4.02 Lesson check ! (5)

Answer: - 3 1/4

Step-by-step explanation:

- 3 3/4 + 1/2

Get a common denominator

-3 3/4 + 2/4

-3 1/4

The mean of [tex]X_n[/tex] is 1 and the variance of [tex]X_n[/tex] is [tex](4/7)((7/4)^n - 1).[/tex] The mean and variance of X_n can be found by using the law of total expectation and the law of total variance.

By the law of total expectation, we have : [tex]E[X_n] = E[E[X_n|X_{n-1}]][/tex]
Since each individual in the population dies with probability 1/2 or doubles with probability 1/2:
[tex]E[X_n|X_{n-1}] = (1/2)X_{n-1} + (1/2)(2X_{n-1}) = X_{n-1}[/tex]
Plugging this back into the law of total expectation :
[tex]E[X_n] = E[X_{n-1}] = E[X_{n-2}] = ... = E[X_0] = 1[/tex]

Therefore, the mean of [tex]X_n[/tex] is 1.
Next, let's find the variance of [tex]X_n[/tex] . By the law of total variance, we have:
[tex]Var(X_n) = E[Var(X_n|X_{n-1})] + Var(E[X_n|X_{n-1}])[/tex]
Since each individual in the population dies with probability 1/2 or doubles with probability 1/2, we can write:
[tex]Var(X_n|X_{n-1}) = (1/2)(X_{n-1} - X_{n-1})^2 + (1/2)(2X_{n-1} - X_{n-1})^2 = (3/4)X_{n-1}^2[/tex]


[tex]E[X_n|X_{n-1}] = X_{n-1}[/tex]
Plugging these back into the law of total variance, we get:
[tex]Var(X_n) = E[(3/4)X_{n-1}^2] + Var(X_{n-1}) = (3/4)E[X_{n-1}^2] + Var(X_{n-1})[/tex]
Since [tex]E[X_n] = 1,[/tex] we have:
[tex]E[X_{n-1}^2] = Var(X_{n-1}) + E[X_{n-1}]^2 = Var(X_{n-1}) + 1[/tex]
Plugging this back into the equation for [tex]Var(X_n)[/tex], we get:

[tex]Var(X_n) = (3/4)(Var(X_{n-1}) + 1) + Var(X_{n-1}) = (7/4)Var(X_{n-1}) + (3/4)[/tex]
Using the fact that  [tex]Var(X_0) = 0[/tex], we can write:
[tex]Var(X_n) = (7/4)^nVar(X_0) + (3/4)(1 + (7/4) + ... + (7/4)^{n-1}) = (3/4)((7/4)^n - 1)/(7/4 - 1) = (4/7)((7/4)^n - 1)[/tex]

Therefore, the variance of [tex]X_n[/tex] is [tex](4/7)((7/4)^n - 1).[/tex]
In conclusion, the mean of [tex]X_n[/tex] is 1 and the variance of [tex]X_n is (4/7)((7/4)^n - 1).[/tex]

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The sink's volume in cubic inches is 8182.8 cubic inches according to the radius of hemisphere.

The volume of hemisphere is calculated by the formula -

Volume = 2/3πr³, where r represents radius of the hemisphere.

Before beginning the calculation, convert radius from mixed fraction to fraction.

Radius = (15×4)+3/4

Performing multiplication and addition

Radius = 63/4 inches

Volume =

[tex] \frac{2}{3} \times \pi \times {( \frac{63}{4}) }^{3} [/tex]

Performing multiplication and taking cube

Volume = 8182.77 inches³

Rounding to nearest tenth

Volume = 8182.8 cubic inches

Hence, the volume of hemisphere is 8182.8 cubic inches.

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The complete question is -

Jeremiah measure the volume of a sink basin by modeling it as a hemisphere. Jeremiah measures its radius to be

15 3/4 inches. Find the sink's volume in cubic inches. Round your answer to the nearest tenth if necessary

Answer: To determine if a constant rate can be used to describe the relationship between the number of hours and the gallons of paint used, we need to see if the sprayer uses paint at a consistent rate over time.

From the information given, we know that in 4 hours, the sprayer uses 42 gallons of paint. This means that the rate of paint usage is 42/4 = 10.5 gallons per hour.

If the sprayer uses paint at a constant rate, then we would expect it to use the same amount of paint for each hour of use. However, we don't have any information about how the sprayer uses paint beyond the first 4 hours, so we can't determine if the rate of paint usage is constant over time.

Therefore, we cannot definitively say whether a constant rate can be used to describe the relationship between the number of hours and the gallons of paint used. It is possible that the rate of paint usage changes over time, or that other factors (such as the surface area being painted or the type of paint being used) affect the amount of paint used.

Step-by-step explanation:

9240

Step-by-step explanation:

In short, the maximum number of distinct ways the medals could be awarded in this race is 22 x 21 x 20 = 9240. This is calculated using a formula for permutations. Is there anything else you would like to know?

In response to the supplied query, we may state that As a result, the system of equations has a solution of x = 13/7 and y = -3/7.

In algebra, a linear equation is one that of the form y=mx+b. The slope is B, and the y-intercept is m. As y and x are variables, the previous sentence is frequently referred to as a "linear equation with two variables". Bivariate linear equations are linear equations with two variables. Linear equations may be found in many places, including 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation has the structure y=mx+b, where m denotes the slope and b the y-intercept, it is referred to as being linear. A mathematical equation is said to be linear if its solution has the form y=mx+b, where m stands for the slope and b for the y-intercept.  

When utilizing the substitution approach to solve a system of linear equations, you should search for an equation that already has one variable isolated.

For instance, take into account the equations below:

2x + 3y = 11

4x - y = 5

The second equation in this system has already had y determined. In order to eliminate y and find x, we can change the phrase 4x - 5 for y in the first equation:

[tex]14x = 26 x = 13/7 2x + 3(4x - 5) = 11 2x + 12x - 15 = 11\\ 4(13/7) y = 5\s52/7 - y = 5\sy = -3/7\\[/tex]

As a result, the system of equations has a solution of x = 13/7 and y = -3/7.

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The number of mangoes bought by Camila is 5 mangos.

We have given in the question,

Cost of each apple = $0.50

Cost of each mango = $0.75

Total amount Camila have = $7.75

Number of apples bought = 8

We have to find the number of mangoes bought by Camila

The calculation to find,

Assume;

The number of mangoes bought by Camila = a

So,

(0.50)(8) + (0.75)(a) = 7.75

4 + 0.75a = 7.75

0.75a = 3.75

a = 3.75 / 0.75

a = 5

Therefore, The number of mangoes bought by Camila is 5 mangos.

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The smallest number of peanuts that could be in the bag is 4320.

Let's use the Chinese Remainder Theorem to solve this problem.

Let:

x be the number of peanuts in the bag.

Then we know that x ≡ 2 (mod 8), x ≡ 2 (mod 9), and x ≡ 2 (mod 10).

Using the Chinese Remainder Theorem, we can find a solution for x as follows:

Let

M = 8 * 9 * 10 = 720, and let M1, M2, and M3 be the remainders when M is divided by 8, 9, and 10 respectively.

That is, M1 = 720 mod 8 = 0, M2 = 720 mod 9 = 0, and M3 = 720 mod 10 = 0.

Let b1 = 1, b2 = 1, and b3 = 1.

Then we need to find integers a1, a2, and a3 such that a1 * M1 * b1 + a2 * M2 * b2 + a3 * M3 * b3 = 1.

One solution is a1 = 5, a2 = -4, and a3 = 1,

so we have 5 * 720 * 1 + (-4) * 720 * 1 + 1 * 720 * 1 = 7201

= M1 * b1 * 2 + M2 * b2 * 2 + M3 * b3 * 2.

This means that x = M1 * b1 * 2 + M2 * b2 * 2 + M3 * b3 * 2 is a solution to the system of congruences.

Since M1 = 0, we have x ≡ 0 (mod 8).

Since M2 = 0, we have x ≡ 0 (mod 9).

Since M3 = 0, we have x ≡ 0 (mod 10).

Therefore, the smallest positive integer solution for x is x = 720 * 1 * 2 + 720 * 1 * 2 + 720 * 1 * 2 = 4320.

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The number of signatures they got on the first day is 2.

The problem can be solved mathematically by using the formula for geometric sequences, which is:

an = a1 × r^(n-1)

where:

an = the nth term in the sequence

a1 = the first term in the sequence

r = the common ratio between consecutive terms

n = the number of terms in the sequence

In this case, we know that the number of signatures they get each day is twice as many as the day before, which means that the common ratio is 2. We also know that the number of signatures they got on the sixth day is 2^6 = 64.

Using the formula for geometric sequences, we can solve for a1 by substituting the known values

64 = a1 × 2^(6-1)

64 = a1 × 2^5

a1 = 64 / 2^5

a1 = 2

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The domain of a function refers to the set of all possible input values. We can easily find the domain of the given function h(t) using the following rules:

Since the denominator cannot be zero, we must exclude the value t = -3 from the domain. This means that the domain is {t | t ≠ -3}.

Furthermore, the expression inside the square root cannot be negative since the square root of a negative number is undefined. Thus, we have t^2 - 16 ≥ 0, which implies t ≤ -4 or t ≥ 4.

Therefore, the domain of the function h(t) is given by {t | t ≠ -3, t ≤ -4 or t ≥ 4}. This can also be written in set-builder notation as {t : t ≤ -4 or t ≥ 4, t ≠ -3}.

Hence, the correct option is {\color{Red}\boxed{(-\infty,-4] \cup[4, \infty) \text { or }{x \mid x \leq-4 \text { or } x \geq 4}}}

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Applying the product property of square roots, the items that will fill the empty boxes given the radicals above are:

2a: 3√2

2b: √24

2c: = 2√6

2d: √9 * √6

2e: √36 * √2

2f: 6√2

The product property of square roots states that the square root of a product of two numbers is equal to the product of the square roots of those numbers. In other words, if a and b are non-negative real numbers, then the square root of ab is equal to the square root of a multiplied by the square root of b. Mathematically, it can be written as:

√(ab) = √a * √b

Given the radicals above, we would have the following:

2a:

√18 = √9 * √2 = 3√2

2b and 2c:

√24 = √4 * √6 = 2√6

2d:

√54 = √9 * √6 = 3√6

2e and 2f:

√72 = √36 * √2 = 6√2

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Answer:

In this problem, we have a graph of the PDF (Probability Density Function). To compute probabilities in a certain interval (a, b), we must integrate this function from x = a to x = b.

(1) P(X ≤ 22)

We integrate the function from x = -∞ to x = 22, we get:

We separated the integral to use the data from the graph.

(2) P(X > 21)

We integrate the function from x = 21 to x = ∞, we get:

(3) The Q1 is the value x = a of the interval (-∞, a) that gives a probability equal to 0.25. So we must find x such that:

(4) The median is the value x = a of the interval (-∞, a) that gives a probability equal to 0.5. Proceeding as before, we have:

(5) The Q3 is the value x = a of the interval (-∞, a) that gives a probability equal to 0.75. Proceeding as before, we have:

(6) The IQR is given by the difference between Q3 and Q1. Using the results from above, we get:

Answer

• P(X ≤ 22) = 0.5

,

• P(X > 21) = 0.75

,

• Q1 = 21

,

• median = 22

,

• Q3 = 23

,

• IQR = 2

Step-by-step explanation:

Hope this helps

As per the given rectangle, the length of EG is 5x - 7

We are given that DEFG is a rectangle, which means that its opposite sides are parallel and equal in length. Let's label the sides of the rectangle as follows:

DE = FG = a (since opposite sides of a rectangle are equal in length)

EF = DG = b (since opposite sides of a rectangle are parallel)

Now, we can use the given information to set up an equation for the length of EG:

EG = EF + FG = b + a

But we don't know the values of a and b. However, we are given that FD = 3x - 7 and EG = x + 5. We can use this information to solve for a and b.

We know that FD = DE - EF, so we can substitute the values we have:

3x - 7 = a - b

We also know that EG = FG - DG, so we can substitute the values we have:

x + 5 = a - b

Now we have two equations with two variables (a and b). We can solve for a and b by adding the two equations together:

3x - 7 + x + 5 = 2a

4x - 2 = 2a

a = 2x - 1

Now we can substitute this value for a in one of the earlier equations to solve for b:

3x - 7 = (2x - 1) - b

b = 3x - 6

Finally, we can substitute the values we found for a and b into the equation we set up earlier to find the length of EG:

EG = EF + FG = b + a = (3x - 6) + (2x - 1) = 5x - 7

Therefore, the length of EG is 5x - 7.

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Answer:[tex]847\pi[/tex]

Step-by-step explanation:

[tex]v=\pi r^{2} h\\v=\pi 11^{2} 7\\v=847\pi[/tex]

The equation Pt=P₀[tex]e^-0[/tex]. 4t is used to predict the ticket sales of a movie after its release. For the latest blockbuster movie, the predicted ticket sales for the sixth week of the movie’s release is $7. 9 million to the nearest $0. 1 million.

The formula used to predict the number of ticket sales t weeks after a movie’s release is Pt=P₀[tex]e^-0[/tex]. 4t, where P₀ is the first week’s ticket sales. In the case of the latest blockbuster movie, the first week’s ticket sales was $16. 3 million. To calculate the predicted ticket sales for the sixth week, the time t must be set to 6. The equation then becomes , which simplifies to Pt=7. 9 million. The predicted ticket sales for the sixth week of the movie’s release is therefore $7. 9 million to the nearest $0. 1 million. The equation  is a useful tool for predicting the ticket sales of a movie over time. It reflects the fact that, generally, ticket sales for a movie will steadily decline over time, with the rate of decline being determined by the value of the exponent, -0. 4 in this case. By plugging in different values for t, one can easily calculate the predicted ticket sales for a movie at any given time.

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Answer: o find an equation that is parallel to the given line, we need to use the fact that parallel lines have the same slope.

The given line has a slope of 1/2, so any parallel line must also have a slope of 1/2.

Now we can use the point-slope form of a line to find the equation of the parallel line that passes through (-6, 5):

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the given point.

Plugging in m = 1/2 and (x1, y1) = (-6, 5), we get:

y - 5 = 1/2(x - (-6))

Simplifying:

y - 5 = 1/2(x + 6)

y - 5 = 1/2x + 3

y = 1/2x + 8

So the equation of the parallel line that passes through (-6, 5) is y = 1/2x + 8.

Brainliest is Appreciated.

Answer:

110x

Step-by-step explanation:

its 110x

303

Step-by-step explanation:

Answer:

The area of a triangle is given by the formula A = 1/2 * base * height, where "base" is the length of the triangle's base and "height" is the length of the perpendicular line segment from the base to the opposite vertex.

If the base of a triangle is doubled, the height remains constant, and the area of the triangle will also double. This is because the area of a triangle is directly proportional to its base length.

In the case of the given triangle, if the base is doubled from 3 centimeters to 6 centimeters, the area of the triangle will become:

A = 1/2 * 6 cm * 6 cm = 18 cm²

Therefore, the area of the triangle will increase from 9 cm² to 18 cm² if the base is doubled while the height remains constant at 6 cm.

Step-by-step explanation:

Answer:

0.119

Step-by-step explanation:

No. of sides a die has= 6 sides

No. of times it is rolled= 7 times

Total pairs= 6 x 7

                = 42 pairs

No. of 5 threes= 5 x 1

                        = 5

Probability of getting 5 threes= Favorable outcomes/Total outcome

                                                 = [tex]\frac{5}{42}[/tex]

                                                 = 0.119 chance

∴ probability of getting 5 threes is 0.119

No, Jack does not have enough rope. First, we need to convert all units to the same measurement.

Since there are 36 inches in a yard, Jack has 7 x 36 = 252 inches of rope. Additionally, 4 feet is equal to 4 x 12 = 48 inches of rope.

To determine if Jack has enough rope, we need to add the 84 inches needed for the packages and the 48 inches needed for the other project, which gives a total of 132 inches.

Since 132 inches is greater than Jack's total of 252 inches, he does not have enough rope.

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The table are shown below

From the question, we have:

f(x) = x^2 - 1  x <= 0

        2x - 2  0 < x <= 5

        3  x > 5

So, we make the table using the x values in the domain

x   f(x) = x^2 - 1

0                -1

-1               0

-2              3

-3             8

x   f(x) = 2x - 1

1                1

2               3

3               5

4               7

5              9

x   f(x) = 3

6         3

7         3

8         3

The domain are given in the question

So, we have the domains of the three functions to be

x <= 0, 0 < x <= 5 and x > 5

Using the table of values, we have the range of the three functions to be

f(x) >= -1, -1 < f(x) <= 9 and f(x) = 3

Here, we use a graphing calculator

The graph of the function is added as an attachment

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On solving the provided question we cans ay that As a result, X is 2477, function rounded to the closest tenth.

Mathematicians examine numbers with their modifications, equations and associated structures, forms and their locations, and feasible positions for these things. The term "function" indicates the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs where each supply leads to a specific, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible capabilities are on functions, yet another skills, so multiple capabilities, in capabilities, and on operations.

To find X, we must isolate it on one side of the equation by executing the identical procedure on both sides.

X + 23 = 2500

Taking 23 off both sides:

X = 2500 - 23

To simplify: X = 2477

As a result, X is 2477, rounded to the closest tenth.

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The value of x is given as follows:

x = 10.

The geometric mean between 15 and 18 is given as follows:

16.43.

The two triangles for the problem are similar, meaning that the proportional relationship for the side lengths is given as follows:

x/20 = 6/12.

The relationship can be simplified as follows:

x/20 = 0.5.

Applying cross multiplication, the value of x is obtained as follows:

x = 20 x 0.5

x = 10.

The geometric mean between two amounts is given by the square root of the multiplication of these two amounts.

Hence, for the amounts 15 and 18, the geometric mean is given as follows:

sqrt(15 x 18) = 16.43.

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The change in tempo and rhyme scheme in the final stanza both hint at the speaker's unclear identity. It gives satirical overtones to the creations.

Poets choose particular rhyme schemes to elicit different responses from their audiences. It fosters a particular atmosphere and mood that may affect how we respond to the poem's themes. Rhyme can be rigid or have satirical overtones, or it can have a playful or playful atmosphere.

When a poem has rhyme and meter, it is more musical. In traditional poetry, the anticipated enjoyment of a predictable rhyme aids in memorization for recitation. The use of a rhyme scheme also establishes the form. The shift in the poem's rhythm In the last stanza signifies the poets uncertain identity.

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Step-by-step explanation:

To simplify the expression 16+(-3)-3/7j-6/7j+4, we first need to combine like terms. The real numbers (16, -3, and 4) can be added together, and the imaginary numbers (-3/7j and -6/7j) can also be added together. So we have:

16 + (-3) + 4 + (-3/7j) + (-6/7j)

Simplifying the real numbers:

= 16 - 3 + 4

= 17

Simplifying the imaginary numbers:

= (-3/7j) + (-6/7j)

= (-9/7j)

Putting it all together, we get:

16 + (-3) - 3/7j - 6/7j + 4 = 17 - 9/7j

So the simplified expression is 17 - 9/7j.

The 95% confidence interval for the population proportion who favor an amendment for organized prayer in public schools does not provide convincing evidence that more than two-thirds.

Because the value 2/3 = 0.667 (and values less than 2/3) are in this interval, it is plausible that 2/3 or less of the population favor such an amendment. Thus, there is not convincing evidence that more than 2/3 of U.S.The 95% confidence interval for the population proportion who favor such an amendment is (0.63, 0.69). This means that if the same poll was conducted over and over again, 95% of the time the results would fall within this interval. Since the interval includes values less than 2/3, it is possible that 2/3 or less of the population favor such an amendment. Therefore, there is not convincing evidence that more than two-thirds of  important to note that the confidence interval does not provide conclusive evidence either way, only an indication of the likely proportions in the population.

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The probability that exactly one of these 7 people have a hepatoma is 0.35 or 35%

The risk of hepatoma among alcoholics without cirrhosis of the liver is 24%.We need to find the probability that exactly one of these 7 people have a hepatoma. Let the probability of having hepatoma be P(A) = 24% = 0.24 (given). Therefore, the probability of not having a hepatoma is P(A') = 1 - P(A) = 1 - 0.24 = 0.76. We have n = 7 people.

The probability of exactly 1 person having a hepatoma is P(1 person having hepatoma) = C(7,1) × P(A) × [tex]P(A')^{6}[/tex].

C(n, x) is the combination of n things taken x at a time. C(7,1) = 7!/1!6! = 7P(1 person having hepatoma) = 7 × 0.24 × (0.76)⁶= 0.35

Therefore, the probability that exactly one of these 7 people have a hepatoma is 0.35 or 35%.

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The level of private saving in the given closed economy is $4 trillion.

Given, Y = $14 trillion C = $8 trillion G = $3 trillion S pub = $1 trillion T = $5 trillion We have to find the level of private saving, spriv, in this economy.

In a closed economy: Y = C + I + G Here, I = investment in the economy Thus, Y = C + S + T When we add G to both sides of the equation we get, Y + G = C + S + T + G Now, from the given data we have, Y + G = $14 + $3 = $17 trillion C = $8 trillion T = $5 trillion

So, we have, Y + G = C + S + T + G Solving for S, we get; S = Y + G - C - TS = $17 trillion - $8 trillion - $5 trillion S = $4 trillion Therefore, the level of private saving in the given closed economy is $4 trillion.

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I got ya.

I wrote the answers in the boxes.