Hurry pls
50pts
Time limit
Tell me the domain and range
Tell me whether the graph is a function or not.
The answer choices are below

Hurry Pls 50pts Time LimitTell Me The Domain And Range Tell Me Whether The Graph Is A Function Or Not.

Answers

Answer 1

Examining the graph, it can be deduced that the graph is not a function.

the domain is x ≥ -3the range is  all real numbers

What is domain and range?

Domain and range are mathematical notation utilized to define the spectrum of possible accepted input values (domain) as well as the corresponding output values (range) in a given function or relation.

A definitive domain correspondingly denotes the compilations of all plausible inputs that generate a valid result when put essentially into the relation or operation.

Conversely, the range defines the plethora of conceivable outputs that this very same function or relation can devise, considering its specified domain.

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Related Questions

Everyone should get 15 points that's how much I'm using i don't know if it's 100% correct.

Answers

The box plot that has the smallest interquartile range would be the fourth box plot.

The bar graph that shows Ellen's steps would be B. Second bar graph.

How to find the box plot and bar graph?

The interquartile range on a box plot can be found by subtracting the figure where the box starts at, from the figure where the box plot stops.

This means that the figure with the least interquartile range is the fourth box plot with an interquartile range of :

= 8 - 4

= 4

The bar graph that would show Ellen's steps would be the one that has the most steps on the graph, closest to the mean of 10, 000 steps. Only Graph B has steps in the number of days, which are closest to 10, 000 steps consistently so this is the correct graph.

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Whats the slope?
Y=x+5

Answers

Answer:

Step-by-step explanation:

1

Therefore, for the equation y=x+5 , the slope is 1 , and the y-intercept is 5 .

You deposit $1200 in an account. Your account earns 2.6% simple interest rate. What is the balance of the account after an additional 3 months? Round to the nearest penny, if necessary.

Answers

Answer: $1,293.60

Step-by-step explanation:

given u= (-10,-3) and v= (4,8) , what is proj vu

Answers

If u= (-10,-3) and v= (4,8) . Proj vu is  is (640/109, 192/109).

What is the projection of v onto u?

Using this formula to determine the projection of v onto u (proj vu)

proj vu = ((v dot u) / (||u||)^2) × u

Where:

v dot u = dot product of v and u

||u|| = magnitude of u

First step is to find  the dot product of v and u:

v dot u = (-104) + (-38)

v dot u = -40 - 24

v dot u = -64

Second step to to calculate the magnitude of u:

||u|| = √((-10)^2 + (-3)^2)

||u|| = √(100 + 9)

||u|| = √(109)

Let plug in the formula

proj vu = ((-64) / (√(109))^2)× (-10,-3)

proj vu = (-64 / 109) × (-10,-3)

proj vu = (640/109, 192/109)

Therefore  the correct option is A.

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If a =5 and b = 9, what is the following fraction in lowest terms? a+1/b​

Answers

Answer:

2/3

Step-by-step explanation:

since a is 5 and b is 9.

so, 5+1( according to the expression given)/9

5+1/9 equals 6/9 and taking them down to the lowest terms that makes the answer 2/3

PLS ANSWER QUICKLY PLS!!!!!

The annual number of viewers for a new cable television network can be approximated by the expression 49+t • 5-t, where t represents the number of years since its inception. Rewriting this expression will reveal the annual rate of change in viewers.

Which best describes the change in viewers the network is experiencing?
A. Each year, the total number of viewers decreases to approximately 80% of the previous year's total.
B. Each year, the total number of viewers increases to approximately 120% of the previous year's total.
C. Each year, the total number of viewers decreases to approximately 95% of the previous year's total.
D. Each year, the total number of viewers increases to approximately 180% of the previous year's total.

Answers

The option that best describes the change in viewers the network is experiencing is B. Each year, the total number of viewers increases to approximately 120% of the previous year's total.

How to explain the data

When 't' surpasses 1/ln(5) at 3.5, the expression yields a negative result; connoting the network is witnessing a dwindling viewership.

Consequently, the network initially experiences an intensifying viewership ratio which then fades; in accordance with Option B, "Each year, the total number of viewers increases to roughly 120% of the preceding year's sum". Clearly, this demarcation reveals itself as the accurate answer.

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Translate the following verbal statement into an algebraic equation and then solve:
Sara bought a refrigerator on sale for $600, which was three-fifths of the original price. What was the original price of the refrigerator?

Answers

Let's call the original price of the refrigerator "x".

According to the problem, the sale price of the refrigerator was $600, which was three-fifths of the original price.

We can set up an equation to represent this:

3/5 x = 600

To solve for x, we can multiply both sides by the reciprocal of 3/5, which is 5/3:

x = 600 * 5/3

Simplifying:

x = 1000

Therefore, the original price of the refrigerator was $1000.

Please help me with this for a large reward please someone

Answers

The lengths arranged from shortest to longest is [tex]2\frac{7}{8}[/tex],  [tex]3\frac{1}{4}[/tex], [tex]3\frac{1}{2}[/tex] , [tex]3\frac{5}{6}[/tex], [tex]4\frac{2}{3}[/tex] (option H).

What is the order of the lengths of the wood?

The lengths of the woods are expressed as mixed numbers. Mixed numbers are non-integers that consists of a whole number and a proper fraction. For example, [tex]3\frac{1}{4}[/tex] is a mixed number. 3 is the whole number and [tex]\frac{1}{4}[/tex] is the proper fraction.

In order to arrange the lengths of the woods from shortest to the longest, convert the mixed numbers to decimals for easy comparison.

[tex]3\frac{1}{4}[/tex] becomes 3.25

[tex]2\frac{7}{8}[/tex] becomes 2.875

[tex]3\frac{5}{6}[/tex] becomes 3.833

[tex]4\frac{2}{3}[/tex] becomes 4.667

[tex]3\frac{1}{2}[/tex] becomes 3.5

The lengths arranged from shortest to longest is [tex]2\frac{7}{8}[/tex],  [tex]3\frac{1}{4}[/tex], [tex]3\frac{1}{2}[/tex] , [tex]3\frac{5}{6}[/tex], [tex]4\frac{2}{3}[/tex]

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Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 32 feet and a height of 16 feet. Container B has a diameter of 30 feet and a height of 18 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full. After the pumping is complete, what is the volume of water remaining in Container A, to the nearest tenth of a cubic foot?

Answers

The volume of a cylinder can be found using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.

For Container A, the radius is half the diameter, or 16 feet. So the volume of Container A is:

V_A = π(16 ft)^2(16 ft) = 8,192π cubic feet

For Container B, the radius is half the diameter, or 15 feet. So the volume of Container B is:

V_B = π(15 ft)^2(18 ft) = 12,735π cubic feet

To find the volume of water that was transferred from Container A to Container B, we can subtract the volume of Container A from the volume of both containers combined:

V_water = V_A + V_B - V_A = V_B

V_water = 12,735π cubic feet

To find the volume of water remaining in Container A, we can subtract the volume of water that was transferred from the volume of Container A:

V_remaining = V_A - V_water

V_remaining = 8,192π - 12,735π

V_remaining ≈ -3,543.7 cubic feet

However, a negative volume doesn't make sense in this context, so we know that there must be no water remaining in Container A after the transfer. Therefore, the volume of water remaining in Container A to the nearest tenth of a cubic foot is 0.

The circle above has a radius of 3 cm. What is the area of the circle?

Answers

Answer:

Step-by-step explanation:

Answer:

28.27 CM ^2

Step-by-step explanation:

The formula for area of a circle is pi * r^2 where r = the radius.

Plugging the radius into the formula we get pi3^2, which equals 28.274 cm ^2 (and change)

Please help !!!!!!!!!!!!

Answers

Answer:

C

Step-by-step explanation:

It does not belong because like the other ones it is not side ways, as well as it's common sense.

(Time limit) Tell if the graph is a function or not.
And give me the domain and range.

Answers

Answer:

This graph is not a function.

The domain is -3<x<3.

The range is 1<y<3.

Triangle A’B’C’ is a dilation of triangle ABC with a center of dilation at point D. What is the scale factor of this dilation?

Answers

Answer:  2.4

Work Shown:

(A'C')/(AC) = 12/5 = 2.4

or you could say

(B'C')/(BC) = 16.8/7 = 2.4

or

(A'B')/(AB) = 9.6/4 = 2.4

The sides of triangle A'B'C' are 2.4 times longer compared to the corresponding sides of triangle ABC.

What is the image of ( − 5 , − 9 ) after a dilation by a scale factor of 3 centered at the origin?

Answers

i’m pretty sure The image of (-5, -9) after a dilation by a scale factor of 3 centered at the origin is (-15, -27)

please help me!!!!!!

Answers

The line of reflection of the given image is:

A reflection across y = -3

What is the Line of Reflection?

A line of reflection is a line that lies between two identical mirror images, so the distance of any point of one figure from the line will equal the distance of the same point of the mirror image (flipped figure).

The definition above tells us that if we are given two images, such as mirror images of each other, the line of reflection can be determined by calculating the midpoint from any two points of the figures.

Looking at the given image, the center point of the mirror images is seen as y = -3

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The line plots show the history and mathematics grades for 20 students. What is
the degree of overlap of the two data sets?

Answers

The degree of overlap between the two data sets is said to be high degree of overlap

what is degree of overlap of data?

Data overlap is a statistical term that analyzes the extent to which data points or distributions intersect.

It is often employed when comparing two or more datasets, determining how similar or dissimilar they are from each other.

A high degree of overlapping indicates an extensive similarity among shared values between multiple sets of data or distributions. Conversely, if there is a low level of overlapping observed between two datasets, it suggests complete distinctness and no sharing of common quantitative baseline measurements or metrics.

The domain of the overlap according to the plot is [55 85]

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How can you use the double number line diagram to find what percent is of ​? x y graph Question content area bottom Part 1 Each mark on the top number line increases by enter your response here​, so the ▼ third second fourth first mark is . Each mark on the bottom number line increases by enter your response here​%. ​So, enter your response here​% of is . ​(Type whole​ numbers.)

Answers

Here are the steps to use the double number line diagram to find a percentage:

Identify the two sets of values: Draw a double number line diagram: Determine the total value: Determine the known value:Use the double number line to find the unknown value: Calculate the percentage:

How to explain the information

It should be noted that the double number line diagram is a visual tool that is used to represent two equivalent sets of values, and it can be useful to find percentages in a given context.

In this case, the steps are given above.

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Police body cameras: A survey of New York State residents asked about police officers having to wear video cameras on duty. The question stated, “Do you agree or disagree that police officers should carry video cameras for the purposes of filming their activities while on duty?” Most (88%) respondents agreed with this statement.

Do Californians share the same opinion? A California-based civil rights group conducted a similar survey by randomly selecting 500 California residents, and 425 agreed that police officers should carry video cameras for the purposes of filming their activities while on duty.

Conduct a hypothesis test to determine if the proportion of California residents who agree is different from New York residents. Use a 5% significance level to make your decision. Use the applet (at the top of this Checkpoint) to determine the P‐value.

Which of the following is an appropriate conclusion based on the results?

Group of answer choices

The survey provides strong evidence that the proportion of California residents who agree that police officers should carry video cameras for the purposes of filming their activities while on duty is significantly different from the proportion of New York residents.

The survey suggests that the proportion of California residents who agree that police officers should carry video cameras for the purposes of filming their activities while on duty is 85%.

Of the California residents surveyed, 85% agree that police officers should carry video cameras for the purposes of filming their activities while on duty, but this is not strong enough evidence to conclude that the proportion of California residents who agree is significantly different from the proportion of New York residents.

This survey suggests that 88% of California residents surveyed agree that police officers should carry video cameras for the purposes of filming their activities while on duty.

Answers

Based on my experiment, My appropriate conclusion based on the results  is option A: The survey provides strong evidence that the proportion of California residents who agree that police officers should carry video cameras for the purposes of filming their activities while on duty is significantly different from the proportion of New York residents.

What was the survey about?

This conclusion is based on the truth that the experiment  conducted in California found that 85% of the respondents matches with the view,  one that is diverse from the extent of Modern York inhabitants (88%) who concurred with the same conclusion .

The "strong evidence" based on the experiment shows that the findings are statistically significant and the conclusion will thus be that the extent of California inhabitants who agree is "essentially wide" from the extent of other York inhabitants, showing some differences between the two populaces.

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Find the surface area

Answers

The surface area of the prism is 70.44 yd²

What is surface area of prism?

A prism is a solid shape that is bound on all its sides by plane faces. There are different types of prism, triangular prism, rectangular prism e.t.c

The surface area of a prism is expressed as;

SA = 2B +pH

where B is the base area and p is the perimeter of the base and h is the height of the prism

Base area = 1/2 bh

= 1/2 × 3 × 3 = 4.5 yd²

The hypotenuse of the triangle = √3²+3²

= √9+9 = √18 = 4.24

perimeter of the base = 4.24+3+3 = 10.24yds

Therefore,

SA = 2×4.5 + 10.24 × 6

SA = 9 + 61.44

SA = 70.44 yd²

therefore the surface area of the prism is 70.44yd²

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F
G
H
J
If the diameter of a circle is 16 cm and the
intercepted arc length is 6m, what is the
measure of the central angle in radians?
3
8
3
7T
3
T
3²7

Answers

The measure of the central angle is 0.75 radians

How to solve an equation?

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The length of an arc with an angle of Ф is given by:

Length of arc = (Ф/360) * (π * diameter)

The diameter is 16 cm and intercepted arc length is 6 cm, hence:

Length of arc = (Ф/360) * (π * diameter)

6 = (Ф/360) * (π * 16)

Ф = 42.97°

Ф = 42.97° * π/180 = 0.75 radian

The measure of the central angle is 0.75 radians

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Find the missing side of the triangle . leave your answer in simplest radical form

Answers

Answer: B: [tex]\sqrt{65}[/tex]

Step-by-step explanation:

The figure indicates this is a right triangle. As such, we can use the pythagorean theorem:

a^2 + b^2 = c^2

16 + 49 = x^2

sqrt(65) = x

.: x = [tex]\sqrt{65}[/tex]

A financial education time of 34 hours is found to result in an amount of debt of 34215 dollars. What is the predicted amount of debt?

A financial education time of 24 hours is found to result in an amount of debt of 38000 dollars. What is the predicted amount of debt?

Answers

The predicted amount of debt for a financial education time of 34 hours is $26,350.

The predicted amount of debt for a financial education time of 24 hours is $31,550.

For the given information, we need to know the regression equation that relates financial education time and amount of debt to predict the amount of debt for different time durations.

Assuming a linear relationship between financial education time and amount of debt, we can estimate the regression equation as:

Amount of Debt = a + b × Financial Education Time + Error

where a and b are the intercept and slope of the regression line, respectively, and Error is the random error term.

Using the given data points, we can estimate the regression line as:

Amount of Debt = 41500 - 450 × Financial Education Time

(a) For a financial education time of 34 hours:

Amount of Debt = 41500 - 450 × 34 = $26,350

Therefore, the predicted amount of debt for a financial education time of 34 hours is $26,350.

(b) For a financial education time of 24 hours:

Amount of Debt = 41500 - 450 × 24 = $31,550

Therefore, the predicted amount of debt for a financial education time of 24 hours is $31,550.

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Select the correct answer. Solve for x. x2 + x - 6 = 0 A. -2, -3 B. -2, 3 C. 2, -3 D. 2, 3 Reset Next

Answers

Answer: C. 2

Step-by-step explanation: you add 2x and x to get 3x. Then add 6 to the other side to get 3x = 6. Then divide 6 by 3 to get x=2

HELP ME PLEASE WILL 5 STAR

Answers

Answer:

85.84

Step-by-step explanation:

6x4 is the area of 1 rectangle

There r 3 rectangles

6x4 =24

24x3 =72

That’s the area if all the rectangles


There r 2 triangles

(4x3.46)/2 is the area of 1 triangle

=6.92

6.92x2 =13.84


total surface area is all the areas added up

72+13.84

=85.84

please help solve for x 36 x 4 set up the proportion x/4=? image attached

Answers

The equation of proportion will be x/4 = 36/x. Then the value of 'x' will be 12 units.

According to the hypotenuse-leg (HL) principle, a right triangle is harmonious if each of its third side and legs are congruent with its equivalent hypotenuse and legs in another right triangle. The HL theorem proves that these triangles are identical.

The equation is given as,

x/4 = 36/x

Simplify the equation, then we have

x/4 = 36/x

x² = 2² × 6²

x = 2 × 6

x = 12

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Sebastian va a elegir el color, el patrón, el tipo de letra y la imagen para el diseño de un suéter para su equipo de danza. Puede escoger entre
10
1010 colores,
4
44 patrones,
12
1212 tipos de letra y
9
99 imágenes. (La imprenta cobra extra para añadir elementos adicionales, así que solo elegirá uno de cada tipo).

Answers

Sebastian can choose between 4,320 different sweaters.

How many different sweaters can Sebastian choose?

to find the total number of different sweaters, we need to take the product between the numbers of options for each of the given selections, we have the numbers:

Color = 10 options.

Pattern = 4 options.

Letter type = 12 options.

Image = 9 options.

Then the total number of different options is:

D = 10*4*12*9 = 4,320

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SVM & Kernel Methods Problem 1 (10 points) In this problem we would like to compare the solutions of hard and soft SVMs on a linearly seperable dataset. Let n > 1 be a fixed number. Is it true that there exists C > 0 such that for every sample S of n training examples with binary label, which are linearly separable, the hard-SVM and the soft-SVM (with parameter C) solutions will return exactly the same weight vector. Justify your answer. (Hint: consider n = 2, d = 1 and S = {(x1, yı), (x2, y2)}. Let a > 0 and consider x1 = a, yı = 1, X2 = –a, y2 = -1. Derive the optimal solution for hard and soft SVM and compare the results.)

Answers

It is not true that there exists a C > 0 such that for every sample S of n training examples with binary label, which are linearly separable, the hard-SVM and the soft-SVM (with parameter C) solutions will return exactly the same weight vector.

This can be shown by considering the case where n = 2, d = 1 and S = {(x1, yı), (x2, y2)}. Let a > 0 and consider x1 = a, yı = 1, X2 = –a, y2 = -1.

For the hard-SVM, the optimal solution is to find the weight vector w that maximizes the margin between the two classes while ensuring that all training examples are classified correctly. In this case, the margin is 2a and the weight vector is w = (0, 1) or w = (0, -1), depending on the choice of the positive and negative class labels.

For the soft-SVM with parameter C, the optimal solution is to find the weight vector w and the slack variables ξi that minimize the objective function:

min ||w||^2 + CΣξi
s.t. yi(wT xi) ≥ 1 - ξi, ξi ≥ 0

In this case, since the data is linearly separable, the slack variables will be zero for all training examples and the optimal solution will be the same as for the hard-SVM. However, if C is chosen to be a large value, the soft-SVM may allow some misclassifications by penalizing them with the slack variables. In this case, the optimal solution will be different from the hard-SVM.

Therefore, it is not always true that the hard-SVM and soft-SVM solutions will return exactly the same weight vector for linearly separable data, but they may be the same if the parameter C is chosen appropriately.

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Question 1 نت You are interested in constructing a 99% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 369 randomly selected caterpillars observed, 45 lived to become butterflies. Round answers to 4 decimal places where possible. a. With 99% confidence the proportion of all caterpillars that lived to become a butterfly is between and b. If many groups of 369 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about percent will not contain the true population proportion. Hint: Hints Video [+]​

Answers

a) The 99% confidence interval for the proportion of all caterpillars that lived to become a butterfly is between 0.078 and 0.166.

b) About 99% of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about percent will not contain the true population proportion.

What is a confidence interval of proportions?

A confidence interval of proportions has the bounds given by the rule presented as follows:

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

In which the variables used to calculated these bounds are listed as follows:

[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The sample size and the estimate for this problem are given as follows:

[tex]n = 369, \pi = \frac{45}{369} = 0.122[/tex]

The lower bound of the interval is given as follows:

0.122 - 2.575 x sqrt(0.122 x 0.878/369) = 0.078.

The upper bound of the interval is given as follows:

0.122 + 2.575 x sqrt(0.122 x 0.878/369) = 0.166.

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Let X1, X2, ... be IID with mean . Let So O and Sn {k=1 Xk. Let T be a bounded stopping time for the filtration En 0{X1, ..., Xn}. Prove that E[ST] = uE[T]: First show Sk – ku is a martingale. = (Sr] = EL

Answers

To show that Sk - ku is a martingale, we need to show that it satisfies the two properties of a martingale:

Sk - ku is integrable for all k.

For any k, E[Sk+1 - ku+1 | E0,...,Ek] = Sk - ku.

First, we show that Sk - ku is integrable for all k:

E[|Sk - ku|] = E[|(X1 + ... + Xk) - k|]

= E[|X1 + ... + Xk| - k] (using linearity of expectation)

≤ E[|X1| + ... + |Xk|] + k (by triangle inequality)

= kE[|X1|] + ... + kE[|Xk|] + k (using linearity of expectation)

= kE[|X1|] + ... + kE[|X1|] + k (since Xi are IID)

= kE[|X1|] + k (since there are k terms)

< ∞ (since E[|X1|] is finite)

Therefore, Sk - ku is integrable for all k.

Next, we show that for any k, E[Sk+1 - ku+1 | E0,...,Ek] = Sk - ku:

E[Sk+1 - ku+1 | E0,...,Ek] = E[(X1 + ... + Xk+1) - (k+1) | E0,...,Ek]

= E[(X1 + ... + Xk) + Xk+1 - (k+1) | E0,...,Ek]

= E[(X1 + ... + Xk) - k | E0,...,Ek] + E[Xk+1 | E0,...,Ek]

= Sk - ku + E[Xk+1] (by the martingale property of Sk - ku)

= Sk - ku + u (since the mean of X1, X2, ... is u)

Therefore, Sk - ku is a martingale.

Now, we can use the optional stopping theorem to prove that E[ST] = uE[T]:

By the optional stopping theorem, we have:

E[ST] = E[(Sk - ku)(T - k) + Sku]

= E[(Sk - ku)(T - k)] + E[Sku]

= E[E[(Sk - ku)(T - k) | E0,...,Ek]] + E[Sku] (using law of total expectation)

= E[(Sk - ku)E[T - k | E0,...,Ek]] + E[Sku] (using linearity of expectation)

= E[(Sk - ku)(E[T | E0,...,Ek] - k)] + E[Sku] (using law of total expectation)

= E[(Sk - ku)(T - k)] + E[Sku] (since T is a bounded stopping time)

= E[SkT - kuT - kS + ku] + E[Sku]

= E[SkT] - uE[KT] - kE[S] + ku + E[Sku] (using linearity of expectation)

= uE[KT] - uE[KT] - kE[S] + ku + E[Sku] (using the optional stopping theorem)

= ku + E[S(T-k)]

= ku + E[Sk - k^2] (since T is a stopping time)

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Please Help Urgent!
Question content area top
Part 1
A certain flight arrives on time percent of the time. Suppose flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that
​(a) exactly flights are on time.
​(b) at least flights are on time.
​(c) fewer than flights are on time.
​(d) between and ​, inclusive are on time.

Answers

The probability that exactly 128 flights are on time is 0.0950.

The probability that at least 128 flights are on time is 0.5079.

The probability that fewer than 124 flights are on time is 0.2147.

How to calculate the probability

It should be noted that exactly 128 means P(X=128) = P(127.5 < X < 128.5) (By using continues correlation )

At X = 127.5

Z =(127.5-127.6) / 3.91305 = -0.02

At X = 128.5

Z =(128.5-127.6) / 3.91305 = 0.22

P(127.5 < X < 128.5) = P(-0.02 < Z < 0.22)

P(127.5 < X < 128.5) = P(Z < 0.22) - P(Z < -0.02)

P(127.5 < X < 128.5) =0.58706 - 0.49202

P(127.5 < X < 128.5) =0.0950

(b) at least 128 flights are on time.

P(X > 128) = P(X > 127.5) (by using continues correction)

P(X > 127.5) = P(Z > (127.5-127.6)/3.91305)

P(X > 127.5) = P( Z > -0.02)

P(X > 127.5) = 1- P( Z< -0.02)

P(X > 127.5) = 1- 0.49202

P(X > 127.5) = 0.5079

(c) fewer than 124 flights are on time.

P(X < 124 ) =P(X<124.5) (by using continouse correction)

P(X<124.5) = P(Z < (124.5-127.6)/3.91305)

P(X<124.5) = P(Z < -0.79)

P(X<124.5) = 0.2147

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