If events X and Y are independent, then find P(X and Y). P(X)= 2/3 and
P(Y) = 3/4

O 17/12
O 5/7
O 1/2
O 1/4

Answer:

\(z=\frac{931-1131}{\frac{333}{\sqrt{30}}}=-3.290\)  

Now we can calculate the p value using the alternative hypothesis:

\(p_v =P(z<-3.290)=0.0005\)  

Since the p value is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly less than 1131

Step-by-step explanation:

Information given

\(\bar X=931\) represent the sample mean

\(\sigma=333\) represent the population standard deviation

\(n=30\) sample size  

\(\mu_o =1131\) represent the value to check

\(\alpha=0.05\) represent the significance level

z would represent the statistic

\(p_v\) represent the p value

System of hypothesis

We want to verify if the true mean is less than 1131, the system of hypothesis would be:  

Null hypothesis:\(\mu \geq 1131\)  

Alternative hypothesis:\(\mu <1131\)  

The statistic is given by:

\(z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}\) (1)  

Reaplacing we got:

\(z=\frac{931-1131}{\frac{333}{\sqrt{30}}}=-3.290\)  

Now we can calculate the p value using the alternative hypothesis:

\(p_v =P(z<-3.290)=0.0005\)  

Since the p value is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly less than 1131

Answer:

A. Choosing the third person listed on every fifth page of the phone book is stratified sampling.

Step-by-step explanation:

Stratified sampling involves grouping the population into subgroups before sampling. It provides a more manageable and cheaper means of sampling data by placing the population into grouped strata. The only problem is that this sampling method cannot be used in a data population that cannot be stratified. In this question, the phone book is stratified into subgroups of every five pages, and the third person listed is chosen to represent the subgroup

α & β are the zeroes of the Polynomial 3x² + 5x + 7.

The value of 1/α² + 1/β²

On comparing with standard form of a Quadratic equation i.e., ax² + bx + c = 0 ;

Let,

a = 3

b = 5

c = 7

We know that,

Sum of the zeroes = - b/a

⟹ α + β = - 5/3 -- equation (1)

Product of the zeroes = c/a

⟹ αβ = 7/3 -- equation (2)

Now,

We have to find:

⟹ 1/α² + 1/β²

Taking LCM we get,

⟹ (β² + α²)/(α²β²)

we know that,

(a + b)² = a² + b² + 2ab

⟹ (a + b)² - 2ab = a² + b²

⟹ (α + β)² - 2αβ = α² + β²

Again using aⁿ * bⁿ = (ab)ⁿ we get,

⟹ [ (α + β)² - 2αβ ] / (αβ)²

Putting the values from equations (1) & (2) we get,

⟹ [ ( - 5/3)² - 2(7/3) ] / (7/3)²

⟹ (25/9 - 14/3) * (3/7)²

⟹ (25 - 3 * 14)/3 * (9/49)

⟹ ( - 17)/3 * 9/49

⟹ - 51/49

∴ The value of 1/α² + 1/β² is - 51/49.

I hope it will help you.

Regards.

Answer:

siso your answer refer in pic

ANSWER

α+β=24

α−β=8

(α−β)

2

=(α+β)

2

−4αβ=8

2

or,24

2

−4αβ=64

or,4αβ=576−64=512

or,αβ=128

⇒x

2

−(α+β)x+αβ=0

or,x

2

−24x+128=0

Hence x

2

−24x+128=0 is the quadratic polynomial for the required condition

Answer:

The most basic quadratic function is y = x2. This is also called the parent function of a quadratic function. Sometimes you will see it written in function notation as f(x) = x2. The graph of y = x2 looks like the graph below.

Answer:

$13.00 per person

Step-by-step explanation: you divide $26 by 2

Upper

daysThe(a) The time for an individual to recover from an infectious disease, is estimated to be between 4.02 and 5.98 days. (d) The structured SIR model assumes homogeneous mixing, constant population, recovered immunity.

(a) To calculate the time for an individual to recover with a 95% confidence level, we can use the properties of the normal distribution. The 95% confidence interval corresponds to approximately 1.96 standard deviations from the mean in both directions.

Given:

Mean (μ) = 5 days

Standard deviation (σ) = 0.5 days

The confidence interval can be calculated as follows:

Lower limit = Mean - (1.96 * Standard deviation)

Upper limit = Mean + (1.96 * Standard deviation)

Lower limit = 5 - (1.96 * 0.5)

= 5 - 0.98

= 4.02 days

Upper limit = 5 + (1.96 * 0.5)

= 5 + 0.98

= 5.98 days

Therefore, the time for an individual to recover from the infectious disease with a 95% confidence level is between approximately 4.02 and 5.98 days.

(b) To simulate the epidemic using the SIR model, we need additional information about the transmission rate and the duration of infectivity.

(c) Without the transmission rate and duration of infectivity, we cannot determine the fraction of the total population that will have come down with the infectious disease once the epidemic is over.

(d) The structured model in this case is the SIR (Susceptible-Infectious-Recovered) model, which is commonly used to study the dynamics of infectious diseases. The major assumptions associated with the SIR model include:

Homogeneous mixing: The model assumes that individuals in the population mix randomly, and each individual has an equal probability of coming into contact with any other individual.

Constant population: The model assumes a constant population size, without accounting for birth, death, or migration rates.

Recovered individuals develop immunity: The model assumes that individuals who recover from the infectious disease gain permanent immunity and cannot be reinfected.

No vaccination or intervention: The basic SIR model does not incorporate vaccination or other intervention measures.

These assumptions simplify the model and allow for mathematical analysis of disease spread dynamics. However, they may not fully capture the complexities of real-world scenarios, and more sophisticated models can be developed to address specific contexts and factors.

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The time spent by Noah exercising is 130 minutes

From the question, we have the following parameters that can be used in our computation:

using the above as a guide, we have the following:

Vera = 60% * Noah

So, we have

60% * Noah = 78

Divide both sides by 60%

Noah = 130

Hence, Noah exercised for 130 minutes

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The increase in the minimum wage from $8.10 to $15, indicates that the percentage increase in the minimum wage is 85.\(\overline{185}\)%

A percentage represent the number, amount, proportion or ratio of an item to another (possibly larger) item per hundred (100) units of the comparison or larger item.

Percentages, quantitatively describes the idea of the amount of a substance. It is a measure of the amount or occurrence of an item.

The specified original minimum wage at Ben's Burger = $8.10

The new amount to which the minimum wage is increased = $15

The percentage increase can be obtained using the formula;

\(\% \ increase = \frac{New - Original}{Original} \times 100\)

The percentage increase is therefore; ((15 - 8.10)/8.1) × 100 = 85.\(\overline{185}\) %

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Answer:A

Step-by-step explanation:

they are alternate exterior angles so, x+y=180

The kind of triangle in the image above is a scalene triangle.

A scalene triangle is a type of triangle that has three sides with different lengths. It is one of the three main types of triangles, the other two being isosceles and equilateral triangles. They also have three different angles.

Scalene triangles do not have any congruent sides or angles, making them the most diverse and versatile type of triangle. They can be used to construct many different shapes and figures, and have many unique properties and characteristics that make them useful in a variety of fields, including mathematics, physics, and engineering.

In the image given, the three sides of the triangle appears to be of different sizes.

Therefore, we can conclude that the triangle is a scalene triangle.

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Answer:

8 pounds

Step-by-step explanation:

20/5=4

2*4=8

hope this helps :3

if it did pls mark brainliest

Answer:

Mindy would need 8 pounds of blueberries to make 20 blueberry pies.

Step-by-step explanation:

Since 5 blueberry pies requires 2 pounds, you can multiply both numbers by 4 to get 20 blueberry pies requiring 8 pounds.  

Answer:

Step-by-step explanation:

Can you show me all other answer choices? I know obviously that A) isn't the right answer.

Answer:

x = 8

y = 36

Step-by-step explanation:

The triangle shown in the image is an isosceles triangle.

We can find the value of x using the above mentioned information:

∠B = ∠A

5x = 40 divide both sides by 5

x = 8

The sum of interior angles in a triangle is equal to 180°.

Since ∠B and ∠C are both 40°:

40 + 40 + 3y - 8 = 180 add/subtract like terms

72 + 3y = 180 subtract 73 from both sides

3y = 108 divide both sides by 3

y = 36

In the Fixed deposit account, you will not be able to withdraw your money before time without a penalty fee from the bank and you will receive a fixed amount of interest on your original deposit.

In a Fixed-Term Deposit account, an account is opened with a bank wherein, the bank pays a guaranteed interest rate on the sums deposited for a fixed period or tenure.

This type of account allows you to earn higher returns (interest) on funds lying idle in your Savings Account.

Banks are free to charge their own penalty fee in the case of premature withdrawal of Fixed Deposit.

At the end of the stipulated period, the deposit will automatically be renewed unless you update your maturity instructions.

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Answer:

24\(x^{6} y^{3}\)

Step-by-step explanation:

Answer:

24x^6y^3

Step-by-step explanation:

The least common multiple of two or more non zero whole numbers is the smallest whole number that is divisible by each of those numbers.  

Answer: 9m^2 - 4n + 12

Step-by-step explanation:

To factor out the greatest common factor (GCF) from the expression 9m^2 - 4n + 12, we need to find the largest common factor of all the terms.

Let's examine each term individually:

9m^2: The only common factor between 9 and m^2 is 1.

-4n: The only common factor between -4 and n is 1.

12: The factors of 12 are 1, 2, 3, 4, 6, and 12. However, there is no common factor between 12 and the other terms.

Since there is no common factor other than 1, we cannot factor out anything more significant than 1. Therefore, the factored form of the expression 9m^2 - 4n + 12 is simply the original expression itself:

To factor out the greatest common factor (GCF) from the expression 9m^2 - 4n + 12, let's first identify the GCF of the coefficients. In this case, the GCF of 9, -4, and 12 is 1 since there is no common factor greater than 1.

Next, we'll factor out the GCF from each term:

9m^2 = (9)(m^2)

-4n = (-4)(n)

12 = (12)(1)

Now we can rewrite the expression factoring out the GCF:

9m^2 - 4n + 12 = (1)(9m^2) + (1)(-4n) + (1)(12)

Simplifying this, we get:

9m^2 - 4n + 12 = 9m^2 - 4n + 12

Since there is no common factor other than 1, the expression cannot be further factored.

Answer:

the area of triangle formula is A = B*H  / 2

so it means 16 square = (x+4) x /2

so x²+4x -32=0, D' = 2²- (-32)= 36, sqrt of D' = 6

so x = -2 -6 = -8 or x= -2 +6 = 4

x must be positive so x = 4

Step-by-step explanation:

The given statement " When the film is placed into the XCP (extension cone paralleling) holder with the smooth side of the film towards the throat, after processing, it will appear darker" is false because it will  lighter, not darker.

The smooth side of the film is the side that interacts with the X-ray radiation and receives the image, while the emulsion side contains the light-sensitive crystals that react to the radiation.

Placing the smooth side towards the throat ensures that the image is sharp and clear, as the X-ray beam travels through the teeth and soft tissues before reaching the film.

After processing, the exposed areas of the film turn dark, representing the captured X-ray image, while the unexposed areas remain light or clear.

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Answer:

y = - x² - 15x - 56

Step-by-step explanation:

y = - (x + 8)(x + 7) ← expand factors using FOIL

  = - (x² + 15x + 56) ← distribute parenthesis by - 1

y = - x² - 15x - 56 ← in standard form

Ernest hypothesis is correct because the graph of an object that is resting is horizontal.

Emma's hypothesis is incorrect because the graph of an object that is moving is an inclined line.

In the graph we see a horizontal line between 120 and 150 min, the the object is resting.

Ernest hypothesis is correct.

Answer:

Book of 240 pages has 12 booklets in total

Book of 160 pages has 8 booklets in total.

Total booklets both the books have in total = 20

Step-by-step explanation:

Given - There are two books: one of 240 pages and the other of 160 pages. If the 2 books are made up of booklets with the same number of pages (between 16 and 28),

To find - How many booklets do the two books have in total?

Proof -

Given that, Number of pages of a booklet is between 16 and 28.

So, The number that lies between 16 and 28 will have to divide the number of pages of both the books.

(Because given that both the books are made up of booklet with the same number of pages)

By inspection, we get

The number of pages of a booklet = 20

because

240/20 = 12 and 160/20 = 8

∴ we get

1 booklet = 20 pages

i.e.

20 pages = 1 booklet

⇒1 page = \(\frac{1}{20}booklet\)

⇒240 pages = \(\frac{240}{20}booklet\) = 12 booklet

So, we get

The book of 240 pages has 12 booklets in it.

Now,

1 page = \(\frac{1}{20}booklet\)

⇒160 pages = \(\frac{160}{20}booklet\) = 8 booklet

So, we get

The book of 160 pages has 8 booklets in it.

∴ we get

Book of 240 pages has 12 booklets in total

Book of 160 pages has 8 booklets in total.

So, Total booklets both the books have = 12 + 8 = 20

Answer:

x=-2.5

Step-by-step explanation:

Move the 13 to the other side making it a negative. 4.8x=1-13. simplify 4.8x=-12. 12 divided by 4.8 is 2.5.

Answer:

So, The answer would be 1=k

Step-by-step explanation:

My step is to make a T-chart, as u make it put X on one side and Y on the other

So what i did was i put 0 for both of them because it had start at 0

then i followed the line to the dot as i did that It has 6,6 so then i figured out what multiply all those number and the answer was 1=k

And another way you could do it was to make 6,6 and fraction like 6/6 then divde them both and get 1=k

So you would put the answer as 1

thats it Answer-1

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Answer:

Step-by-step explanation:

The inequality that models the given situation will be y*$22 + x*$38 ≤ $220 And some solutions are (1, 1), (1, 2), (2, 2).

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

To find the inequality, we need to define the variables that we will use, the variables are:

x = number of pants bought.

y = number of shirts bought.

Then Knowing the price of each individual item, the total cost will be given by:

C = y $22 + x $38

And Lee has $220 to spend, thus the maximum amount that he can spend is $220, we have the inequality:

y*$22 + x*$38 ≤ $220

Now, to find solutions we just need to find some values of x and y that make the inequality true, i.e , one solution is x = 1 and y = 1.

1*$22 + 1*$38 ≤ $220

$60 ≤ $220

Therefore, This is true, so (1, 1) is a solution.

Hence Another solutions are (2, 2), (1, 2), (0, 3), etc.

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Given:

The three vertices of the parallelogram are (-3,9), (0,-3), (6,-6).

To find:

The fourth vertex of the parallelogram.

Solution:

Consider the three vertices of the parallelogram are A(-3,9), B(0,-3), C(6,-6).

Let D(a,b) be the fourth vertex.

Midpoint formula:

\(Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\)

We know that the diagonals of a parallelogram bisect each other. So, the midpoints of both diagonals are same.

Midpoint of AC = Midpoint BD

\(\left(\dfrac{-3+6}{2},\dfrac{9+(-6)}{2}\right)=\left(\dfrac{0+a}{2},\dfrac{-3+b}{2}\right)\)

\(\left(\dfrac{3}{2},\dfrac{3}{2}\right)=\left(\dfrac{a}{2},\dfrac{-3+b}{2}\right)\)

On comparing both sides, we get

\(\dfrac{3}{2}=\dfrac{a}{2}\)

\(3=a\)

And,

\(\dfrac{3}{2}=\dfrac{-3+b}{2}\)

\(3=-3+b\)

\(3+3=b\)

\(6=b\)

Therefore, the fourth vertex of the parallelogram is (3,6).

The probability that the randomly selected park, which has been recently updated with new picnic tables, is a rural park is approximately 0.222 or 22.2%.

To determine the probability that the randomly selected park, which has recently been updated with new picnic tables, is a rural park, we can use conditional probability.

Let's define the events:

A: The park is rural.

B: The park has been updated with new picnic tables.

We are given the following information:

There are 30 urban parks, of which 10 have been updated with new picnic tables.

There are 18 rural parks, of which 4 have been updated with new picnic tables.

We need to find P(A|B), which represents the probability that the park is rural (event A) given that it has been updated with new picnic tables (event B).

Using Bayes' theorem, the formula for conditional probability, we have:

P(A|B) = (P(B|A) * P(A)) / P(B)

P(B|A) represents the probability that a rural park has been updated with new picnic tables. From the given information, we know that out of the 18 rural parks, 4 have been updated with new picnic tables. Therefore, P(B|A) = 4/18.

P(A) represents the probability of selecting a rural park. There are a total of 48 parks (30 urban + 18 rural), and 18 of them are rural. Therefore, P(A) = 18/48.

P(B) represents the overall probability of selecting a park that has been updated with new picnic tables. This includes both urban and rural parks. From the given information, we know that out of the 30 urban parks, 10 have been updated with new picnic tables, and out of the 18 rural parks, 4 have been updated with new picnic tables. Therefore, P(B) = (10 + 4) / 48 = 14/48.

Plugging these values into the formula:

P(A|B) = (P(B|A) × P(A)) / P(B)

P(A|B) = (4/18) × (18/48) / (14/48)

P(A|B) = (4/18) × (18/14)

P(A|B) ≈ 0.222

Therefore, the probability that the randomly selected park, which has been recently updated with new picnic tables, is a rural park is approximately 0.222 or 22.2%.

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Answer:

2,3

Step-by-step explanation:

Answer:

  12 units

Step-by-step explanation:

You want to know the perimeter of rectangle ABCD after it has been dilated by a factor of 1.

The original rectangle ABCD has a perimeter of ...

  P = 2(L +W) = 2(4 +2) = 12

The perimeter of the dilated rectangle is the original perimeter multiplied by the dilation factor:

  P' = 12·1 = 12

The dilated rectangle has a perimeter of 12 units.

__

Additional comment

Dilation by a factor of 1 changes nothing at all. The center of dilation is irrelevant.