 - θ) = 3/5

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Answer:

To calculate the fish population in 2020, we need to first find the fish population in 2018, 2019, and then use that to find the population in 2020.

In 2018, the fish population would be:

36,000 - (10% of 36,000) = 36,000 - 3,600 = 32,400

In 2019, the fish population would be:

32,400 - (10% of 32,400) = 32,400 - 3,240 = 29,160

Finally, to find the fish population in 2020, we can repeat the same process:

29,160 - (10% of 29,160) = 29,160 - 2,916 = 26,244

Therefore, the fish population in 2020 was approximately 26,244.

Step-by-step explanation:

Answer:

50⁰

Step-by-step explanation:

Add 130 plus 50 to get 180.

Answer:

x = 50°

Step-by-step explanation:

In a parallelogram consecutive angles are supplementary, thus

∠ BAC + ∠ ABD = 180°, that is

130° + ∠ ABD = 180° ( subtract 130° from both sides )

∠ ABD = 50°

Since ACDB and FGHE are congruent then corresponding angles are congruent, thus

∠ FEH = ∠ ABD = 50° =x

The probability that a person who tests positive has the disease is 0.032

we can use Bayes' theorem. Let's denote the following events

A: A person has the disease

B: The person tests positive

We are given the following probabilities

P(A) = 2% = 0.02 (probability of a person having the disease)

P(B|A) = 91.4% = 0.914 (probability of testing positive given that the person has the disease)

P(B|not A) = 4.2% = 0.042 (probability of testing positive given that the person does not have the disease)

We want to find P(A|B), the probability that a person has the disease given that they test positive.

By Bayes' theorem, we have

P(A|B) = (P(B|A) × P(A)) / P(B)

P(B), the probability of testing positive, we can use the law of total probability

P(B) = P(B|A) × P(A) + P(B|not A) × P(not A)

P(not A) represents the complement of having the disease, which is 1 - P(A).

Substituting the values

P(B) = (0.914 × 0.02) + (0.042 × (1 - 0.02))

P(B) = 0.01828 + 0.04116

P(B) = 0.05944

Now, let's calculate P(A|B)

P(A|B) = (0.914 × 0.02) / 0.05944

P(A|B) = 0.01828 / 0.05944

P(A|B) ≈ 0.032

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Answer:

minutes took to finish the race = 54 minutes

Step-by-step explanation:

It's known that:

\(speed = \frac{distance}{time}\)

then:

\(time = \frac{distance}{speed}\)

IN THE 1ST 10 MILES:

time = \(\frac{10}{25} = \frac{2}{5} = 0.4 hours\)

IN THE 2ST 10 MILES:

time = \(\frac{10}{20} = 0.5 hours\)

Hence, Overall time took to finish the race = 0.4 + 0.5 = 0.9 hours

time in minutes = 0.9 × 60 = 54 minutes


Another Solution:

Overall speed = \(\frac{S_1 + S_2}{2}\), Where: S1: 1st speed, S2: 2nd speed

then:

speed = \(\frac{25 + 20}{2}= 22.5 mph\)

Hence, time took = \(\frac{20}{22.5} = 0.9 hours = 54 minutes\)




hope you find this easy to understand....

Have any questions? Write in the comments.

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Answer: 71.25 meters

Step-by-step explanation:

1. 498.75/7

2. 71.25

Mia made 7 trips to visit her grandmother. she walked 498.75 meters in all, mia walks on each trip is 71.25 m

Mia made 7 trips to visit her grandmother

she walked 498.75 meters in all

In order to calculate the distance she walks on each trip, we calculate it by dividing the total distance by the number of trips

The total distance is 498.75

The number of trips is 7

walk on each trip is 498.75/ 7 = 71.25

Therefore, mia made 7 trips to visit her grandmother. she walked 498.75 meters in all, mia walks on each trip is 71.25 m

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Answer: Hello!

-2-(-5) can also be written as -2 + 5.

When subtracting a negative, you're essentially adding, because you are subtracting a negative value. So we would add 5 to -2.

Hope this helps!

Answer:

(B) 16.7 kg

Step-by-step explanation:

First, start by converting everything to kilograms (using unit converters):

\(250g(\frac{10^{-3}kg}{1g})=250*10^{-3}kg=0.25kg\)

Then, add all the weights together:

\(100kg+0.25kg+150kg+0.25g=250kg+0.5kg=250.5kg\)

Now, divide this number by 15 (since they are packed in 15 bags):

\(\frac{250.5kg}{15}=16.7 kg\)

(B) 16.7 kg