Which of the following is an arithmetic sequence?

The centroid is 1/3 of the vertical distance between QV

QV = 3 x VT = 3 x 5 = 15

QT = 15-5 = 10

Answer:

The probability distribution for the  number of heads occurring in three coin tosses are P(X1) = 1, P(X2)= 2/3, P(X3)= 2/3, P(X4)= 1/3, P(X5)= 2/3, P(X6)= 1/3, P(X7)= 1/3 and P(X8)= 0

Step-by-step explanation:

The question is incomplete. Here is the complete question;

The sample space, S, of a coin being tossed three times is shown below, where Hand T denote the coin

landing on heads and tails respectively.

S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

Let X = the number of times the coin comes up heads. What is the probability distribution for the  number of heads occurring in three coin tosses?

Probability is the likelihood or chance that an event will occur.

Probability = expected outcome/total outcome of event

From the question given, the total number of sample space will be our total outcome during each toss = 3

If X is the number of times the coin comes up heads, the number of times the coin turn up all heads will be the expected outcome during each throw.

Probability distribution P(Xi)= [tex]\frac{n(Xi)}{n(S)}[/tex]

Xi is the probability that the head turns up at each throw.

n(Xi) is the expected outcome during each toss

n(S) is the total outcome during each toss

During the first throw, the head turns up three times (HHH), the probability that heads turns up ia 3/3 = 1

P(X1) = 1

During the second, third and fifth throw, the head turns up two times, the probability that heads turns up during this times will be 2/3

P(X2)= 2/3

P(X3)= 2/3

P(X5)= 2/3

During the fourth, sixth and seventh throw, the head turns up just once, the probability that heads turns up during this times will be 1/3

P(X4)= 1/3

P(X6)= 1/3

P(X7)= 1/3

Since no head turns up during the eight throw, the probability that heads turns up during this time will be 0/3 which is 0.

P(X8)= 0

The probability distribution for the  number of heads occurring in three coin tosses are P(X1) = 1, P(X2)= 2/3, P(X3)= 2/3, P(X4)= 1/3, P(X5)= 2/3, P(X6)= 1/3, P(X7)= 1/3 and P(X8)= 0

Answer:

The guy who answered on top meant B if you didn't understand what he said

Step-by-step explanation:

:)

Answer:

2x^2 -3x -8

Step-by-step explanation:

f(x) = 2x^2 - 5

g(x) = 3x + 3,

(f - g)(x)=  2x^2 - 5 -(3x + 3)

Distribute the minus sign

(f - g)(x)=  2x^2 - 5 -3x - 3

Combine like terms

            = 2x^2 -3x -8

Answer:

Step-by-step explanation:

The arrow with two tips is translated as "if and only if". The symbols [tex]\land, \lor[/tex] and read as "and" and "or"respectively.

If we have the following p: it is hot today. q: it is sunny r: it is raining

Then

i. q ↔ p : It is sunny if and only if it is hot today.

ii. p ↔ ( q ˄ r ) : it is hot today if and only if it is sunny and it is raining

iii. p ↔ ( q ˅ r) : it is hot today if and only if it is sunny or it is raining

iv. r ↔ ( p ˅ q) : it is raining if and only if it is hot today or it is sunny

Answer:

Always

Step-by-step explanation:

If the irrational parts of the numbers have zero sum, the sum is rational. If not, the sum is irrational. It is true, for example, for 2 7, 3. It is false, for example, for3+2 5,−2 5 .

Answer:

always

Step-by-step explanation:

Rational numbers can be expressed as a fraction of two integers. So, adding two rationals is the same as adding two such fractions.

Answer:

Step-by-step explanation:

a) Rearranging the given data in ascending order, it becomes

36, 38, 43, 44, 44, 45, 50, 55, 56, 57, 56, 60, 62, 65, 69

n = 15

The mean = (55 + 56 + 44 + 43 + 44 + 56 + 60 + 62 + 57 + 45 + 36 + 38 + 50 + 69 + 65)/15 = 52

Median = 55

b) Range = 69 - 36 = 33

The median divides the data set into two halves, lower and upper. The median of the lower halve is the first quartile, Q1 while the median of the upper halve is the third quartile, Q3

First quartile, Q1 = 44

Third quartile, Q3 = 60

Inter quartile range, IQR = Q3 - Q1 = 60 - 44 = 16

Variance = (summation(x - mean)²/n

Variance = (55 - 52)^2 + (56 - 52)^2 + (44 - 52)^2 + (43 - 52)^2 + (44 - 52)^2 + (56 - 52)^2 + (60 - 52)^2 + (62 - 52)^2 + (57 - 52)^2 + (45 - 52)^2 + (36 - 52)^2 + (38 - 52)^2 + (50 - 52)^2 + (69 - 52)^2 + (65 - 52)^2/15

Variance = 93.467

Standard deviation = √variance

Standard deviation = √93.467 =

9.668

The data does not contain any outliers.

Answer:

5

To find the first term

T(1)=(1×2)+3

=2+3

=5

Answer:

37.27% probability that he or she will have a heart attack.

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Periodontal disease

Event B: Heart attack

Researchers discovered that 82% of people who have suffered a heart attack had periodontal disease, an inflammation of the gums.

This means that [tex]P(A|B) = 0.82[/tex]

Only 33% of healthy people have this disease.

This means that [tex]P(A) = 0.33[/tex]

Suppose that in a certain community heart attacks are quite rare, occurring with only 15% probability.

This means that [tex]P(B) = 0.15[/tex]

If someone has periodontal disease, what is the probability that he or she will have a heart attack

[tex]P(B|A) = \frac{0.15*0.82}{0.33} = 0.3727[/tex]

37.27% probability that he or she will have a heart attack.

Answer:

Because of absence of options, I have listed statements that are true; according to the model.

Step-by-step explanation:

To answer this, we find all possible explanations to the model. First, we know that:

X = time in office (in days)

Y = approval rating (in percentage)

The constant term in the model is 70

So the true statements that can be derived are:

(A) Y is inversely related to X. This is obvious because of the difference in sign of the coefficient of Y and that of X.

The coefficient of Y is +1

The coefficient of X is -0.01

Y has a positive coefficient while X has a negative coefficient.

The inverse relationship hence implies that the more days the politician spends in office, the less his percentage approval rating (and vice versa)!

Testing;

If X = 10 days, Y = 69.9%

If X = 20 days, Y = 69.8%

If X is 30 days, Y = 69.7%

(B) The rate at which approval rating drops is very slow; compared to the increase in number of days in office. A 10 day increase in number of days in office only results in a 0.1 or 10% decrease in percentage approval ratings.

(C) The longer a politician stays in office, the less his approval rating.

(D) The percentage approval rating is greatly influenced or increased by the constant term 70

Answer:

The 95% confidence interval for the population mean (calorie count of the snacks bars) is (130.32, 161.68).

Step-by-step explanation:

The question is incomplete:

"A random sample of a specific brand of snack bar is tested for calorie count, with the following results: 149, 145,140,160,149,153,131,134,153. Assume the population standard deviation is σ=24 and that the population is approximately normal. Construct a 95% confidence interval for the calorie count of the snack bars."

We start by calculating the mean of the sample:

[tex]M=\dfrac{1}{9}\sum_{i=1}^{9}(149+145+140+160+149+153+131+134+153)\\\\\\ M=\dfrac{1314}{9}=146[/tex]

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is know and is σ=24.

The sample mean is M=146.

The sample size is N=9.

As σ is known, the standard error of the mean (σM) is calculated as: [tex]\sigma_M=\dfrac{\sigma}{\sqrt{N}}=\dfrac{24}{\sqrt{9}}=\dfrac{24}{3}=8[/tex]

The z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_M=1.96 \cdot 8=15.68[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 146-15.68=130.32\\\\UL=M+t \cdot s_M = 146+15.68=161.68[/tex]

The 95% confidence interval for the population mean is (130.32, 161.68).

Answer:

20 grams

Step-by-step explanation:

10 grams is 50%. 50% x 2= 100%. so you do 50/100=10/20, and you will get 2. Apply that to the 10, 10 x 2=20.

Answer: 16.1 ounces per minute

Step-by-step explanation:

in 7 days, he painted by 4 hours each day, so we have a total of 28 hours.

In a hour we have 60 minutes, so we have a total of:

28*60 = 1680 minutes.

He used 211 gallons, and knowing that 1 gallon is 128 ounces, then 211 gallons is:

211*128 ounces = 27,008 ounces.

Then the ounces dispensed each minute are:

R = 27,008/1680 ounces per minute = 16.1 ounces per minute

Answer:

1st one, I think so. I'm pretty positive

Answer:

Step-by-step explanation:

So, in this image, there are 6 blocks in total!

The little guy standing in front would only be able to see the bottom two cubes, along with the top two, making 4 blocks in total! :3

#SpreadTheLove <3

Answer:

Probability that 100 or fewer of these Americans could only converse in one language is 0.8599.

Step-by-step explanation:

We are given that a recent study reported that 73% of Americans could only converse in one language.

A random sample of 130 Americans was randomly selected.

Let [tex]\hat p[/tex] = sample proportion of Americans who could only converse in one language.

The z score probability distribution for sample proportion is given by;

                                 Z  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, p = population proportion of Americans who could only converse in one language = 73%

           [tex]\hat p[/tex] = sample proportion = [tex]\frac{100}{130}[/tex] = 0.77

           n = sample of Americans = 130

Now, probability that 100 or fewer of these Americans could only converse in one language is given by = P( [tex]\hat p[/tex] [tex]\leq[/tex] 0.77)

      P( [tex]\hat p[/tex] [tex]\leq[/tex] 0.77) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{0.77-0.73}{\sqrt{\frac{0.77(1-0.77)}{130} } }[/tex] ) = P(Z [tex]\leq[/tex] 1.08) = 0.8599                    

The above probability is calculated by looking at the value of x = 1.08 in the z table which has an area of 0.8599.

Answer: P = 0.28

Step-by-step explanation:

If we pick it at random, the probability of selecting each tile must be equal. this means that the probability of picking a tile of a giving color is equal to the number of the tiles of that color divided the total number of tiles.

We have 14 beige tiles and 20 + 14 + 16 = 50 tiles in total.

Then the probability of piking a beige tile is:

P = 14/50 = 0.28

Answer:

1/4

Step-by-step explanation:

Let's denote the probabilities as following:

Probability that a teenager has a sister:

P(A) = 12/28

Probability that a teenager has a brother:

P(B) = 7/28

Probability that a teenager has both a sister and a brother:

P(A⋂B) = 3/28

Probability that a selected teenager has a sister also has a brother, or in other words, he/she has a brother, given he/she had a sister:

P(B|A)

Let's apply the formula of conditional probability to work out P(B|A)

P(B|A) = P(A⋂B)/P(A) = (3/28)/(12/28) = (3*28)/(12*28) = 3/12 = 1/4

=> Option C is correct

Hope this helps!

Answer:

  y = 0; z = -5

Step-by-step explanation:

Excluded values are ones that make the fraction "undefined." That will be the case when the denominator is zero.

When y = 0, the denominator is zero.

When z = -5, the denominator is zero.

Excluded values are y = 0; z = -5.

Answer:

-5

Step-by-step explanation:

Answer:

11/15

Step-by-step explanation:

1 hour = 60 minutes

44 minutes out of 60 minutes is the fraction

44/60 = 11/15

Answer:

Null hypothesis H0: p = 0.01

Alternative hypothesis Ha: p < 0.01

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

For the case above;

The null hypothesis is that the proportion of people with colon polyps expected to die from colon cancer remains 0.01 with or without colonoscopy.

H0: p = 0.01

The alternative hypothesis is that the proportion of people who die from colon cancer after having polyps removed in a colonoscopy is significantly less than the expected proportion (without a colonoscopy) of 0.01.

Ha: p < 0.01

Answer:

(a)Distance traveled by each explorer travel as Mars rotates by 1 radian

(b)Number of hours it takes Mars to rotate 1 radian=3.9152 hours

(c)Speed of each explorer around Mars.

Step-by-step explanation:

Part A

For any given parallel of latitude[tex]\text{Circumference}=2\pi R \cos \beta$ where \beta$ is the angle of latitude.[/tex]

Opportunity landed at 2° south latitude, where Mars’ radius is about 2110 miles.

[tex]\text{Circumference at 2\°S latitude}=2\pi*2110* \cos 2^\circ\\=13249.44$ miles[/tex]

Phoenix landed at 68° north latitude, where Mars’ radius is about 790 miles.

[tex]\text{Circumference at 68\°N latitude}=2\pi*790* \cos 68^\circ\\=1859.44$ miles[/tex]

Part B

Next, we determine the distance (Length of arc) covered by each explorer as Mars rotates by 1 radian.

[tex]\text{Length of arc (in radian)}=\dfrac{\theta}{2\pi} \times $Circumference[/tex]

Opportunity's Distance

[tex]=\dfrac{1}{2\pi} \times 13249.44\\\\ =2108.71$ miles[/tex]

Phoenix's Distance

[tex]=\dfrac{1}{2\pi} \times 1859.44\\\\ =295.94$ miles[/tex]

Part C

Mars rotates on its axis once every 24.6 Earth-hours.

Therefore:

[tex]\dfrac{24.6}{2\pi} \approx $ 3.9152 hour per radian[/tex]

Part D:Speed of each explorer

[tex]\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]

[tex]\text{Speed of Opportunity = }\dfrac{2108.71}{3.9152}\\$=538.59 miles per hour\\\\Speed of Phoenix =\dfrac{295.94}{3.9154}\\=75.59$ miles per hour[/tex]

Answer:

3.00

Step-by-step explanation:

3.14 is rounded to 3.00

Answer:

141.3 m²

Step-by-step explanation:

V= πr²h

V=3.14*(6/2)²*5= 141.3 m²

Answer:

a) 10% of the babies with 36 months of age weigh less than 11kg, and 100 - 10 = 90% weigh more.

b) 90% of the newborn females have a lenght of less than 53.3 cm and 100 - 90% = 10% have a length higher than 53.3 cm.

Step-by-step explanation:

Meaning of a percentile:

When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.

(a) The 10th percentile of the weight of males 36 months of age in a certain city is 11.0 kg.

10% of the babies with 36 months of age weigh less than 11kg, and 100 - 10 = 90% weigh more.

(b) The 90th percentile of the length of newborn females in a certain city is 53.3 cm.

90% of the newborn females have a lenght of less than 53.3 cm and 100 - 90% = 10% have a length higher than 53.3 cm.

Answer:

Step-by-step explanation:

The explanation is given in the attached picture below

Answer:

[tex]5y^3/5y^-2[/tex] = [tex]y^5[/tex]

Step-by-step explanation:

[tex]5y^3/5y^-2[/tex]

as 5 is both in numerator and denominator it will get cancelled so we have now expression

[tex]y^3/y^-2[/tex]

we will use  law of indices wherein if there is

[tex]a^x/a^y = a^(x-y)[/tex]

which means that if the base is same in numerator and denominator then we have to subtract the power of denominator from numerator to get the reduced form using this concept

here power in numerator is 3 and power in denominator  is -2

hence we will be subtracting -2 from 3

[tex]y^3/y^-2 = y^(3-(-2) = y^(3+2) = y^5[/tex]

Thus,

[tex]5y^3/5y^-2[/tex] = [tex]y^5[/tex]

Length and width of rectangle is 86 unit and 15 unit

Given that;

Perimeter of a rectangle = 202

Length of rectangle = 26 + 4[Width]

Find:

Dimensions of rectangle

Computation:

Assume;

Width of rectangle = a

So,

Length of rectangle = 4a + 26

Perimeter of a rectangle = 2[l + b]

202 = 2[(4a + 26) + a]

101 = 4a + 26 + a

5a + 26 = 101

5a = 75

a = 15

Width of rectangle = 15 unit

Length of rectangle = 4a + 26

Length of rectangle = 4(15) + 26

Length of rectangle = 60 + 26

Length of rectangle = 86 unit

Learn more:

https://brainly.com/question/16669749?referrer=searchResults

Answer:

Height h = 5 cm

Step-by-step explanation:

Given;

Volume of box V = 180 cm^3

Base area of box A = 36 cm^2

Height = h

Volume = base area × height

height = volume/base area

h = V/A

Substituting the values;

h = (180cm^3)/(36cm^2)

Height h = 5 cm

Answer:

The best data structure in storing card is an array.

The best choice for a shopping cart is hash-maps. the advantage of harsh mark is that they are dynamic in nature.

Waiting lists are managed by a method called the  First In First Out. when an individual is  waiting  for too long, he or she should be given the first chance for service.

Sorted links are a better options for storing tickets.

Step-by-step explanation:

Solution

In other to store the cards the best structure to be applied here is an array.

Now, we are aware the array size, which comprises of 52 items, and hence card vales can be  easily stored  For standard 52-deck cards, a 2D array of size 4x15 can also be applied, with 4 being color count, and 13 being card in each color.

In this example, the better option for shopping cart is hash-maps, because it is dynamic in nature for instance, when items are  removed and more often, and also, there is a need for mapping of item ID or name to its actual database, so these values can be kept or stored as key-value pairs.

Waiting lists are normal managed in a way of First In First Out, since a person is waiting longer should be given the first chance for service. this FIFO method is best used by a Queue. so this online waiting list can best be used by a queue.

For tickets storing, a better option will be the sorted linked lists. because the tickets are to be stored in a large amount, and there will be deletions and insertions in large quantity. so keeping them in a sorted list will reduce the resource usage and the trade-off made as high search time will also have less effect, as there will be a limited number of searches.

Answer:

135°, 63°, 63°, 99°

Step-by-step explanation:

Find attached the diagram used in solving the question.

We would use formula for sum of interior angles to get each exterior angle.

From the diagram, we added additional variables to be able to solve for sum of interior angles.

Sum of angle on a straight line = 180°

a° +15z° = 180°

b° +7z° = 180°

c° +7z° = 180°

d° +11z° = 180°

Where a,b,c and d are interior angles

Sum of interior angles = 180(n-2)

n = number of sides

For quadrilateral, n= 4

a°+b°+c°+d° = 180(n-2)

180-15z +180-7z+180-7z+180-11z = 180(4-2)

720-40z = 180(2)

720 - 360 = 40z

z = 360/40

z = 9

Each exterior angle:

15z = 15×9 = 135°

7z = 7×9 = 63°

7z = 7×9 = 63°

11z = 11×9 = 99°

Answer:

Step-by-step explanation:

The null hypothesis: Mean verbal reasoning GRE score of the engineering graduate students at the technical university is less than or equal to the national average: u ≤ 150

The alternative hypothesis: Mean verbal reasoning GRE score of the engineering graduate students at the technical university is greater than the national average: u > 150

Since the p-value of 0.0099 was gotten which is less than the significance level of 0.05, we reject the null hypothesis and conclude that actually there is a statistically significant evidence to prove that the mean verbal reasoning GRE score of the engineering graduate students at the technical university is greater than the national average