The 3rd and 6th term of a
linear sequence are 16 and
34 respectively. Find the
sum of the first six terms.​

The z score that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution is ±0.77.

Given that the z score separates the 56% of the distribution from the area in the tails of the standard normal distribution.

In a normal distribution in with mean μ and standard deviation σ, the z score of a measure X is as under:

Z=(X-μ)/σ

It is used to measure how many standard deviations the measure is from the mean.

After finding the z score we have to look at the z score table and find the p value associated with this z score, which is the percentile of X.

The normal distribution is symmetric which means that the middle 56% is between the 11th and 67th percentile. Looking at the z table the z scores are Z=±0.77.

Hence the z score that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution is ±0.77.

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Answer: 2

Step-by-step explanation:

Brust's votes equaled 2 times the sum of Pitt's votes and 400:

The total number of votes received was 2012:

Solve for P by substitution:

Find B:

Answer:

a)   Total # of votes:   B + P = 2012

     Brust vs Pitt:   B = 2(P + 400)

b)   1608 = votes for Brust

      404 = votes for Pitt

      Brust won by 1204 votes

Step-by-step explanation:

Given variables:

Given information:

Create a system of linear equations using the given variable and information:

Substitute the second equation into the first equation and solve for P:

⇒ 2(P + 400) + P = 2012

⇒ 2P + 800 = 2012

⇒ 3P = 1212

⇒ P = 404

Substitute the found value of P into the first equation and solve for B:

⇒ B + 404 = 2012

⇒ B = 1608

Therefore:

To find how many votes Brust won by, subtract the total number of votes for Pitt from the total votes for Brust:

⇒ 1608 - 404 = 1204

The smallest p-value is always associated with the z-score that is furthest away from the mean. This is because the tails of the normal distribution curve have less area and thus represent smaller p-values. The correct answer is option (d) z = -3.24.

In a hypothesis test, there are two hypotheses: the null hypothesis (H0) and the alternative hypothesis (H1).

The null hypothesis is the one we're testing, while the alternative hypothesis is the one we're trying to support or prove.

A two-tailed alternative hypothesis is one in which we are interested in whether a parameter is not equal to a certain value, as opposed to one-tailed alternative hypotheses, in which we are interested in whether the parameter is greater than or less than a certain value.

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If the customer keeps the higher of the two prizes awarded, the probability the customer will receive at least $100 is 0.10

The probability that the customer will receive at least $100, P(X>100) is obtained below:

The probability that the customer will receive at least $100 is obtained by adding the corresponding probabilities of X=100 and, X=1000

Given from the table of probabilities, P(X=100)=0.08, and P(X=1,000)

P[X>100]=P(X=100)+P(X=1,000)

              =0.08+0.02

               =0.10                                  

​      

The question is incomplete, the complete question is given below:

A real estate developer is awarding one of four prizes to customers who view new properties. The prizes are awarded randomly through drawings. Prize values and their associated probabilities follow:

PRIZE VALUE   PROBABLITY

$10                          0.80

$20                          0.10

$100                  0.08

$1000                  0.02

one customer has two chances to receive a prize. if the customer keeps the higher of the two prizes awarded, what is the probability the customer will receive at least $100?

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Answer:373248

Step-by-step explanation:

72^3 = 373248

Answer:12

Step-by-step explanation:

2+8+6(24)73=12

The equation in spherical coordinates is ρ = 5. This equation represents a sphere centered at the origin with a radius of 5 units in the ρ direction.

To write the equation \(x^2 + y^2 + z^2 = 25\) in spherical coordinates, we need to express x, y, and z in terms of the spherical coordinates (ρ, θ, φ).

In spherical coordinates, ρ represents the distance from the origin to the point, θ represents the azimuthal angle measured from the positive x-axis in the xy-plane, and φ represents the polar angle measured from the positive z-axis.

To transform the Cartesian coordinates (x, y, z) to spherical coordinates, we can use the following equations:

x = ρ sin(φ) cos(θ)

y = ρ sin(φ) sin(θ)

z = ρ cos(φ)

Now let's substitute these equations into the given equation:

\((x^2) + (y^2) + (z^2) = 25\)

(ρ sin(φ) cos(θ))² + (ρ sin(φ) sin(θ))² + (ρ cos(φ))² = 25

ρ² (sin²(φ) cos²(θ) + sin²(φ) sin²(θ) + cos²(φ)) = 25

ρ² (sin²(φ) (cos²(θ) + sin²(θ)) + cos²(φ)) = 25

ρ²(sin²(φ) + cos²(φ)) = 25

ρ²= 25

This simplifies to:

ρ = 5

Therefore, the equation in spherical coordinates is ρ = 5. This equation represents a sphere centered at the origin with a radius of 5 units in the ρ direction.

In spherical coordinates, the equation ρ = 5 describes all points that are at a distance of 5 units from the origin, regardless of the values of θ and φ.

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Considering the given quadratic equation, it is found that the quickest way to find the maximum height is given by:

c. Complete the square.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

The maximum height is at the vertex, which is found completing the squares, hence option c is correct.

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The intersection, union, and complement sets based on the universal set U = {2, 4, 6, 8}, are;

a. A ∩ B = {∅}

b. A ∪ B = {2, 4, 6, 8}

c. (A ∪ B)' = {∅}

The universal set is the set to which the other sets are subsets, and one which contains all the elements.

The Universal set is; U = (2, 4, 6, 8)

The set A = (2, 4)

The set B = (6, 8)

Therefore;

a. The set A ∩ B is the set of elements common to both sets A and B

Therefore no elements common to both sets A and B, therefore;

A ∩ B = {∅}

b. The set A ∪ B is the set that contains elements in set A and elements in set B as well as elements in set A ∩ B

The set A ∪ B = {2, 4, 6, 8}

c. The set of the complement of the union of the set A and B is the set that contains elements that are not in the union of set A and B

A ∪ B = {2, 4, 6, 8} = U,

U' = {∅}

Therefore (A ∪ B)' = {∅}

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Mark sets aside $404 for more supplies.

Mark spent $175 on supplies, so his total cost is $175.

Mark sold 6 pieces of artwork for $70 each, so he earned 6 * $70 = $420 from these pieces.

He sold 15 - 6 = 9 pieces of artwork at $85 each, so he earned 9 * $85 = $765 from these pieces.

His total revenue is $420 + $765 = $1185.

His profit is his revenue minus his cost: $1185 - $175 = $1010.

He plans to set aside 40% of his profit for more supplies, so he will set aside 0.4 * $1010 = $404.

Therefore, Mark sets aside $404 for more supplies.

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Using Pythagorean theorem, The height of the tree is approximately 47.98 feet.

According to Pythagoras' Theorem, the square of a right-angled triangle's hypotenuse side is equal to the sum of the squares of its other two sides. The three sides of this triangle are known as the Perpendicular, Base, and Hypotenuse.

tan(angle) = opposite side / adjacent side

The opposite side is the height of the tree and the adjacent side is the distance from Jerome to the base of the tree (90 feet).

tan(33) = height / 90

height = tan(33) * 90

The height of the tree is approximately 47.98 feet.

Keep in mind this is an approximation as the angle in question is not a right angle and also the unit is not given so the final result is not accurate.

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the constant term is the one that is multiplied by a variable or letter, so in this case the constant term is 0.25

The rate of change (slopes) and initial value (y-intercepts) are as follows:

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

A line of best fit is also referred to as a trend line and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.

By critically observing the graph which models the given data, we can logically deduce the following rate of change (slopes) and initial value (y-intercepts):

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Answer:

(Answer D)

Step-by-step explanation:

Please use " ^ " to indicate exponentiation:  y = -8x^2 - 2, y = -8x^2

The graph of y = -8x^2 is an inverted parabola with vertex at (0, 0).

That of y = -8x^2 - 2 is the same as above, except that the whole graph has been shifted 2 units down (Answer D).

Answer: 60

Step-by-step explanation:10 x 6 = 60 ( Also, 6x6x6x6x6x6x6x6x6x6 = 60

At a continuous speed of 20 miles per hour, it takes 2 minutes to cross this bridge.

The unitary method is used to calculate the value of a single unit and then multiply that value by itself in order obtain the desired value. Unitary refers to a single, unique, or solitary unit. As a result,

this method's objective is to establish values in terms of a single unit. If a car can drive 44 kilometer two litres of gas, for instance, the unitary approach can be used to calculate how many kilometers it can travel on one litre of gas. The value of a single unit is determined by the unitary technique, and also the value of the required quantity of units can then be calculated using this value.

given,

 0.76 miles = (4024/5280) miles

Speed =20 miles per hour

Time: =(Distance / Speed) = (0.76/20)

= 0.038 ( in hours )

into minutes = 2 min

At a continuous speed of 20 miles per hour, it takes 2 minutes to cross this bridge

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The multiplier in this case is approximately 2.778. equilibrium income is approximately $480.45 million.

To answer questions 3, 4, and 5, we need to use the given equations and formulas to calculate the equilibrium production, multiplier, and equilibrium income.

3. Equilibrium production (Y) is determined by the income identity equation:

Y = C + I + G + X

Given:

C = 300 + 0.8Yd

I = $300 million

G = $100 million

X = $100 million

Substituting these values into the equation, we have:

Y = (300 + 0.8Yd) + 300 + 100 + 100

Simplifying the equation, we find:

Y = 800 + 0.8Yd

To find the equilibrium production, we need to know the value of Yd (disposable income), which is not given in the question. Therefore, we cannot determine the specific value for equilibrium production (Y).

4. To find the equilibrium income, we need to consider the consumption function, investment, government expenditures, tax rate, and net exports.

Given:

C = 300 + 0.8Yd

I = $200 million

G = $200 million

t = 0.2

X = 100 - 0.04Y

Using the formula for equilibrium income:

Y = 1 / (1 - b(1 - t)) * (I + G + X)

Substituting the given values, we have:

Y = 1 / (1 - 0.8(1 - 0.2)) * (200 + 200 + (100 - 0.04Y))

Simplifying the equation, we find:

Y = 1 / (1 - 0.8(0.8)) * (400 + 100 - 0.04Y)

Y = 1 / (1 - 0.64) * (500 - 0.04Y)

Y = 1 / 0.36 * (500 - 0.04Y)

Y = 2.7778 * (500 - 0.04Y)

2.7778Y = 1388.89 - 0.1111Y

2.8889Y = 1388.89

Y = 480.45

The equilibrium income is approximately $480.45 million.

5. The multiplier can be calculated using the formula:

Multiplier = 1 / (1 - b(1 - t))

Given that b (the marginal propensity to consume) is 0.8 and t (the tax rate) is 0.2, we can calculate the multiplier:

Multiplier = 1 / (1 - 0.8(1 - 0.2))

Multiplier = 1 / (1 - 0.8(0.8))

Multiplier = 1 / (1 - 0.64)

Multiplier = 1 / 0.36

Multiplier ≈ 2.778

The multiplier in this case is approximately 2.778.

Comparing the multiplier from question 4 (2.778) with the multiplier from question 3 (unknown as we couldn't determine the equilibrium production), we see that they are different. The difference in the multiplier can be due to changes in the consumption function, investment, government expenditures, tax rate, and net exports. Each of these factors can affect the multiplier and lead to different results.

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Answer :  there are 16 different orders in which heads or tails could occur when tossing four coins

a) In tossing four coins, each coin has two possible outcomes: heads or tails. Since each coin toss is independent of the others, we can multiply the number of outcomes for each coin together to determine the total number of different orders:

Number of outcomes for one coin = 2 (heads or tails)

Number of outcomes for four coins = 2 * 2 * 2 * 2 = 16

Therefore, there are 16 different orders in which heads or tails could occur when tossing four coins.

b) Here's a tree diagram illustrating all the possible results:

                   H

               /       \

              /         \

             /           \

            H             T

          /   \         /   \

         /     \       /     \

        H       T     H       T

       / \     / \   / \     / \

      H   T   H   T H   T   H   T

c) The tree diagram corresponds to the calculation in part (a) because each branch of the tree represents one possible outcome for the four coin tosses. Starting from the top, we have two branches representing the first coin toss: heads (H) or tails (T). From each of these branches, we have two more branches representing the second coin toss, and so on. The total number of branches or terminal nodes in the tree diagram is 16, which matches the calculation of 16 different orders in part (a).

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The probability that monofilament cables will be discovered during the next ten years and that both discoveries will occur within the next twenty years are, respectively, 0.811 and 0.833.

X = time taken to discover Negative gravity

Y = time taken to discover Monofilament Cables

X follow exponential distribution with mean = 10

Y follow exponential distribution with mean = 6

a)P(Y < y) = 1- e^(-y/mean)

 P(Y < 10)

= 1 - e^(-10/6)

= 0.8111

The probability monofilament cables will be discovered within the next 10 years is 0.8111

b)P(X <20 ,Y < 20)= P(X < 20)P(Y < 20)

= (1 - e^(-20/10)) (1 - e^(-20/6))

= 0.8338

The probability both discoveries will take place within the next 20 years

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Answer:

C:  (-8, 2)

Step-by-step explanation:

Given parabola:

\(y=-\dfrac{1}{8}x^2-2x-4\)

For the quadratic equation in the form y = ax² + bx + c, the x-value of the vertex is -b/2a.  

Therefore, the x-value of the vertex of the given parabola is:

\(\implies x=-\dfrac{b}{2a}=-\dfrac{-2}{2\left(-\frac{1}{8}\right)}=-8\)

To find the y-value of the vertex, input x = -8 into the given equation:

\(\implies y=-\dfrac{1}{8}(-8)^2-2(-8)-4=4\)

Therefore, the vertex (h, k) of the parabola is (-8, 4).

The focus of the parabola is (h, k+p) where:

Therefore:

\(\implies \textsf{Focus}=\left(-8,4+\dfrac{1}{4\left(-\frac{1}{8}\right)}\right)=\left(-8,2)\)

The most accurate point estimate of the sample standard deviation's population counterpart is the sample standard deviation.

A parameter is a set value that is calculated from each member of the population and is known as the population standard deviation. One type of statistic is the sample standard deviation. It is therefore determined using data from a small portion of the population.In order to determine the population standard deviation, we divide the total by the number of data points (N). But in order to determine the sample deviation, the sum is divided by the number of data points minus 1. (N-1). To ascertain the standard deviation, take the square root of the final value.

The most accurate point estimate of the sample standard deviation's population counterpart is the sample standard deviation.A parameter is a set value that is calculated from each member of the population and is known as the population standard deviation. One type of statistic is the sample standard deviation. It is therefore determined using data from a small portion of the population.

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Multiply the average by the number of exams to find total points:

8 x 55 = 440

9 x 60 = 540

The score of the 9th exam is the difference between the two totals:

540 - 440 = 100

They scored a 100

Answer:

1,090,908

Find the half of 727272,then when you find the half,add it to 727272

>727,272÷2=363,636

>727,272+363,636=1,090,908

Step-by-step explanation:

Answer:

1,090,908

Step-by-step explanation:

727,272 divided by 666=

1,092

999 - 666=

333

1,092 x 333=

363,636

727,272 + 363,636=

1,090,908

The code snippet provided is a simple example of a mutual exclusion solution using the flag variables as a way to ensure that only one process can access the critical section (cs1) at a time.

The prefix1 and suffix1 are placeholders that do not have any significance to the functionality of the code.

In this implementation, the while loop keeps checking the value of flag[0] until it becomes false. Once flag[0] is false, the process can proceed to the critical section and execute the code within the curly braces.

Before exiting the critical section, the flag[1] variable is set to true to indicate that the process has entered the critical section. This is necessary because another process may be waiting to access the critical section, and the flag[1] variable serves as a signal to indicate that the critical section is currently being used.

After executing the code within the critical section, flag[1] is set to false to indicate that the process has finished accessing the critical section, and another process can now enter it.

Overall, this implementation is a basic form of mutual exclusion, and more complex algorithms exist to prevent deadlocks and other issues that may arise in concurrent systems.

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Answer:

The basic rule is: If you need to convert from a larger unit to a smaller unit, multiply. If you need to convert from a smaller unit to a larger unit, divide. You will make the number smaller and, as you already know, division is all about making numbers smaller.

Answer:

addiemoss23/this person wrote this NOT me, it is right btw

Step-by-step explanation:

To convert units into smaller units, multiply. When the units are smaller , you need more of them to express the same measure. To convert smaller units to larger units, divide. When the units are larger , you need fewer of them to express the same measure.

Answer:

4

Step-by-step explanation:

x=5*0.8=4

Answer:

here  is the answer

Step-by-step explanation:

we need to find x

therefore,

0.80*x=5 (since it is a factor of 0.80)

x= 5/0.80

x=6+1/4= 6.25 units

If the confidence level were increased to 99%, the width of the confidence interval increases, when decreased to 80%, the width of the confidence interval decreases.

A confidence interval provides a range of estimated values for a population parameter's real value. A confidence level is connected to confidence intervals. The width of the confidence interval grows as the confidence level increases. The width of the confidence interval reduces as the confidence level goes down.

Since the margin of error grows as the confidence level does as well, the confidence interval will be bigger. Hence it increases for 99% and decreases for 80%.

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Answer:

17 is: 48

18 is: A.) Coefficient

19 is: D

20 is: Im not completely sure but I would go with B. as it has multiple interpretations which could make it unwritable as an equation