the first term of an arthimetic sequence is 42 the rule an= an-1 +8 can 1 can be used explain how to write explict rules

Answer:

544 miles

Step-by-step explanation:

160 miles= 5 hours in order to see how much she traveled in 1 hour you need to divide so do 160 divided by 5 = 32 then do 32x17 which would be 544.

I hope it helps you!

~XxBells is a cute girlxX~

Kaylee would travel 544 miles in 17 hours if she continued at the same rate.

A mathematical number is known as distance measures "how much ground an object has traveled" while moving. Distance is defined as the product of speed and time.

distance = rate × time

We know that Kaylee drove 160 miles in 5 hours, so her rate is:

rate = distance / time = 160 miles / 5 hours = 32 miles/hour

Now we can use this rate to find out how far she would travel in 17 hours:

distance = rate × time

distance = 32 miles/hour × 17 hours

distance = 544 miles

Therefore, Kaylee would travel 544 miles in 17 hours if she continued at the same rate.

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It takes approximately 55 mins for the sample to decay to one - fourth of its original amount.

In the given statement is:

λ = 2.5 x 10^-2 [tex]min^{-1}[/tex]is the rate constant of the nucleus

To solve this problem, we use

N(t) = [tex]N_{0}[/tex]e^-λt

and since we are looking for the time it takes to decay the nucleus to one -fourth of its original amount, we set

N(t) = 1/4 [tex]N_{0}[/tex] = 0.25[tex]N_{0}[/tex]

We can substitute this in the decay equation:

0.25[tex]N_{0}[/tex] =[tex]N_{0}[/tex] e^-λt

Cancel the like terms

0.25 = e ^-λt

Take the natural logarithm of both sides:

㏑(0.25) =㏑(e^-λt)

㏑(0.25)= -λt

Solve for the time t:

t = - ㏑(0.25)/λ

Substitute the given rate constant :

t = ㏑(0.25) / 2.5 x 10^-2 [tex]min^{-1}[/tex]

t = -1.3863 /2.5 x 10^-2 [tex]min^{-2}[/tex]

t = 55.452mins

It takes approximately 55 mins for the sample to decay to one - fourth of its original amount.

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The number that is halfway between the numbers -46.3 and 46.31 will be 46.305.

We are given the two numbers:

- 46.30 and 46.31

Now, we need to find a number that is halfway between the given numbers.

For this, we need to find the mid point between the two numbers that is given to us.

Mid point is calculated as:

| x | + | y | / 2

Substituting the values in the expression, we get that:

46.3 + 46.31 / 2

= 92.61 / 2

= 46.305

Therefore, we get that, the number that is halfway between the numbers -46.3 and 46.31 will be 46.305.

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The function rule for g(x) is g(x) = -4x

The function is given as

f(x) = 4x

The transformation is given as reflection across the x-axis

The rule of this transformation is

(x, y) = (x, -y)

So, we have

g(x) = -f(x)

This gives

g(x) = -4x

Hence, the function rule for g(x) is g(x) = -4x

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Polynomials which have (x-4) as a factor are a. x³ - 13x - 12 = 0 and c. x³ + 6x + 5x - 12 = 0.

An algebraic equation having two or more than two terms is called a polynomial.

According to the given question we have determine which of the following polynomials have (x-4) as a factor.

One way is factoring each of these polynomials.

Another way is given x - 4 is a factor,

∴ x - 4 = 0

x = 4 must satisfy the polynomial which has a factor of (x-4).

Now we have to replace x with 4 in each of the given polynomials and if LHS = RHS then (x -4) is a factor.

a. x³ - 13x - 12 = 0

(4)³ - 13(4) - 12 = 0

64 - 52 - 12 = 0

64 - 64 = 0. (LHS = RHS).

b. x³ + 8x² + 19x + 12 = 0

(4)³ + 8(4)² + 19(4) + 12 ≠0

Here you don't need to calculate further because in LHS sum of these terms won't be zero.

c. x³ + 6x + 5x - 12 = 0.

x³ + 11x - 12 = 0.

64 + 44 - 12 ≠ 0.

d. x³ - x² - 10x - 8 = 0.

64 - 16 - 40 - 8 = 0.

64 - 64 = 0, (LHS = RHS).

e. x² - 4

16 - 4 ≠ 0.

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The minimum wage per hour = $2

Here we need to find the value of minimum wage per hour in 1975

As is given that the earning minimum wage is $80 for working 40 hours.

40-hour work gives = $80

1-hour work gives = $80/40

                             = $2

Therefore the minimum wage per hour in 1975 is $2

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Answer:

(-2, 32, -21)

Step-by-step explanation:

You just multiply B by 3 and then subtract the corresponding parts. For example -2 -(0*3). and then 14-(-6*3)

The value of constant v is 3.75 if y varies directly as x and when

x = 8 and y = 30.

Let v be any constant.

According to the given question.

y varries directly as x.

⇒ y ∝ x

⇒ y = vx                    (beacuse v is constant)

Here, it is give that x = 8 and y = 30.

Thereofre, the value of constant v when y = 30 and x = 8 is given by

y = vx

⇒ 30 = v(8)

⇒ 30/8 = v

⇒ v = 3.75

Hence, the value of constant v is 3.75 if y varies directly as x and when

x = 8 and y = 30.

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Answer:

Step-by-step explanation:

the number is y

you are told

y+0.5y=27

Therefore,

1.5y = 27.

If you divide by 1.5 on both sides, you'll get 18 which is your answer.

18+9=27

Answer:

slope=y2-y1/x2-x1

=-6-(-6)/9-6

=0/3

any fraction in which numerator is 0 is 0.

Greetings from Brasil...

For rotation, we can use the expression:

Let rotate 180° - specifically for this angle, 180°, either counterclockwise or clockwise

SEN 180 = 0 and COS 180 = - 1

V(X; Y) → V'(- X; - Y)

V(0; - 2) → V'(0; - (- 2))

___________________________________
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well, let's convert the mixed fraction to improper fraction firstly, then let's check their difference.

[tex]\stackrel{mixed}{15\frac{3}{5}}\implies \cfrac{15\cdot 5+3}{5}\implies \stackrel{improper}{\cfrac{78}{5}}\qquad \impliedby \textit{that's for just 1 day} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\LARGE after 6 days}}{\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} }\implies \cfrac{468}{5} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{change in bushels}}{\cfrac{468}{5}~~ - ~~\cfrac{78}{5}}\implies 78\qquad \impliedby \textit{so 6 days later he's got 78 more bushels}[/tex]

Answer:

AC = 8

BC = 10

AH = 4.8

Step-by-step explanation:

A = 1/2(AB)(AC)

24 = 1/2(6)(AC)

AC = (24)(2)/(6) = 8

BC^2 = AB^2 + AC^2 = 6^2 + 8^2 = 36 + 64 = 100

BC = 10

A = 1/2(AH)(BC)

24 = 1/2(AH)(10)

AH = (24)(2)/(10) = 48/10 = 4.8

Answer:

22 - 4x

Step-by-step explanation:

4(3-x) + 10  Distribute the 4

4(3) - 4x +10

12 - 4x +10

22 - 4x

Based on the fact that Raven is trying to decide between two plumbing services, the costs of the service charge are:

The Service cost for Service provider A is:

= 50 x  1.5 + (50 x ((1.75 / 1.5) - 1)

= $83.33

Service cost for Service provider B is:

= Number of hours x Cost per hour

= 60 x 1.75

= $105

The cheaper plumber is Service provider A.

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Answer:

A) The percentage of the bacteria increasing each hour is 15% per hour

B) When t=0 the population of bacteria is 3000 bacteria

C) After 24 hours the a sensible degree of accuracy in population is about 85875 (since only whole numbers count)

Step-by-step explanation:

A) To find the percentage of the bacteria increasing each hour the growth rate needs to be determined. To find it you need to subtract 1.15 by since the formula for exponential growth is a(1+r)^t one is added to the rate so to inverse it 1.15 needs to be subtractied by one to get 0.15. At this point you found the decimal rate to find the percentage you multiply 0.15 by 100 to make it a whole number and it results in 15%

B) To determine the size if the population when t=0 you substitute the variables t for 0 to get 3000×1.15^0 to get 3000 (remember anything times 0 is 0). Another way is to keep in mind that 3000 is the initial amount because that's the number with no variable with it.

C) To find the population after 24 hours substitute t for 24. After substituting t and multiplying 3000×1.15^24 the exact answer is 85875.52857. To find the answer in a sensible degree of accuracy you would round it to the nearest whole number which is 85876 since the dight in the tenths place is 5 or greater than the answer is rounded up by one.

The linear function that represents the line giving by the point slope equation y-2=4(x-3) is f(x) = 4x - 10

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

Also note that f(x) = y

Isolate the y then add 2 from both sides:

y - 2 = 4(x-3)

y - 2+ 2 = 4(x-3)+2

y = 4(x-3) + 2

Note that the equation is : y = 4(x-3) + 2

Now Distribute 4 to all terms within the parenthesis

y = 4(x-3) + 2

y = 4x - 12 + 2

Simplify. Combine like terms

y = 4x - 10 ; or f(x) = 4x - 10.

Hence, The linear function that represents the line giving by the point slope equation y-2=4(x-3) is f(x) = 4x - 10

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4.8 packages will need for the use of one year.

No. of used packages of printer paper during 10 months = 4 Packages

As we know that there is 12 months in a year,

To determine the number of packages need for the year, first we have to find the number of package is being use in one month.

S0,  No. of used package in 1 month = 4/10 = 0.4 Package

Now, we will determine the number of packages for the use of one year, by multiplying the No. of used package in 1 month with 12.

No. of packages for the use of one year = 12 × 0.4

                                                                   = 4.8 Packages

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For the bucket to hold the 10 litres, then it s said to contains 2.64 gallons.

A multi-step procedure encompassing multiplication as well as division by a mathematical factor is known as unit conversion. We can measure weight, length, and temperature in a variety of ways.

Now, per the given question;

The total amount a bucket contains is 10 litres.

Noe, the conversion of litres in gallons is given as;

1 litres = 0.26 gallons.

Thus, 10 litres = 10×0.264

= 2.64 gallons.

Therefore, the bucket will contain 2.64 gallons.

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Answer:

$2.08 per pound  

Step-by-step explanation:

1.52+1.08= 2.6pound

6.50/2.6=$2.5 per 2.6 Ibs

(turn the pound to a whole number)

2.6/2= 1.3 so 2,6/1.3= 2Ibs

(what you do to one side must be done to the other)

$2.5/1.3 =2.08

Answer: ( -2, 4)

Step-by-step explanation:

Volume is equal to [tex]a^{3}[/tex] where an is the width or length of its edges.

The number of cubic units that a cube totally occupies is determined by its volume. The cubic unit of measurement for the volume of a cube includes [tex]centimetres^{3}[/tex], [tex]metres^{3}[/tex], [tex]inches^{3}[/tex], [tex]feet^{3}[/tex], etc.

A solid three-dimensional figure with 6 square faces or sides is known as a cube. The total amount of space a cube takes up is its volume. The cube's square shape means that all of its sides are square, and as a result, all of its edges would be of equal length. As a result, the cube's length, breadth, or height are all equal.

If a cube's length, breadth, and height are equal to "a," then;

Cube volume = a[tex]\times[/tex]a[tex]\times[/tex]a.

Therefore, Volume of cube is [tex]a^{3}[/tex] where a is the length of the edge.

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The length of the new garage will be approximately 8.83 meters.

The length is referred as the side of a rectangle or a square. Ideally we use length to measure the larger side of a rectangle, but for a square all sides are equal and so can be called length.

The are of a square is given by the square of any side .

Given the area of the square is 52 square meters.

The new are of the square is 50% more.

Increased amount =  50% of 52 = 26 meters²

New area of square = 52 + 26 meters² = 78 meters²

Now we know that the area of a square is given by (side)² .

Therefore  (side)²= 78

or, side = √78

or, side = 8.8317...

or, side ≈ 8.83 meters

Therefore the length of the new garage is approximately 8.83 meters.

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The hypothesis is called the alternative hypothesis test.

According to the statement

We have to explain about the alternative hypothesis.

So, For this purpose, we know that the

The alternative hypothesis is one among ll|one amongst |one in every of} two mutually exclusive hypotheses in a hypothesis test. the choice hypothesis states that a population parameter doesn't equal a specified value.

From the given information:

she randomly selects houses during this neighborhood and compares their estimated market price within the current year to their estimated value within the previous year. suppose that data were collected for a random sample of 8 houses, where each difference is calculated by subtracting the market price of the previous year from the value of the present year.

Then

the alternative hypothesis test usually suggests that there's an opportunity of variation (difference) within the data observed.

Hence, since we are told the "real real estate agent believes that the values of homes within the neighborhood she works in have increased (the chance of variation) from last year," which "each difference is calculated by subtracting the market price of the previous year from the market price of this year," we are able to reach the conclusion that this can be an example of an alternate hypothesis test.

So, The hypothesis is called the alternative hypothesis test.

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Based on the number of movies that each of the 8 students saw in the past year, the mean number of movies is 12.875 movies

To find the mean of a distribution of numbers such as the number of movies seen in the past year, sum up the number of movies watched and then divide it by the number of students.

The mean number of movies watched by the students is therefore:

= Sum of movies watched / Number of students

= (6 + 14 + 14 + 16 + 14 + 18 + 15 + 6) / 8 students

= 103 / 8

= 12.875 movies

Rest of the question is:

Find the mean number of movies that the students saw.

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Answer:

U = 4

Step-by-step explanation:

We take 3/9 and simplify it, making 1/3.

We multiply both by 12 to eliminate denominators, so the new numbers are 4 and U.

U = 4

Answer:

false

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

to determine if (9, 10 ) is a solution, substitute x = 9 into the equation and if y = 10 then it is a solution.

y = 2(9) - 8 = 18 - 8 = 10

then (9, 10 ) is a solution of the equation