Given that in an arithmetic series a8 = 1 and a30=-43, find the sum of terms 8 to 30.

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Answer:

The correct answer is D. 3x² - x + 3

Step-by-step explanation:

4x² - x + 6 - (x² + 3)

= 4x² - x² - x + 6 - 3

= 3x² - x + 3

A new sample size of at least 537 fish to estimate the true mean length with a margin of error of 0.5 centimeters and 95% confidence.

To determine the size of a new sample so that the true mean length is estimated with a margin of error of 0.5 centimeters with 95% confidence, we need to find the standard error of the mean and use it in the formula for the margin of error.

The formula for the margin of error is: ME = z * (σ/√n)

where z is the z-score corresponding to the desired confidence level, σ is the standard deviation of the population, and n is the sample size.

We can estimate the standard deviation of the population using the sample variance, which is given as 34.9.

The standard deviation is the square root of the variance, so σ = √34.9

= 5.91.

To find the standard error of the mean, we divide the standard deviation by the square root of the sample size:

SEM = σ/√n

= 5.91/√n We want the margin of error to be 0.5 centimeters, so we can set up the equation:

0.5 = z * (5.91/√n)

To solve for n, we need to know the value of z for a 95% confidence level.

This corresponds to a z-score of 1.96. Substituting this into the equation gives: 0.5 = 1.96 * (5.91/√n)

Simplifying and solving for n gives: √n = 1.96 * (5.91/0.5) √n

n =(23.18)

n = 537

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The speed at which the distance between the ships is changing at 7 PM is 207.3 knots.

To find the speed at which the distance between the ships is changing, we can use the concept of relative velocity.

At noon, ship A is 40 nautical miles due west of ship B.

From then until 7 PM, a total of 7 hours have passed.

Ship A is sailing west at 17 knots, so it would have traveled a distance of 17 knots x 7 hours = 119 nautical miles westward.

Ship B is sailing north at 19 knots, so it would have traveled a distance of 19 knots x 7 hours = 133 nautical miles northward.

Using the Pythagorean theorem, the distance between the two ships at 7 PM can be calculated as follows:

Distance = √((40 + 119)² + (133)²)

= √(159² + 133²)

= √(25281 + 17689)

= √42970

= 207.3 nautical miles

Therefore, the speed at which the distance between the ships is changing at 7 PM is 207.3 knots.

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The distance between the ships is changing at a rate of 552 knots at 7 PM. At 7 PM, ship A will have been sailing west for 7 hours, covering a distance of 7 x 17 = 119 nautical miles. Similarly, ship B will have been sailing north for 7 hours, covering a distance of 7 x 19 = 133 nautical miles.

To find the distance between the ships at 7 PM, we can use the Pythagorean theorem. Let's call the distance between the ships at noon D.

Using the Pythagorean theorem, we have:
\(D^2 = (40 + 119)^2 + (133)^2\)

Simplifying, we get:
\(D^2 = 159^2 + 133^2\)

Calculating, we find:
D ≈ 204 nautical miles

Now, we need to find how fast the distance between the ships is changing at 7 PM. To do this, we differentiate the equation for D with respect to time t:

\(\frac{dD}{dt} = 2(40 + 119)(17) + 2(133)(0) = 552\; knots\)

Therefore, the distance between the ships is changing at a rate of 552 knots at 7 PM.

In conclusion, the distance between the ships is changing at a rate of 552 knots at 7 PM.

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Answer:

35 dimes and 60 nickels

Step-by-step explanation:

let d = # of dimes and n = # of nickels

We know that Timmy has a total of 95 coins, consisting of dimes and nickels

So d + n = 95

The total value of his bank is $6.50

A dime is worth $0.10 and a nickel is work $0.05

So 0.10d + 0.05n = $6.50

Note that we've just created a system of equations that we can solve

We have the two equations

0.10d + 0.05n = 6.50 and d + n = 95

There are many different methods we can use to solve this system but the easiest way in this situation is probably going to be the substitution method.

First we are going to want to rearrange the terms of the second equations so that one of the variables are defined.

d + n = 95

- subtract d from both sides -

n = 95 - d

We now defined "n"

Now that we have defined one of the variables we can plug in ( or substitute ) the value of it into the other equation. Once we substitute it we can solve for the other variable.

0.10d + 0.05n = 6.50

n = 95 - d

0.10d + 0.05(95 - d) = 6.50

we now solve for d

0.10d + 0.05(95 - d) = 6.50

step 1 distribute the 0.05

0.05 * 95 = 4.75 and 0.05 * -d = -0.05d

0.10d + 4.75 - 0.05d = 6.50

step 2 combine like terms 0.10d  - 0.05d = 0.05d

0.05d + 4.75 = 6.50

step 3 subtract 4.75 from both sides

0.05d = 1.75

step 4 divide both sides by 0.05

0.05d / 0.05 = d and 1.75 / 0.05 = 35

d = 35

Now that we have found the value of one variable we can plug it into one of the equations and solve for the other variable ( note that the equation that we use does not matter, we will acquire the same answer )

d + n = 95

d = 35

35 + n = 95

subtract 35 from both sides

n = 60

We can conclude that he has 35 dimes and 60 nickels

Answer:

e=5+2f

Step-by-step explanation:

The given equation is

x^2 + 7x = 8

By subtracting 8 from both sides, it becomes

x^2 + 7x - 8 = 0

We would find two terms such that their sum or difference is 7x and the product is - 8x^2. The terms are - x and 8x. Replacing 7x with - x and 8x, we have

x^2 - x + 8x - 8 = 0

By factorising, we have

x(x - 1) + 8(x - 1) = 0

Since x - 1 is common, it becomes

(x + 8)(x - 1) = 0

x + 8 = 0 or x - 1 = 0

x = - 8 or x = 1

Option C is correct

The system of equations has one solution. The two equations are intersecting lines.

The substitution method is one of the algebraic methods to solve simultaneous linear equations. It involves substituting the value of any one of the variables from one equation into the other equation.

We have the equations are:

y = 12 x + 2 ___eq.(1)

2y = x + 4 ____eq.(2)

You have to plug in y for 12x+2 in the second equation.

2(12x+2)=x+4

Simplify the equation:

24x + 4 = x + 4

Subtract 24x from each side

4 = -23x+4

Subtract 4 from each side

0 = 23x

Divide each side by 23

x=0

Now, plug in 0 to one equation.

y=12(0)+2

y=2

The lines intersect at one point, (0,2)

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If the randomly selected student denies having a visa, the probability that the student also denies having a mastercard is 0.

To calculate the probability that a student denies having a Mastercard given that they have already denied having a Visa, we need to use conditional probability. Let's use the notation:

Dv: the event that a student denies having a Visa

Dm: the event that a student denies having a Mastercard

We want to find P(Dm | Dv), the probability that a student denies having a Mastercard given that they have already denied having a Visa.

We can use Bayes' rule to calculate this probability:

P(Dm | Dv) = P(Dv | Dm) * P(Dm) / P(Dv)

We know that the probability of a randomly selected student denying having a Mastercard is P(Dm) = 0.4, as given in the problem.

We also know that the probability of a randomly selected student denying having a Visa, given that they do not have a Mastercard, is P(Dv | not Dm) = 0.9, as given in the problem. This means that the probability of a student having a Visa and a Mastercard is P(not Dv and not Dm) = 0.1.

To find the probability of a randomly selected student denying having a Visa, we can use the law of total probability:

P(Dv) = P(Dv | Dm) * P(Dm) + P(Dv | not Dm) * P(not Dm)

P(Dv) = 0.6 * 0.4 + 0.1 * 0.6

P(Dv) = 0.24 + 0.06

P(Dv) = 0.3

Therefore, we have:

P(Dm | Dv) = P(Dv | Dm) * P(Dm) / P(Dv)

P(Dm | Dv) = 0 * 0.4 / 0.3

P(Dm | Dv) = 0

This means that the probability that a student denies having a Mastercard, given that they have already denied having a Visa, is 0. In other words, if a student denies having a Visa, they cannot also deny having a Mastercard.

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The probability that each of the four randomly selected State College hockey games resulted in six goals being scored is 0.0034 or 0.34%.

Given that;

The number of goals scored at State College hockey games follows a Poisson distribution with a mean of 3 goals per game.

Now, for the probability that each of the four randomly selected State College hockey games resulted in exactly six goals being scored, use the Poisson probability formula.

The Poisson distribution formula is given by:

\(P(x; \mu) = \dfrac{(e^{-\mu} \times \mu^x) }{x!}\)

Where P(x; μ) is the probability of getting exactly x goals in a game with a mean of μ goals.

In this case, x = 6 and μ = 3;

Let's calculate the probability for each game:

\(P(6; 3) = \dfrac{(e^{-3} \times 3^6)}{6!}\)

Now, since we want all four games to have exactly six goals, multiply the individual probabilities together:

P(all 4 games have 6 goals) = P(6; 3) P(6; 3) P(6; 3) P(6; 3)

Now, let's calculate the probability:

\(P = \dfrac{(e^{-3} \times 3^6)}{6!} \dfrac{(e^{-3} \times 3^6)}{6!} \dfrac{(e^{-3} \times 3^6)}{6!} \dfrac{(e^{-3} \times 3^6)}{6!}\)

Simplifying this expression, we get:

\(P = \dfrac{(e^{-3} \times 3^6)^4}{(6!)^4}\)

\(P = 0.34\%\)

Hence, The probability that each of the four randomly selected State College hockey games resulted in six goals being scored is 0.0034 or 0.34%.

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Answer:

90 Miles I think

Step-by-step explanation:

40/4=10

10x9=90

Answer:

20:25 probably don't quote me

Answer:

4th option

Step-by-step explanation:

The factors of a³ + b³ are

a³ + b³ = (a + b)(a² - ab + b² )

Answer:

4th option

Step-by-step explanation:

Answer:

where is the photo?

Step-by-step explanation:

Where is the photo, I need you to give me more details so i can officially answer your question, thank you :)

Answer:

\(\frac{1}{32 m^{15} n^{35}}\)

Step-by-step explanation:

\((2m^3n^7)^{-5}\)

= \(2^{-5} m^{-15} n^{-35}\)

= \(\frac{1}{2^{5} m^{15} n^{35}}\)

=\(\frac{1}{32 m^{15} n^{35}}\)

OPTION E is the correct answer.

Hope it helps you...

Answer:

It should be $33 - - - - -

Step-by-step explanation:

45 + 30 = 75

75 × 0.44 = 33

Answer:

It's $33

Step-by-step explanation:

There are 8,519,680 hexadecimal numbers. The result is obtained by using the multiplication principle.

Hexadecimal number system is a numbering system with the base of 16. The 16-digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. They are usually denoted by the subscript 16. For example, 429AD₍₁₆₎.

How many combination of hexadecimal numbers that can be made if:

Let's broke the problem into 3 cases.

Using the multiplication principle, we can multiply them all.

The combination of hexadecimal numbers is

= 10 × 13 × 16³

= 8,519,680

Hence, the combination that can be made is 8,519,680 hexadecimal numbers.

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The set of ordered pairs that has an error is Set D, where the reflection of the point (3, 2) across the y-axis should be (-3, 2) instead of (3, -2).

The reflection of a point across the y-axis involves changing the sign of the x-coordinate while keeping the y-coordinate the same. Let's examine each set of ordered pairs:

Set A: The original point is (6, 8). When reflected across the y-axis, the x-coordinate becomes -6, while the y-coordinate remains the same as 8. So the reflection is (-6, 8). This set is correct.

Set B: The original point is (1, 1). When reflected across the y-axis, the x-coordinate becomes -1, while the y-coordinate remains the same as 1. So the reflection is (-1, 1). This set is correct.

Set C: The original point is (0, 3). When reflected across the y-axis, the x-coordinate remains the same as 0, and the y-coordinate remains the same as 3. So the reflection is (0, 3). This set is correct.

Set D: The original point is (3, 2). However, the recorded reflection as (3, -2) is incorrect. The correct reflection should be (-3, 2), where the sign of the x-coordinate changes, while the y-coordinate remains the same.

Therefore, the set of ordered pairs that has an error is Set D, where the reflection of the point (3, 2) across the y-axis should be (-3, 2) instead of (3, -2).

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Answer:

Step-by-step explanation:

To evaluate the given expression, we need to substitute the given values for x, y, and z. The expression becomes:

yz + x²

Substituting the given values, we get:

(6.1 * 0.2) + (3.2^2)

This simplifies to:

1.22 + 10.24

Therefore, the value of the expression is approximately 11.46.

11.46

gimme brainlyest gang

Answer:

The answer would be 48 since it would be 4 x 12

Answer:

$15

Step-by-step explanation:

If the 5 people where each paying $12 to rent the equipment, that means the cost of the equipment can be found multiplying 5 and 12 to get 60. Now that we know that the cost of the equipment is $60, if one person bailed out, there are now 4 people to rent it. You can find how much each person pays if they each pay the same amount by dividing 60 by 4. Once you do                      $60 ÷ 4 people = 15. So each person pays $15.

I hope this helps :)

Answer:

I think the question is from Sequence.

on the basis that I have studied I think this is the way. if I am wrong sorry

Answer:

y=x(t)+y-int

Step-by-step explanation:

Where:

Y= distance

x=speed

t=time

y-int= starting height

If you can post a rate and starting height I can answer part B

Keep in mind if she is traveling down then y-int will be 0<x and the rate will be negative

Answer:

1 1/8 ga / 13.5 mi = .0833 ga / mi

1 / .0833 ga/mi = 12 mi / ga

or .0833 ga/mi * 13.5 mi = 1.25 ga

Answer:   C. Amy used the incorrect inequality symbol. The solution set should be [1.25, ∞)

Step-by-step explanation:

Answer:

Amy used the incorrect inequality symbol. The solution set should be [1.25, ∞).

Step-by-step explanation:

edge

Answer:

After 1.2 seconds