An arithmetic sequence has this recursive formula: What is the
explicit formula?

you need to plug the coordinates into the slope formula, which is m=(y2-y1)/(x2-x1).

m=(9-6)/(5-4)

m=(3)/(1)

m=3

A quadratic equation in one unknown;

has two roots. In order to determine these roots, we need to apply certain operations. We can get information about the existence of these roots by discrimination. Below is the discrimination formula.

If we apply discriminant for the above equation, we obtain the following expression;

If the discriminant number is greater than [tex]0[/tex], the equation has two real and distinct roots.

Now let's remember our formula for finding the roots and solve the problem using the discriminant value.

Therefore;

Other root is;

The sequence of transformations that we should apply is the one that appears on the top left option:

Reflection across the y-axis followed by a rotation of 90° counterclockwise.

We can see that the blue figure is on the third quadrant, and the "spiral" part is pointing upwards.

First, we would want to apply a rotation of 90° clockwise, this will move the blue figure to the second quadrant, and now the "spiral" part will point thowards the right.

Now you can see that the red figure is a reflection along the y-axis of the blue figure, so we need to apply that transformation.

Concluding, the sequence of transformations is:

Notice that this is equivalent to:

Then the correct option is the one in the top left corner.

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Part a

There will be $2850 in the account after 8 years

Part b

The amount of interest earned in 5 years is $218.75

The principal amount = $2500

The interest rate = 1.75%

The time period = 8 years

Part a

The simple interest

A = P(1  + rt)

Substitute the values in the equation

A = 2500(1 + (1.75/100)×8)

A = 2500( 1 + 0.14)

A = 2500( 1.14)

A = $2850

Part b

The time period = 5 years

Simple interest = Prt

= 2500 × (1.75/100) × 5

= 2500 × 0.0175 × 5

= $218.75

Hence,

Part a

There will be $2850 in the account after 8 years

Part b

The amount of interest earned in 5 years is $218.75

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Theoretical flow time = 58 minutes

The complete question is

Mamossa Assaf Inc. fabricates garage doors. Roofs are punched in a roof punching press (15 minutes per roof) and then formed in a roof forming press (8 minutes per roof). Bases are punched in a base punching press (3 minutes per base) and then formed in a base forming press (10 minutes per base), and the formed base is welded in a base welding machine (12 minutes per base). The base sub-assembly and the roof then go to final assembly where they are welded together (10 minutes per https://brainly.com/question/27786618garage) on an assembly welding machine to complete the garage. Assume one operator at each station.

Roof → Roof - punch(15 min) → Roof-form(8 min) →→→→→→→→↓

                                                                                      (10)Assembly→ Door

Base → Base - punch(3 min) → Base - form(10 min) → weld(12 min)↑

Roof path = 15 + 8 = 23

Base path = 3 + 10 + 12 =25

Theoretical flow time = Roof path + base path + assembly = 23 + 25 +10 = 58 mins

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The best solution for the given equation is x=4

What are logarithmic functions?

The inverse function to exponentiation in mathematics is called the logarithm. Accordingly, the exponent to which b must be raised in order to obtain a number x is determined by its logarithm to the base b.

Use Property:

logb(xy)=logbx+logby and logby = x ⇔ x^b = y

log2(x(x−2))=3
2^3 =x^2 −2x
8=x^2−2x
0=x^2−2x−8
0=(x−4)(x+2)
x−4=0
or
x+2=0
x=4
or
x=−2
Hence, x=4

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Answer: X=16

Step-by-step explanation:

trust,, also good luck to plato 2b algebra people

Answer:

  1 1/2

Step-by-step explanation:

You want the other number when one of the two numbers that have a product of 7 is 4 2/3.

Let x represent the unknown factor. Then we have ...

  (4 2/3)x = 7

  (14/3)x = 7 . . . . . . write as improper fraction

  x = (3/14)(7) . . . . . multiply by the inverse of the coefficient of x

  x = 3/2 = 1 1/2

The other number is 1 1/2.

The given expression rewritten in simplified exponential form is [tex]5x^{\frac{3}{2}}[/tex]

From the question, we are to rewrite the given expression is simplified exponential form.

The given expression is

[tex]\sqrt{\sqrt{25^{2} x^{6} } }[/tex]

First, we will evaluate the inner square root

[tex]\sqrt{25^{\frac{2}{2} } x^{\frac{6}{2} } }[/tex]

[tex]\sqrt{25 x^{3 } }[/tex]

Simplifying further

[tex]\sqrt{25 } \times \sqrt{x^{3}}[/tex]

[tex]5\times x^{\frac{3}{2}}[/tex]

= [tex]5x^{\frac{3}{2}}[/tex]

Hence, the expression in simplified form is [tex]5 x^{\frac{3}{2}}[/tex]

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The joint relative frequency of students who use a computer in a traditional class is of:

37%.

The relative frequency of an event in an experiment is calculated as the number of desired outcomes in the context of the experiment divided by the number of total outcomes in the context of the experiment.

In this problem, we want the joint relative frequency of students who use a computer in a traditional class, hence the total and desired outcomes are given as follows:

Hence the joint relative frequency of students who use a computer in a traditional class is calculated as follows:

28/74 = 37%. (rounded down).

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Answer:

14%



Step-by-step explanation:

1. I took the test

2.Likes running and swimming=28

Total=200

28/200=.14

.14 in percent form is 14%

PLS GIVE BRAINLIST MEAN THE WORLD

The average rate of change of the function is 0.2 inches per day

A rate of change describes how one quantity changes in relation to another quantity. Mathematically, it is defined as the change in one divided by the change in the other quantity.

In this case, the average rate of change of the function g(n) from n=1 to n=5 will be:

Given the function, g(n) = 10(1.02)ⁿ

average rate of change  = g(5)-g(1) / n₅-n₁

g(5) = 10(1.02)⁵ = 11.0

g(1) = 10(1.02)¹ = 10.2

average rate of change  = 11.0-10.2 / 5-1

                                        = 0.8/4

                                        = 0.2 inches per day

Therefore,  the average rate of change from n=1 to n=5 is 0.2 inches per day

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Answer:

Step-by-step explanation:

-4(x - 1) + 6x =34

-4x + 4 + 6x = 34

-4x + 6x + 4 = 34

2x + 4 = 34

2x + (4-4) = (34-4)

2x = 30

2x/2 = 30/2

x = 15

Answer: 5:1

Step-by-step explanation: 10:2 can be simplified by dividing both by 2, making it 5:1

The ladder is 13 m long and leans against a window 5 m high, then the ladder leaned to the other side without moving its feet to reach the 12 m high window.

if we imagine a leaning ladder it will look like a right triangle and it will remind us of the Pythagorean theorem. do you remember the pythagorean theorem?

The Pythagorean theorem explains the relationship or relationship between the lengths of the sides of a right triangle.

The Pythagorean theorem reads: "The square of the length of the hypotenuse (hypotenuse) in a right triangle is equal to the sum of the squares of the lengths of the other sides".

in the picture, let's say if the width of the street is a, the height of the window is b and the length of the stairs is c.

in this case we will find the width of the street, namely a, then we use formula a² = c² - b² .

then it will be

b = 12

c = 13

a² = c² - b²

a² = 13² - 12²

a² = 169 - 144

a² = 25

a = 5

The critical value is 2.65

Given,

The confidence interval = 99%

Sample size, n = 12

We have to find the critical value;-

Critical value;-

A critical value is the test statistic's value that establishes a confidence interval's upper and lower boundaries or the level of statistical significance for a given test.

Here,

The sample size n = 12,

Then, the degrees of freedom is n - 1 = 12 - 1 = 11

The critical value= t₀.₀₀₁/2 = t₀.₀₀₅

Using the t-table and selecting df =12  and  since it’s a 2 tail the corresponding t-score is 2.65

Therefore, the critical value is 2.65

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Answer:

1.38461538462

Step-by-step explanation:

Answer:

Step-by-step explanation:

an equation that takes two or more steps to solve is called a multi-step equation. let's take a multi-step equation that will satisfy the given condition:

4x - 8 = 22 + x

4x -x = 22 + 8      

3x = 30

x = 10          

Answer:  y=(3/4)x+2

Step-by-step explanation:

1. Find the slope (change of y/change of x)

(5-(-4))/(4-(-8)

9/12

SLOPE: 3/4

2. Find the y-intercept. Insert the points into an equation and find b.

5=(9/12)(4)+b

5=3+b

b=2

Y-INTERCEPT=2

Answer: miles per hour = mi/hr = 17.5mi/0.25hr = 17.5*4mi/0.25*4hr = 70mi/hr

Step-by-step explanation:miles per hour = mi/hr = 17.5mi/0.25hr = 17.5*4mi/0.25*4hr = 70mi/hr

Step-by-step explanation:

18.75 miles in 1/4 hour.

that is the ratio 18.75 / 1/4

but we want the miles in an hour.

so, how many 1/4 are in a whole ?

well, 4.

so we need to multiply the ratio by 4/4 (so that on one hand we multiply the denominator by 4 to make it a whole, and on the other hand we are not changing the value of the ratio) :

18.75 × 4 / (1/4 × 4) = 75 miles / 1 hour = 75 mph.

Answer:

$28

Step-by-step explanation:

5.5%=0.055

1.54/0.055=28

The solution to the system is x = 0, y =2, z = 5

Given the following system:

x+ 2y+z=9      -------- (1)

x- y+3z = 13    -------- (2)

2z = 10            -------- (3)

From (3):

2z = 10

z = 10/2 = 5

Put z = 5 into (1) and (2):

x+ 2y+z=9

x+ 2y+5 = 9

x +2y = 9-5

x +2y = 4     -------- (4)

x- y+3z = 13

x -y + 3(5) = 13

x-y + 15 = 13

x-y = 13 -15

x-y = -2     --------   (5)

Using elimination method on (4) and (5):

Subtracting (5) from (4):

x +2y = 4

x-y =   -2

3y = 6

y = 6/3 = 2

Put y = 2 into (4):    

x +2y = 4

x + 2(2) = 4

x + 4 = 4

x = 4-4 = 0

Therefore, the solution is x = 0, y =2, z = 5. The 3rd option is the answer.

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The 98% confidence interval of the true mean is 43.02 million < true mean < 13.80

Given,

Number of social networking sites being surveyed = 6

Sample mean = 9.05 million visitors per month

Standard deviation = 5 million

We have to find the 98% confidence interval of the true mean;

Here,

Sample mean, x = 9.05 million

Standard deviation, σ = 5 million

Sample size, n = 6

z score of 98% is 2.326

Now,

9.05 million - 2.326 × (5 million / √6) < true mean < 9.05 million + 2.326 × (5 million / √6)

43.02 million < true mean < 13.80

Therefore,

The 98% confidence interval of the true mean is 43.02 million < true mean < 13.80

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You can ask where you don't understand.

The equation of the parallel line is 4x + 5y - 12 = 0

The equation is given as

4x + 5y + 2 = 0

The x-intercept is also given as

x-intercept = 3

We have

4x + 5y + 2 = 0

Make y the subject

5y = -4x - 2

Divide through by 5

y = -4x/5 - 2/5

The equation of a line can be represented as

y = mx + c

Where

slope = m

By comparing the equations, we have:

m = -4/5

This means that the slope of 4x + 5y + 2 = 0 is =4/5

The slopes of parallel lines are equal

This means that the slope of the other line is -4/5

The equation of the parallel line is then calculated as

y = m(x - x₁) +y₁

Where

m = -4/5

(x₁, y₁) = (3, 0) i.e. the x-intercept

So, we have

y = -4/5(x - 3) + 0

Multiply through by 5

5y = -4(x - 3)

Open the brackets and evaluate

5y = -4x + 12

This gives

4x + 5y - 12 = 0

Hence, the parallel line has an equation of 4x + 5y - 12 = 0

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The gallons of milk were in each container originally is 2.4 and 4.8 gallons respectively.

Let us say that:

V₁ = initial gallons in the first container

V₂ = initial gallons in the second container.

From the problem statement, we can create the expression:

V₁ = 2 V₂

V₁ – 3 = 45 (V₂ – 2)

Combining the two expressions:

2 V₂ – 3 = 45 (V₂ – 2)

2 V₂ – 3 = 45 V₂ – 9

2.5 V₂ = 6

Divide

V₂ = 6 / 2.5

V₂ = 2.4 gallons

V₁ = 2 V₂:

= 2 × 2.4

= 4.8 gallons

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Complete question

The first container of milk contains twice as much milk as the second contamer After John uses 2 galions of milk from the second container and 3 gallons of milk from the first container, the first container has 4.5 times as much milk as the second, How many gallons of milk were in each container originally?

Answer:

x = 11

Step-by-step explanation:

Let's have  one of the numbers be represented by the variable, x,  and the other number be represented with the variable, y

Since the sum of the two numbers is 55, we can write the following equation:

x + y = 55

Then since one number is 4 times as large as the other, we can write:  y = 4x

We can now substitute this expression for y into the second equation and solve by

combining like terms and using inverse operations to solve for x:

x + y = 55

x + 4x  = 55

5x = 55

5x/5 = 55/5

x = 11

One of the numbers is 11.

Since the sum of the numbers is 55, the other number will be 44.

Answer:

11 and 44

Step-by-step explanation:

→ Write 2 equations

x + y = 55

y = 4x

→ Substitute bottom equation into top

x + 4x = 55

→ Solve

x = 11

→ Find y

4 × 11 = 44

Answer: r = 19.35 ft

Step-by-step explanation:

[tex]Volume = V = \pi r^{2} \frac{h}{3} \\235.5 = \pi r^{2} 15/3\\r^{2} = \frac{235.5}{\pi} 5\\r = \sqrt{374.8} = 19.35[/tex]

Answer:

The effective tax rate for a taxable income of $63,425 is 15.18%.

Step-by-step explanation:

If the steps follow an arithmetic series, the concrete required for the first 12 steps is 140.4.

Given, the first term of the arithmetic series, a=1.8 and the sum of first five terms that is s5=27, we have to find the sum of first 12 steps.

The formula to calculate the sum of the terms in AP is

Sn = n/2 {2a + (n - 1) d}

S5=5/2(2(1.8) +(5-1)d)

27=2.5(3.6+ 4d)

27=9+10d

27-9=10d

18=10d

d=18/10

d=1.8

The common difference d is 1.8.

Now we have to find S12,

S12=12/2(2(1.8) +(12-1)1.8)

= 6(3.6+19.8)

=6(23.4)

=140.4

S12=140.4

Therefore, the concrete required for the first 12 steps is 140.4.

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