Suppose P(t)represents the population of a certain mosquito colony, where. t is measured in days. The current population of the colony is known to be 574 mosquitos; that is, P(0)=574. If P'(0)=50 mosquitos per day, estimate the size of the population in 10 days.

Answer:

(a) The average number of passengers that will be on each flight is 28.8.

(b) Everyone will have a seat on about 84.4% of the flights.

Step-by-step explanation:

The correct question is:

Suppose that past experience shows  that about 10% of passengers who are schedule to take a particular flight fail to show up. For this  reason, airlines sometimes overbook flights, selling more tickets than they have seats, with the  expectation that they will have some no shows. Suppose an airline used a small jet with seating  for 30 passengers on a regional route and assume that passengers are independent of each other in  whether they show up for the flight. Suppose that the airline consistently sells 32 tickets for every  one of these flights.

(a) On average, how many passengers will be on each flight?

(b) How often will they have enough seats for all of the passengers who show up for the flight?

Solution:

Let the random variable X measure the number of passengers (out of 32) who show up for a flight.

For each passenger  there is a 90% chance of showing up, so X is a binomial random variable with n = 32 and p = 0.90.

(a)

The average of a binomial random variable is:

\(\text{Average}=np\)

Compute the average number of passengers that will be on each flight as follows:

\(\text{Average}=np\)

             \(=32\times 0.90\\=28.8\)

Thus, the average number of passengers that will be on each flight is 28.8.

(b)

To have enough seats for all of the passengers who show up for the flight, the value of X must be less than or equal to 30.

Compute the value of P (X ≤ 30) as follows:

P (X ≤ 30) = 1 - P (X > 30)

                = 1 - P (X = 31) - P (X = 32)

                \(=1-[{32\choose 31}\ (0.90)^{31}\ (1-0.90)^{32-31}]-[{32\choose 32}\ (0.90)^{32}\ (1-0.90)^{32-32}]\\\\=1-0.122087-0.034337\\\\=0.843576\\\\\approx 0.844\)

Thus, everyone will have a seat on about 84.4% of the flights.

Answer:

Step-by-step explanation:

4x^2 - 5x + 3 + 2x - 7

4x^2 - 3x - 4

The value of probability P (A or B) is,

P (A or B) = 19/34

We have to given that,

From the Venn diagram, we can observe that there are two events A and event B

n(A ∪ B) = 17 + 2

n(A ∪ B) = 19

And, The sample space would be,

n(S) = 17 + 2 + 15

n(S) = 34

Hence, Using the definition of probability,

P(A) = n(A) / n(S)

P (A) = 17/34

P (A) = 1/2

P(B) = n(B)/n(S)

P(B) = 2/34

P(B) = 1/17

So, We get;

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

P (A or B) = 1/2 + 1/17

P (A or B) = 19/34

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Answer:

Standard form of 400000000 (four hundred million) is 4 x \(10^{8}\)

Step-by-step explanation:

Because there are 8 0s, and its 400 million

Hope this helps!

Answer:

y = -1/3x - 5

Step-by-step explanation:

x + 3y = -15

-x            -x

3y = -x - 15

/3        /3

y = -1/3x - 5

Step-by-step explanation:

Given

5x- c= k

Solving for x

5x = k + c

x = ( k+ c) / 5

Hope it will help :)❤

1)

Surface area of rectangular prism:

SA = 2( hw + lw + lh )

h= height of prism .

w = width of prism .

l = length of prism .

Substitute the values,

h= 4m

w=1.2 m

l= 13.4 m

SA = 2(4*1.2 + 13.4*1.2 + 13.4*4)

SA = 148.96 m²

2)

Surface area of triangular prism:

SA = (S1 +S2 + S3)L + bh

h= height of prism .

b = base of prism .

S1 , S2 , S3 = sides of triangle .

Substitute the values,

SA = (3+ 4 + 0.5)4 + 0.5*3

SA = 31.5 in²

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Answer:

7((x-2)(3x+4))

Step-by-step explanation:

Common factor of 7 in this quadratic formula. \(7(3x^2-2x-8)\); -8 * 3x^2 = -24x^2, now find factors of this product that equal to -2x when added. The factors that fit this is -6x and 4x. So, if you make a generic rectangle you can find the product.  You get 7((x-2)(3x+4))

Answer:

the perimeter of cube is

28×4=112 ft

Answer:112

Step-by-step explanation: 28•4=112ft

so, we know the diameter is 8, so that means its radius is half that, or 4.

\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4\\ \theta =45 \end{cases}\implies A=\cfrac{(45)\pi (4)^2}{360}\implies A=2\pi ~ft^2\)

The statements supported by the data in the table are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

To determine which statements are supported by the data in the table, let's analyze the given information:

The mean number of cars sold in a month is the same at both dealerships.

To calculate the mean, we need to find the average number of cars sold each month at each dealership.

For Admiral Autos:

(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13

For Countywide Cars:

(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13

Since both dealerships have an average of 13 cars sold per month, the statement is supported.

The median number of cars sold in a month is the same at both dealerships.

To find the median, we arrange the numbers in ascending order and select the middle value.

For Admiral Autos: 4, 10, 15, 17, 19

Median = 15

For Countywide Cars: 9, 10, 14, 15, 17

Median = 14

Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.

The total number of cars sold is the same at both dealerships.

To find the total number of cars sold, we sum up the values for each dealership.

For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65

For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65

Since both dealerships sold a total of 65 cars, the statement is supported.

The range of the number of cars sold is the same for both dealerships.

The range is determined by subtracting the lowest value from the highest value.

For Admiral Autos: 19 - 4 = 15

For Countywide Cars: 17 - 9 = 8

Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.

The data for Admiral Autos shows greater variability.

To determine the variability, we can look at the range or consider the differences between each data point and the mean.

As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.

Based on the analysis, the statements supported by the data are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

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By using the concept of internal angles of a triangle, the solution of the system of linear equations related to the geometrical system is (x, y) = (40, 40).

In this system we have a geometrical system formed by two right triangles with a common hypotenuse. Right triangles are triangles where one of its internal angles are right angles and the sum of the measures of the internal angles within a triangle equals 180°. Then, this geometrical system can be modelled by using the following linear equations:

(x + 20) + 90 + 30 = 180         (1)

20 + 90 + (y + 30) = 180         (2)

By using the concept of internal angles of a triangle, the solution of the system of linear equations related to the geometrical system is (x, y) = (40, 40).

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Answer: y=2/7x

Step-by-step explanation:

y = 2/7x .......................

All the solutions are,

⇒ x = 1/2 (w- v)

⇒ x = (b - 9)/(a - 2)

⇒ x = (4 + w) / (7 - v)

⇒ x = 2 / (v + w)

⇒ x = 7v/(3w - 4)

Given that;

Expressions are,

⇒ 6x + v = 4x + w

⇒ ax + 9 = 2x + b

⇒ 7x - w = vx+4

⇒ 6 - wx = vx + 4

⇒ 3(wx - v) = 4(x + v)

We can simplify as;

⇒ 6x + v = 4x + w

⇒ 6x - 4x = w - v

⇒ 2x = w - v

⇒ x = 1/2 (w- v)

⇒ ax + 9 = 2x + b

⇒ ax - 2x = b - 9

⇒ (a - 2)x = b - 9

⇒ x = (b - 9)/(a - 2)

⇒ 7x - w = vx+4

⇒ 7x - vx = 4 + w

⇒ (7 - v) x = 4 + w

⇒ x = (4 + w) / (7 - v)

⇒ 6 - wx = vx + 4

⇒ vx + wx = 6 - 4

⇒ (v + w)x = 2

⇒ x = 2 / (v + w)

⇒ 3(wx - v) = 4(x + v)

⇒ 3wx - 3v = 4x + 4v

⇒ 3wx - 4x = 7v

⇒ (3w - 4)x = 7v

⇒ x = 7v/(3w - 4)

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Answer:

39.2°

Step-by-step explanation:

Vertical angles are always congruent.

Answer:

The angle is 140.8

Step-by-step explanation:

A straight angle is equal to 180°

So 180° minus 39.2° equals the answer

Answer:

B. Add 5y to both sides in the first equation.

Step-by-step explanation:

When we add 5y to both side in the first equation we will see that x = 22 + 5y

Then we can use this information in second equation like this:

-8(22+5y) + 7y = 22 which is a simpler equation and easier to solve.

So the answer to this question is B.

The joint relative frequency for school children who plan to attend camp and have swimming lesson is 44%.

The correct option to the given question is option d.

We are required to find the joint relative frequency for school children who plan to attend camp and have swimming lessons, rounded to the nearest percent.

To find the joint relative frequency, we use the formula as follows:

Joint relative frequency = frequency of interest / total frequency

Joint relative frequency for school children who plan to attend camp and have swimming lessons = 42 / 96

(As we are looking for the students who plan to attend camp and have swimming lessons, we are interested in the first column of the table and the entry at the intersection of the first row and second column.)

Joint relative frequency for school children who plan to attend camp and have swimming lessons = 0.4375

Joint relative frequency for school children who plan to attend camp and have swimming lessons (rounded to the nearest percent) = 44%(option d).

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Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.

We can see that Natalie is reducing the amount she owes by $18 every two weeks.

Therefore, the amount she owes after 2 weeks is $180 - $18 = $162, after 4 weeks is $144, after 6 weeks is $126, and after 8 weeks is $108.

This means that after n weeks, the amount she still owes is:

$180 - $18n

Since she will pay the same amount each week, let's call the weekly payment P. After one week, she will owe:

$180 - P

After two weeks, she will owe:

($180 - P) - P = $180 - 2P

After four weeks, she will owe:

($180 - 2P) - P - P = $180 - 4P

After six weeks, she will owe:

($180 - 4P) - P - P = $180 - 6P

And after eight weeks, she will owe:

($180 - 6P) - P - P = $180 - 8P

We can set up an equation using the information we have:

$180 - 8P = $108

Solving for P, we get:

P = $9

Therefore, Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.

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The complete question:

Natalie borrowed money from her parents to pay for a trip. ​Natalie will ​pay her parents in equal amounts every week until she pays back the ​entire amount she borrowed. ​ ​The table below shows the amount of ​money Natalie still owes her parents at the end of every two weeks for ​the first eight weeks. How much does Natalie pay her parents each week? What is the initial amount Natalie still owes?

Week 0 = $180

Week 2 = $162

Weeks 4 = $144

Week 6 = $126

Week 8 = $108

60

Step-by-step explanation:

(-47)-(-107)

(-47)-1(-107)

-47+107

=60

Answer:

If two sides of a triangle are congruent, then the angles opposite to these sides are congruent.

Step-by-step explanation:

Congruent/Congruency: having the same size and shape congruent triangles.

Theorem 1: If a line is drawn parallel to one side of a triangle to intersect the midpoints of the other two sides, then the two sides are divided in the same ratio.

I hope this helped, have a great day <3

Answer:

Sorry but it's too hard to answer

Answer:

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Answer:

The variable "h" represents: The number of hours

The constant 20 represents: the initial rental price

The variable term 12.5h represents: the hourly rental amount

Step-by-step explanation:

Answer:

1) r = 32

2) symbol is '÷'

3) h = 15/19

Step-by-step explanation:

The approximate 90% confidence interval for this situation is given as follows:

(70244, 70632).

The bounds of the confidence interval are given by the rule presented as follows:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

In which:

From the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.645.

The parameters are given as follows:

\(\overline{x} = 70438, \sigma = 645.3, n = 30\)

The lower bound of the interval is given as follows:

\(70438 - 1.645 \times \frac{645.3}{\sqrt{30}} = 70244\)

The upper bound of the interval is given as follows:

\(70438 + 1.645 \times \frac{645.3}{\sqrt{30}} = 70632\)

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Answer: corresponding angles. lie on the same side of a transversal in corresponding positions with respect to two lines that the transversal intersects if the lines are parallel then the corresponding angles are congruent.

Step-by-step explanation:

Answer:

x + x - 45 = 90

2x - 45 = 90

2x = 135

x = 67.5, so x - 45 = 22.5

The other two angles measure 22.5° and 67.5°.

Answer:

Good luck

Step-by-step explanation:

Sorry I don´t understasnd

The circle parts with overline over them is line segment, such as LQ, the parts with angle sign are angle and part with curve over them is chord.

There are different parts of circle such as chord, radius, diameter, central angle, circumference etc.

In this provided problem, we have to name all the part of the circle shown in the figure.

In the figure,

Thus, the circle parts with overline over them is line segment, such as LQ, the parts with angle sign are angle and part with curve over them is chord.

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Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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a) Probability of occurrence of evant A is equals to the 7/10.

P(not getting a white or a blue shirt), P(Aᶜ ) is equals the 3/10.

Probability of occurrence of evant B is equal to the 1/2.

b) The events A and B are not mutually exclusive

c) Mike's preference is to getting a white shirt with his size L.

We have a probabality based problem. Probability is defined as chance of occurrence of an event or result. It can be calculate as favourable outcomes divided by total possible outcomes. There is total number of avaliabile shirts = 20 i.e., total possible outcomes = 20

Mike is interested in getting a white or a blue shirt in size L. Let us consider two events :

A : Getting a white or a blue shirt

B: Getting a shirt in size L

a) Number of favourable outcomes to getting white or a blue shirt = 9 white or 5 blues

Probability ( Getting a white or a blue shirt) , P(A)

= 9/20 + 5/20 + 0 = 14/20 = 7/10

P(not Getting a white or a blue shirt), P(Aᶜ )

= 1 - P(A) = 1 - 7/10 = 3/10

ii) The number of favourable outcomes for event B, n(B) = 10

So, Probability of getting a shirt in size L, P(B)

= 10/20 = 1/2

b) Mutually exclusive events are defined as the events that can't happen at the same time. In other words AnB = 0 . Here, we see there is total 14 shirts which are in white or blue colors and 10 are in size L , So there is possibility that shirt is white or blue in colour and in size L , i.e, An B ≠0

So, events A and B are not mutually exclusive.

c) Event ,n( A u B )= n(A) + n(B) - n(A n B)

On the basis of all details, we conclude that Mike's preference is to choose white shirt with size L .

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