20 points.

Find the length of XY the midsegment.​

According to the flight on certain routes, the experiment is a binomial experiment and this will be determined by observing that Flights on a certain route are on-time 80% of the time and 10 flights are randomly selected and the number of​ on-time flights is recorded.

(a) This is a binomial experiment since there are only two possible outcomes for each data that is a flight is either on time (p = 80% = 0.8) or late (q = 1 - p = 1 - 0.8 = 0.2).

​(b) Using the formula:

P(a out of n) = (nCa)(pᵃ)(qⁿ⁻ᵃ), where n = 10 flights, a = the number of flights that arrive on time:

P(7/10) = (10C7)(0.8)⁷ (0.2)³= 0.2013

Therefore, 0.2013 chance is there that exactly 7 of 10 flights will arrive on time.

​(c) Fewer than 7 flights are on time means that we must add up the probabilities for P(0/10) up to P(6/10).

P(0/10) + P(1/10) + ... + P(6/10) = 0.1209

This means that 0.1209 chance that less than 7 flights will be on time.

​(d) The probability that at least 7 flights are on time is the exact opposite of part (c), where less than 7 flights are on time. So instead of calculating each formula from scratch, we can simply subtract the answer in part (c) from 1.

1 - 0.1209 = 0.8791.

So there is a 0.8791 chance that at least 7 flights arrive on time.

(e) For this, we must add up P(5/10) + P(6/10) + P(7/10), which gives us

0.0264 + 0.0881 + 0.2013 = 0.3158, so the probability that between 5 to 7 flights arrive on time is 0.3158.

According to the flight on certain routes, the experiment is a binomial experiment

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DISCLAIMER: The question provided is incomplete as some data are missing. The above answer is solved as per a relevant question

According to an​ airline, flights on a certain route are on time 80 ​% of the time. suppose 10 flights are randomly selected and the number of​ on-time flights is recorded. ​(a) explain why this is a binomial experiment. ​(b) find and interpret the probability that exactly 7 flights are on time. ​(c) find and interpret the probability that fewer than 7 flights are on time. ​(d) find and interpret the probability that at least 7 flights are on time. ​(e) find and interpret the probability that between 5 and 7 ​flights, inclusive, are on time.

Answer:c

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Multiply all the points by 2.

Answer:

1) I and III

Step-by-step explanation:

The equation of an exponential function is given by:

y = abˣ

where x is an independent variable, y is a dependent variable, a is the initial value of y (that is value of y at x = 0), b is greater than 1 for an exponential growth while b < 1 for an exponential decay.

Given that x represent years and P(x) represent population. 2013 is represented by x= 0, hence:

At the year 2013 (x = 0), the population is 3810, hence a = 3810.

The equation becomes:

P(x) = 3810(b)ˣ

At 2014 (x = 1), the population is 3943. Hence:

3943 = 3810(b)¹

3810b = 3943

b = 1.035.

Therefore a = 3810, b = 1.035. The correct option is 1) I and III

Since b > 1, this is an exponential growth.

Answer:

which one will we simplify

Using functions we can find that there would be nine roadways for six cities. This is due to the fact that each city must be connected to every other city, and since there are 5 pairs of connected cities, there must be 5 highways.

A function is a statement, concept, or rule that establishes an association between two variables.

Functions in mathematics are required for the development of meaningful relationships. If there are more than one dependent values for a particular independent value, then we are aware of this.

In that situation, the relation is not a function. Nevertheless, if there are multiple dependent values for a given independent value.

The relationship is then a function.

Now as per the question,

The remaining 4 cities must then be connected, which requires building an additional 4 roads, for a total of 9.

There would be 12 roadways for 7 cities.

This is due to the fact that each city must be connected to every other city, and since there are 6 pairs of connected cities, there must be 6 highways.

Then, the final five cities must be connected, which requires five more roads, for a total of twelve.

The number of highways for N cities would be N(N-1)/2.

This is because there are N(N-1)/2 pairs of cities that need to be connected, and each city must be connected to every other city.

For instance, if N = 10, 90 highways or 10× 9 = 90 pairs of cities must be connected.

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The complete question is:

There are five cities in a country, and two are connected with one road that goes straight between them. How many roads would be in this country if there were 6 cities? 7 cities? And N cities?

The domain is all non negative real numbers [0, +∞).

The range of the function is all real numbers ≥ 1.3.

h(t) = 1.3 + 0.01t

models the height of the rock formation after t years.

t ≥ 0 since rock formation grows over time

The domain is all non negative real numbers [0, +∞).

At t = 0, the height of the rock formation =

h(0) = 1.3 + 0.01(0)

= 1.3 meters.

The range of the function is all real numbers ≥ 1.3.

In interval notation, the range is [1.3, +∞).

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A scientist discovered a rock formation that grows at a rate of 0. 01 meters per year. To predict the height, h, of the rock formation after t years, she used the formula h(t)=1. 3+0. 01t

what is the domain and the range if the function

Answer:

40%

Step-by-step explanation:

Since the pie is divided into 10 equal sections, we can assume they are all equivalent areas.  So 4 slices out of the total of 10 would mean that 4/10 or 40% of the pie has disappeared, with you as the only witness.  I suggest removing the evidence by consuming the remaining 6 slices.

A right angled triangle with height = 7, base = 11, by using the Pythagorean theorem, we can calculate the hypotenuse is approximately 13. Therefore, the missing side, x = 13.

In a right angled triangle, using the Pythagorean theorem: sum of the squares of the base and height is equal to the square of the hypotenuse, we can find the hypotenuse x.

\(x^2 = 7^2 + 11^2\)

\(x^2 = 49 + 121\)

\(x^2 = 170\)

Taking the square root of both sides, we get:

x ≈ 13.0384

Rounding this to the nearest tenth, we get:

x ≈ 13.0

Therefore, the length of x is approximately 13.0 units (rounded to the nearest tenth).

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Each normal photo costs $0.15, while each wallet photo is only $0.08 in terms of money.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

Let x be the cost of standard photos and y be the cost of wallet photo.

40x+12y=6.96        ...........(1)

25x+30y=6.15        ..........(2)

Multiplying (1) by 5 and (2) by 2,

200x+60y=34.8

50x+60y=12.3

150x=22.5

x=$0.15

200*0.15+60y=34.8

30+60y=34.8

60y=4.8

y=$0.08

The cost in dollars of each standard photo is $0.15 and the cost in dollars of each wallet photo is $0.08.

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The volume of a stack of 9 books is 1368.75 cubic inches.

To find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.

Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.

Therefore, the volume of the stack of 9 books is:

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Answer:

(-150, 45)

Step-by-step explanation:

The solution to the system is where the two graphs intersect

My best guess from the graph is

(-150, 45)

Answer:

10

Step-by-step explanation:

7(0)+y=10

y=10

Answer: (0, 10)

Step-by-step explanation:

The given expression is in the standard form of linear equations: Ax + By = C, where A and B are constants.

The definition of y-intercept is the point that intersects with the y-axis, meaning that the [x] value of the point will be zero.

To find the y-intercept of an equation, substitute the [x] variable with 0, as mentioned above, the [x] value of a y-intercept is 0.

\(7x+y=10\\\)

\(7(0)+y=10\)

\(0+y=10\)

\(y=10\)

As we find the [y] value is 10, while the given [x] value is 0, therefore, the y-intercept of \(7x+y=10\) is \(\boxed{(0,10)}\).

Hope this helps!! :)

Please let me know if you have any questions

Answer: The number 8 goes into 40 five times, resulting in a final quotient of 2.5.

Step-by-step explanation:

Answer:

Example, the number 8 goes into 20 2.5 times, resulting in a quotient of 2.5

Step-by-step explanation:

Answer:

The time will be 1:00pm(13 hours) at which the degree Celsius will drop down to 8degrees Celsius since the temperature at 12noon was 10 degree Celsius and it is dropping at the rate of 2 degree Celsius.

Step-by-step explanation:

To find extreme values, take the first derivative

\(y = - 3 {x}^{2} + 16x - 16\)

Solve the equation for x.

\(x = \frac{ - 16 + \sqrt{256 - 192} }{ - 6} \)

or

\(x = \frac{ - 16 - \sqrt{256 - 192} }{ - 6} \)

\(x = \frac{ - 16 + \sqrt{64} }{ - 6} \)

or

\(x = \frac{ - 16 - \sqrt{64} }{ - 6} \)

We then get

\(x = \frac{4}{3} \)

or

\(x = 4\)

So our extreme values occur at x=4/3 and x=4

Zeroes:

\( - {x}^{3} + 8 {x}^{2} - 16x\)

\( - x( {x}^{2} - 8x + 16)\)

\( - x(x - 4) {}^{2} \)

\( - x = 0\)

\((x - 4) {}^{2} = 0\)

\(x = 4\)

So we have a double root at 4, and a root of 0. We have two positive roots and one non negative root

End behavior:

Since we have a negative leading coefficient and a odd degree, as x becomes more positive, y will become negative and as x becomes more negative, y will become positive.

Answer

The correct answer is option B, \(x\geq 3\) such that a graph representing the function is given.

The domain of a function is the set of all the function's potential inputs.

We can see that the graph of the function originates from \((-3, 0)\) and goes in the direction of positive \(x-axis\).

So, the domain of the function is \(x\geq 3\).

Thus, the correct answer is option B \(x\geq 3\).

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Manufacturers change the size of compact disks so that they are made of the same material and have the same thickness as a current disk but have one third of the diameter, the moment of inertia will change by a factor of 1/9 or approximately 0.111.

The moment of inertia of a disk is proportional to the square of its radius (I = (1/2)mr^2). If the diameter of the new compact disk is one-third of the diameter of the current disk, then its radius will be one-sixth of the radius of the current disk (r_new = r_current/3). Therefore, the moment of inertia of the new compact disk will decrease by a factor of (1/6)^2 = 1/36, or 19.

Given that the new compact disk has one-third of the diameter of the current disk, the moment of inertia (I) will change as a function of the radius (r) squared. Since the diameter is halved, the radius is also one-third, and the moment of inertia is given by the formula I = k * r^2, where k is a constant.

When we reduce the radius to one-third (r/3), the new moment of inertia (I') can be calculated as:

I' = k * (r/3)^2
I' = k * (r^2/9)

To find the factor by which the moment of inertia has changed, we need to divide the new moment of inertia (I') by the original moment of inertia (I):

Factor = I'/I = (k * r^2/9) / (k * r^2) = 1/9

So, the moment of inertia will change by a factor of 1/9 or approximately 0.111.

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The probability of randomly selecting a male is dependent upon the gender distribution of the population from which the selection is made.

For example, if the population is evenly split between males and females, then the probability of randomly selecting a male would be 50%. Alternatively, if the population had more females than males, then the probability of selecting a male would be lower than 50%.

In general, the probability of randomly selecting a male is determined by the ratio of males to females in the population. For example, if there were twice as many females as males, then the probability of randomly selecting a male would be 33.3%. Similarly, if there were four times as many females as males, then the probability of randomly selecting a male would be 25%.

These probabilities can also be applied to specific populations. For example, the United States Census Bureau estimates that there are 101.8 males for every 100 females in the US population. Therefore, the probability of randomly selecting a male from the US population is approximately 50.9%.

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.23 (three repeating)

tell me if its wrong

Answer:

If the equation is "5/7(x)=3" then the answer's x=21/5

Step-by-step explanation:

Combine multiplied terms into a single fraction.

Multiply all terms by the same value to eliminate fraction denominators.

Simplify.

Divide both sides of the equation by the same term.

Simplify.

The second derivative of v with respect to t, denoted as d²v/dt², is equal to 4

The second derivative of v with respect to t, we will differentiate v twice.

v = 2t² + 7t + 11

First, let's find the first derivative of v with respect to t (dv/dt):

dv/dt = d/dt (2t² + 7t + 11)

Using the power rule of differentiation, we differentiate each term separately:

dv/dt = 2(2t) + 7(1) + 0

dv/dt = 4t + 7

Now, let's find the second derivative of v with respect to t (d²v/dt²):

d²v/dt² = d/dt (4t + 7)

Again, using the power rule of differentiation, we differentiate each term separately:

d²v/dt² = 4(1) + 0

d²v/dt² = 4

Therefore, the second derivative of v with respect to t, denoted as d²v/dt², is equal to 4.

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Answer:

B

Step-by-step explanation:

Both 0.684 and 0.1222 are rational

Answer:

B.

Step-by-step explanation:

Because 0.12222222.... and 0.684 are rational numbers.

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Answer:

Statement 1 and 2

Step-by-step explanation:

If you take t^2 - 16t + 55 and find some of its graphical values, you will get:

Turning point: (8,-9)

Roots: (5,0) and (11,0)

When this graph is plotted and you imagine the x axis to be time (as stated in the question), each of the roots (x - intercept) must be when the swimmer goes under and when they come back up.

This means that the swimmer dived under the water at 5 seconds and came back up at 9, making the first 2 statements correct.

Now the fourth statement is ruled out.

The fifth statement is not plausible as the graph would have to have more than 2 roots for the swimmer to enter the water twice.

That leaves the third statement. If you imagine the depth of the swimmer to be the y axis of our imaginary graph, and we know that the y axis of the turning point is -9, that means that the swimmer's deepest dive was 9 feet under the water, ruling out the third statement too.

Hope this helps :D

Answer:

\(h(t)= (t-5)(t-11)\)

The swimmer comes back up 11 seconds after the timer is started.

The swimmer dives into the water 5 seconds after the timer is started.

Step-by-step explanation:

Given function:

\(h(t)=t^2-16t+55\)

To factor a quadratic in the form \(ax^2+bx+c\),

find two numbers that multiply to \(ac\) and sum to \(b\):

\(\implies ac=55\)

\(\implies b=-16\)

Two numbers that multiply to 55 and sum to -16 are: -11 and -5

Rewrite b as the sum of these two numbers:

\(\implies t^2-11t-5t+55\)

Factorize the first two terms and the last two terms separately:

\(\implies t(t-11)-5(t-11)\)

Factor out the common term (t - 11):

\(\implies (t-5)(t-11)\)

Therefore, the given formula in factored form is:

\(h(t)= (t-5)(t-11)\)

The swimmer's depth is modeled as h(t).  Therefore, when h(t) = 0 the swimmer will be at the surface of the water.

\(\implies h(t)=0\)

\(\implies (t-5)(t-11)=0\)

\(\implies t-5=0\implies t=5\)

\(\implies t-11=0 \implies t=11\)

Therefore, the swimmer will be at the surface of the water at 5 s and 11 s.

The swimmer's maximum depth is the vertex of the function. The x-value of the vertex is the midpoint of the zeros.  Therefore, the x-value of the vertex is t = 8.

Substitute t = 8 into the function to find the maximum depth:

\(\implies h(8)=8^2-16(8)+55=-9\)

So the swimmer's maximum depth is 9 ft.

True Statements

The swimmer comes back up 11 seconds after the timer is started.

The swimmer dives into the water 5 seconds after the timer is started.

Answer:

$26.6633333333

Step-by-step explanation:

You divide $159.98 by 6 lol

The perimeter of the rectangle, when the area is maximized, is approximately 24.63 units. Therefore, correct option is a.

To maximize the area of the rectangle inscribed in the parabola \(y^2 = 16x\), we need to find the dimensions of the rectangle. Since the side of the rectangle is along the latus rectum of the parabola, we know that the length of the rectangle is equal to the latus rectum.

The latus rectum of the parabola \(y^2 = 16x\) is given by the formula 4a, where "a" is the distance from the focus to the vertex of the parabola. In this case, the focus is located at (4a, 0).

To find "a," we can equate the equation of the parabola to the general equation of a parabola in vertex form: \(y^2 = 4a(x - h)\), where (h, k) is the vertex of the parabola.

Comparing the two equations, we get:

4a = 16

a = 4

Therefore, the latus rectum of the parabola is 4a = 4 * 4 = 16 units.

Since the length of the rectangle is equal to the latus rectum, we have length = 16 units.

Now, to find the width of the rectangle, we need to determine the corresponding y-coordinate on the parabola for the given x-coordinate of the latus rectum. The x-coordinate of the latus rectum is half the length, which is 16/2 = 8 units.

Substituting x = 8 into the equation of the parabola, we get:

\(y^2 = 16(8)\\y^2 = 128\\y = \sqrt{128} = 11.31\)

Therefore, the width of the rectangle is approximately 11.31 units.

The perimeter of the rectangle is given by the formula:

Perimeter = 2(length + width)

Plugging in the values, we have:

Perimeter = 2(16 + 11.31)

Perimeter ≈ 2(27.31)

Perimeter ≈ 54.62

Rounding the perimeter to two decimal places, we get approximately 54.62 units, which is equivalent to 24.63 units.

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Other than translation, the other transformation used to create this frieze pattern is:

A 180-degree rotation is a transformation wherein an object or shape obtains a spin of half a full circle, indulging in the metamorphosis of facing the total opposite direction.

To demonstrate this more accurately, each point on the object must transition to a placement that is precisely polar to its primary site; centered by a fixed spot recognized as the axis of revolution.

A close examination of the pattern shows that it is not a reflection, hence making all the options of reflection unsuitable

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A scenario that can be modeled by the linear function y = 25x + 40. is that "John owes a woman $40 and then bought 25 oranges at x dollars each. What is the total amount owed?"

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, John owes a woman $40 and then bought 25 oranges at x dollars each. What is the total amount owed?"

This can be illustrated as:

y = 25x + 40.

where y = total cost.

In conclusion, the scenario is illustrated above.

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The surface area of the stack of cubes could be 6n^2, where n is the number of cubes in each edge of the stack.

This is because each cube has 6 faces, and the total number of faces in the stack is the sum of the faces of all the cubes. Therefore, the surface area of the stack is 6 times the area of one cube times the number of cubes in the stack.

Since the area of one cube is 1 square unit and the number of cubes in each edge is n, the surface area of the stack is 6n^2 square units.In summary, the surface area of the stack of cubes can be calculated using the formula 6n^2, where n is the number of cubes in each edge of the stack.

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