We determined that f(y1, y2) = 6(1 − y2), 0 ≤ y1 ≤ y2 ≤ 1, 0, elsewhere, is a valid joint probability density function. (a) Find the marginal density function for Y1.

I give u the answers of first and second one.

thank you

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Answer:

First answer is 9 or 1 . Second answer is 7 or -7.

Step-by-step explanation:

\((x-5)^{2} =16\)

\(x-5 = 4\)  or \(x - 5 =-4\)

so \(x = 9\) or \(x = 1\)

\(2x^{2} = 98\)

\(x^{2} =49\)

\(x=7\) or \(x = -7\)

The bisection method is a numerical algorithm used for finding roots of a function. This explanation will discuss the process of determining the initial guess in the bisection method.

In the bisection method, the initial guess serves as the starting point for finding a root of a function within a given interval. The key requirement for the initial guess is that it should bracket the root, meaning that the function must have opposite signs at the endpoints of the interval.

To determine the initial guess, you need to identify an interval [a, b] where the function changes sign. This can be done by analyzing the behavior of the function graphically or by examining its values at different points.

Once you have identified an interval that brackets the root, the midpoint of that interval is chosen as the initial guess. The midpoint is computed as (a + b) / 2.

Selecting the midpoint as the initial guess ensures that the root lies within the interval [a, b]. The bisection method then proceeds by iteratively narrowing down the interval until the desired level of accuracy is achieved.

It's important to note that the success of the bisection method depends on choosing a suitable initial guess that satisfies the bracketing condition, leading to a reliable and efficient convergence towards the root.

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Answer:

\(6 = 2p + 8 \\ \\ 2p + 8 = 6 \\ \\ 2p = 6 - 8 \\ \\ 2p = - 2 \\ \\ p = - \frac{2}{2} \\ \\ p = - 1\)

Answer:

(1, 6.71)

Step-by-step explanation:

I'm assuming that you need to solve this by substitution or elimination since you didn't include any context in your question, just the equations.

To solve this by elimination, first, decide on a variable you want to get rid of / cancel out. I chose y. To do this, you need to find the least common multiple (LCM) of 7 and 5, which is 35. Now, multiply the top equation, 21x + 7y = 42, by -5. Multiply the bottom equation, -5x + 5y = 10, by 7. Make sure when you multiply that you either make the 5 or the 7 negative so you can cancel out y. I chose to make 5 negative.

After you multiply by the -5 and the 7, rewrite your new equations:

-105x - 35y = -210

-35x + 35y = 70

Now, add the two equations together. When you do this, the y's cancel out and you're left with -140x = -140. Now, divide both sides by -140, and you're left with x = 1. Plug the value of x into one of your original equations. I chose the bottom equation, -5x + 5y = 10.

-5(1) + 7y = 42   ----->   -5 + 7y = 42.

Add -5 to both sides, which gives you 7y = 47. Divide both sides by 7, which gives you y = 6.71.

The last step is to put the values of x and y into a point: (1, 6.71).

Hope this helps!

There are two possible solutions for the missing term: 1.2247 or -1.2247.

To find the missing term in the geometric sequence 3, ², 0.75, . . ., we can observe the common ratio between consecutive terms.

The common ratio (r) can be found by dividing any term by its preceding term. Let's calculate it:

Common ratio (r) = ² / 3 = 0.75 / ² ≈ 0.3906

Now, to find the missing term, we need to determine whether it is the geometric mean or its opposite.

Option 1: Geometric Mean

The geometric mean can be calculated by taking the square root of the product of two consecutive terms in a geometric sequence. So, let's try this approach:

Missing Term = √(0.75 * ²) ≈ √(1.5) ≈ 1.2247

Option 2: Opposite of the Geometric Mean

In some cases, the missing term can be the negative value of the geometric mean. Therefore, let's consider the negative value of the geometric mean as another possibility:

Missing Term = -√(0.75 * ²) ≈ -√(1.5) ≈ -1.2247

Hence, there are two possible solutions for the missing term: 1.2247 or -1.2247.

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Answer:

7.538461538

Step-by-step explanation:

The term that completes the blank and fits the description is an array

From the question, we understand that:

The term that fits the above highlights is array

Hence, the complete statement is:

array can hold multiple values within a single variable and is defined by having values between square brackets.

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The exact value of sin(π/6) is 1/2.

To find the exact value of sin(π/6), we can use the unit circle or the trigonometric identity for the sine function. In the unit circle, π/6 corresponds to an angle of 30 degrees, which lies in the first quadrant.

At this angle, the y-coordinate of the corresponding point on the unit circle is 1/2. Since sin(θ) represents the ratio of the opposite side to the hypotenuse in a right triangle, for an angle of 30 degrees, sin(π/6) is equal to 1/2.

Alternatively, we can use the trigonometric identity sin(θ) = cos(π/2 - θ). Applying this identity, we have sin(π/6) = cos(π/2 - π/6) = cos(π/3). Now, π/3 corresponds to an angle of 60 degrees, which lies in the first quadrant.

At this angle, the x-coordinate of the corresponding point on the unit circle is 1/2. Therefore, cos(π/3) = 1/2. Substituting this value back into sin(π/6) = cos(π/3), we get sin(π/6) = 1/2.

In both approaches, we find that the exact value of sin(π/6) is 1/2, indicating that the sine function of π/6 radians is equal to 1/2.

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Step-by-step explanation:

= \((a\sqrt{a} + 2a)+(\sqrt{a}+2 )\)

= \(a(\sqrt{a} + 2a)+(\sqrt{a}+2 )\)

= \((a+1)(\sqrt{a} +2)\)

please give me a brainliest answer

The amount of data that we can use is 0.7 gb  .

In the question ,

it is given that

the family of four people shares a 4 gb data plan ,

the sister uses twice as much data as we use .

let the amount of data that we use is "d" ,

so the amount of data that the sister uses = 2d

amount of data used by the parents = 2 gb

So , the equation becomes

total data = data used by parents + data used by us   + data used by sister

On substituting , the values

we get

4 = 2 + d + 2d

4 = 2 + 3d

3d = 4 - 2

3d = 2

d = 2/3

d= 0.6666

d ≈ 0.7 gb

Therefore , The amount of data that we can use is 0.7 gb  .

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Answer:

Jorge needs 1/2 apple to make the snack.

Answer: B: y= -2x +1.

Step-by-step explanation: The y-intercept is (0,1). The slope that passes through the points (-2,5) and (2,-3) is -8/4, which reduces to -2. Once putting all of this into intercept form, it turns out to be y = -2x+1.

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Or just subtract

9.884 * 10^6 - 1.009 * 10^7=

− 2.05999999 × 10^5

Rounded up is:

− 2.06× 10^5

(❁´◡`❁)

Answer:

It will be over at 5:17 pm

Step-by-step explanation:

2:45 +32 would be 3:17, we add 2 hours it would be 5:17

Answer:

5:17 pm

Step-by-step explanation:

Since Brianna started watching a movie at 2:45 p.m and the movie is 2 hours and 32 minutes long

Thus,

2:45 + 2 and 32 Minutes

2 + 2 = 4

45 + 32 = 77 minutes

1 Hour = 60 Minutes

Thus, 77 - 60 =17

Hence, 4 + 1 = 5

Thus, the movie will be over at 5:17 Pm

~Lenvy~

Answer:

The function is linear

Step-by-step explanation: You add the same number ( 4 ) each time meaning it is linear. If it was exponential you would be multiblying by the same number each time.

Answer:

I believe the answer you are looking for is Linear

Step-by-step explanation:

Because

In a linear relationship, the y-values have equal differences.

and

In an exponential relationship, the y-values have equal ratios.

Mark brainliest pls :)

Answer:

y = x - 3

Step-by-step explanation:

Linear functions can't have any exponents or square roots, so it has to be

y = x - 3

Therefore, Drug C has a stronger impact on cell survival compared to Drug A, making it the drug with the greatest effect.

To draw a representation of the survival curve and identify the drug that has the greatest effect on cell survival, we can use a graph where the x-axis represents the drug concentration in μg/ml, and the y-axis represents the percentage of cell survival.

Since Drug B has no IC90 value, it means that it does not reach a concentration that causes a 90% reduction in cell survival. Therefore, we can assume that Drug B has no significant effect on cell survival and can omit it from the survival curve.

For Drug A and Drug C, we have IC90 values of 5 and 3 μg/ml, respectively. This means that when the drug concentration reaches these values, there is a 90% reduction in cell survival.

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If Francine adds 8.0 ml of 3.0 m KOH to 4.0 ml of 6.0 m HBr, then the resulting mixture will be neutral in nature.

To determine whether the mixture is acidic, basic or neutral, litmus test is done or some other tests can also be performed. However, the mathematical calculations help in understanding the reason behind the result of litmus test.

In the given problem, the volume and molarity of the solutions are given, so number of moles can be easily calculated.

Number of moles of KOH = (8.0 mL) x (3.0 mol/L) / 1000 mL/L = 0.024 mol

Number of moles of HBr = (4.0 mL) x (6.0 mol/L) / 1000 mL/L = 0.024 mol

Considering the chemical reaction between KOH (which is a strong base) and HBr ( which is a strong acid), the resulting product will be a salt along with water (in the form of vapors).

KOH + HBr → KBr + H2O

Since, the number of moles of KOH and HBr is same, therefore the resultant solution will have salt with neutral pH.

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Answer:

exact form -219/8

Decimal form - -27.375

Mixed number form - -27 3/8

Answer:

D

Step-by-step explanation:

a^2 cancels out a^5 remaining a^3 denominator

b2 cancels b4 = b2 numerator

c3 cancels out c8 = c5 remaining denominator

36/4 = 9

therefore 9b^2 /a^3 c^5

The simplified expression is 4^((1)/(3)) * 4^((1)/(5)) = 8/15.

To simplify the expression 4^((1)/(3)) * 4^((1)/(5)), we can apply the product of powers property, which states that when multiplying two powers with the same base, we can add their exponents.

In this case, the base is 4, and we have exponents of (1)/(3) and (1)/(5). Adding these exponents, we get:

(1)/(3) + (1)/(5)

To add the fractions, we need to find a common denominator, which in this case is 15. We can rewrite the fractions with the common denominator:

(5)/(15) + (3)/(15)

Now that the fractions have the same denominator, we can add the numerators:

(5 + 3)/(15) = 8/15

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IQR for the data {1, 3, 4, 8, 20} is 5.

Interquartile Range(IQR) for a data is defined as the difference between third quartile and first quartile.

denoted by  IQR=Q₃-Q₁              (Q₃ is third quartile and Q₁ is first quartile)

The five number summary of a data set is represented as

{minimum, first quartile , second quartile , third quartile , maximum}..…(1)

According to the question

{1, 3, 4, 8, 20}

On comparing it with equation   …(1)

minimum=1

Q₁ =3    , Q₂=4 , Q₃=8 , maximum =20

IQR=Q₃-Q₁

Substituting the values we get

IQR=8-3=5.

Therefore , Interquartile Range for the data {1, 3, 4, 8, 20} is 5.

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Answer:

it would be cheaper to buy a pack of 45.

Step-by-step explanation:

Shayley would spend $30 on 20 single bottles because 1.50 times 20 = 30

If each score is doubled, and then 5 is subtracted from that result, then the mean and standard deviation will be 115 and 36 respectively.

A huge group of test results has a mean of 60 and a standard deviation of 18. If each score is doubled and then 5 is deducted from the result, the mean and standard deviation are “ mean = 115; standard deviation = 36”. Mean = 2 x 60 -5 = 120 -5 = 115

2 x 18 = 36 standard deviation

The mean is the average and is calculated as the sum of all the results from the example divided by the total number of events.

The standard deviation (SD) is a statistic used to assess the degree of variation or dispersion in a set of data values.

A low standard deviation indicates that the information points slant toward being near the mean of the set, whereas an exclusive expectation deviation or a high standard deviation indicates that the information points tilt toward being near the mean of the set.

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(a) E(SD) = E(S)E(D) = 0. (b) S and D are independent.

(a) We can start by computing E(S) and E(D) separately:

E(S) = E(RI + R2) = E(RI) + E(R2) = (1/6)(1+2+3+4+5+6) + (1/6)(1+2+3+4+5+6) = 7

E(D) = E(RI - R2) = E(RI) - E(R2) = (1/6)(1+2+3+4+5+6) - (1/6)(1+2+3+4+5+6) = 0

Now, to find E(SD), we can use the fact that S and D are both linear combinations of independent random variables (RI, R2). Therefore, we have:

E(SD) = E((RI + R2)(RI - R2))

= E(RI^2 - R2^2)

= E(RI^2) - E(R2^2) (because RI and R2 are independent)

= (1/6)(1^2+2^2+3^2+4^2+5^2+6^2) - (1/6)(1^2+2^2+3^2+4^2+5^2+6^2)

= 0

Thus, we have shown that E(SD) = E(S)E(D).

(b) To determine if S and D are independent, we need to check if their joint distribution is equal to the product of their marginal distributions. We know that the joint distribution of S and D is given by:

P(S=s, D=d) = P(RI+R2=s, RI-R2=d)

We can rewrite this as:

P(RI=s1, R2=s-s1, RI-R2=d)

Now, we can express this in terms of the marginal distributions of RI and R2:

P(RI=s1)P(R2=s-s1)P(RI-R2=d)

This shows that the joint distribution of S and D can be factored into the product of their marginal distributions. Therefore, S and D are independent.

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