PlEaSe HelP mEakwhtb4qhnga

Answer:

[tex]a_{n}[/tex] = 4n + 11

Step-by-step explanation:

There is a common difference between consecutive terms, that is

19 - 15 = 23 - 19 = 4

This indicates the sequence is arithmetic with explicit rule

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 15 and d = 4 , then

[tex]a_{n}[/tex] = 15 + 4(n - 1) = 15 + 4n - 4 = 4n + 11

Answer:

A and B are exhaustive.

Step-by-step explanation:

Given

[tex]A = \{1,2,4\}[/tex]

[tex]B = \{2,3,4,5,6\}[/tex]

[tex]C =\{3,4\}[/tex]

[tex]D = \{2,4,5\}[/tex]

Solving (a): The mutually exclusive events

These are events that have no common or mutual elements

Events A to D are not mutually exclusive because each of the events have at least 1 common element with one another.

Solving (b): Exhaustive events.

Two events X and Y are said to be exhaustive if:

[tex]S = P(X\ n\ Y)[/tex]

i.e. if the sample space equals the intersection of X and Y

For events A to D, we have:

[tex]A\ n\ B = \{1,2,3,4,5,6\}[/tex]

and the sample space is:

[tex]S = \{1,2,3,4,5,6\}[/tex]

By comparison;

[tex]A\ n\ B = S[/tex]

Hence, A and B are exhaustive.

Answer:

15 days

+

Step-by-step explanation:

A

200 pages / (8 pages / day) =

= 200 pages days / 8 pages =

= 200 days / 8 = 25 days

B

200 pages / (5 pages / day) =

= 200 pages days / 5 pages =

= 200 days / 5 = 40 days

40-25 = 15 days

A will finish 15 days sooner than B.

A will finish her report 15 days sooner than B.

The ratio is defined as a relationship between two quantities, it is expressed one divided by the other.

Writer A averages 8 pages a day,

Number of pages per day written by writer A = 8 per day

Writer A will finish her report = Total pages / per day written by writer A

⇒ 200 pages / (8 pages / day)

⇒ 200 pages days / 8 pages

⇒ 200 days / 8

⇒ 25 days

Writer B averages 5 pages a day

Number of pages per day written by writer B = 5 per day

Writer B will finish her report = Total pages / per day written by writer A

⇒ 200 pages / (5 pages / day)

⇒  200 pages days / 5 pages

⇒  200 days / 5

⇒  40 days

Difference between both of time when they finished their report = 40-25 = 15 days

Hence, A will finish her report 15 days sooner than B.

Learn more about Ratio here:

brainly.com/question/1504221

#SPJ5

Answer:

x = 35

Step-by-step explanation:

The angles shown are vertical angles

Vertical angles are congruent

Hence, 80 = 2x + 10

( Note that we just created an equation that we can use to solve for x )

We now solve for x using the equation we created

80 = 2x + 10

Step 1 subtract 10 from each side

80 - 10 = 70

10 - 10 cancels out

We now have 70 = 2x

Step 2 divide each side by 2

70/2 = 35

2x / 2 = x

We're left with x = 35

Answer:

x+3y =6

2x+8y=-12​

The solutions to your equations are:

x= 42 and y= -12

lets check this

42+-36 =6

84+-96=-12​

Hope This Helps!!!

The inequalities that represent these constraints are x ≤ 500 + 2y and 35x + 50y > 22500²

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the number of product A and y represent the number of product B, hence:

x ≤ 500 + 2y        (1)

Also:

35x + 50y > 22500²    (2)

The inequalities that represent these constraints are x ≤ 500 + 2y and 35x + 50y > 22500²

Find out more on equation at: https://brainly.com/question/2972832

#SPJ2

Answer:

[tex]M = (0,0)[/tex]

Step-by-step explanation:

Given

[tex](4,-5)[/tex] and [tex](-4,5)[/tex]

Required

The midpoint (M)

This is calculated as:

[tex]M = \frac{1}{2}(x_1 + x_2,y_1+y_2)[/tex]

So, we have:

[tex]M = \frac{1}{2}(4-4,-5+5)[/tex]

[tex]M = \frac{1}{2}(0,0)[/tex]

[tex]M = (0,0)[/tex]

Answer: 24 years

Step-by-step explanation:

Based on the information given, we've been given,

Principal = #250

Interest = #120

Interest rate = 2%

Time = Unknown

Interest = PRT/100

120 = (250 × 2 × Time)

Cross multiply

120 × 100 = (250 × 2 × T)

12000 = 500T

Time = 12000/500

Time = 24

It will take 24 years.

Step-by-step explanation:

I cannot really identify and read the provided answer options.

the solution to the sequence 2, 6, 10, 14, 18, ... is

an = 4×(n-1) + 2

recursive that is

a1 = 2

an = an-1 + 4

please pick the right option in your original problem definition that fits to this solution.

The recursive formula that represents the given sequence is:

[tex]a_n = a_{n-1} + 4[/tex]

An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a fixed constant value to the previous term.

This fixed value is called the common difference, and it is the same for all terms in the sequence.

We have,

The given sequence has a common difference of 4 between its consecutive terms.

To represent this sequence using a recursive formula, we can start with the first term and use the common difference of 4 to find each subsequent term.

Let's assume that the first term of the sequence is a1. Then, we can represent the second term [tex]a_2[/tex] as:

[tex]a_2 = a_1 + 4[/tex]

Similarly, we can represent the third term (a3) as:

[tex]a_3 = a_2 + 4[/tex]

Substituting the value of a2 from the above equation, we get:

[tex]a_3 = (a_1 + 4) + 4 = a_1 + 8[/tex]

We can continue this pattern to find the recursive formula for the nth term of the sequence:

[tex]a_n = a_{n-1} + 4[/tex]

where [tex]a_1[/tex]= 2

Thus,

The recursive formula for the given sequence is:

[tex]a_n = a_{n-1} + 4[/tex]

Learn more about arithmetic sequence here:

https://brainly.com/question/10396151

#SPJ7

Answer:

20°

Step-by-step explanation:

perpendicular from the center on a chord of a circle always bisects the chord.

AR=BR

∴m arcAC=m arc BC=20°

Answer:

false

Step-by-step explanation:

The function given in the table is a linear function:

f(x) = 3x+2

Answer:

2

Step-by-step explanation:

The mean is calculated as

mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{2-x+2+x}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2

Answer:

[tex]Range = 11[/tex]

[tex]\sigma^2 = 12.1[/tex]

[tex]\sigma = 3.5[/tex]

Step-by-step explanation:

Given

[tex]Data: 16,12,17,8,15,15,10,11,19,18[/tex]

Solving (a): Range

This is calculated as:

[tex]Range = Highest - Least[/tex]

Where:

[tex]Highest = 19[/tex]

[tex]Least = 8[/tex]

So:

[tex]Range = 19 - 8[/tex]

[tex]Range = 11[/tex]

Solving (b): The population variance

First, calculate the population mean using:

[tex]\mu = \frac{\sum x}{n}[/tex]

So:

[tex]\mu = \frac{16+12+17+8+15+15+10+11+19+18}{10}[/tex]

[tex]\mu = \frac{141}{10}[/tex]

[tex]\mu = 14.1[/tex]

So, the population variance is:

[tex]\sigma^2 = \frac{\sum(x - \mu)^2}{n}[/tex]

[tex]\sigma^2 = \frac{(16 - 14.1)^2 + (12 - 14.1)^2 +............... + (19- 14.1)^2 + (18- 14.1)^2}{10}[/tex]

[tex]\sigma^2 = \frac{120.9}{10}[/tex]

[tex]\sigma^2 = 12.09[/tex]

[tex]\sigma^2 = 12.1[/tex] --- approximated

Solving (c): The population standard deviation.

This is calculated as:

[tex]\sigma = \sqrt{\sigma^2[/tex]

[tex]\sigma = \sqrt{12.09[/tex]

[tex]\sigma = 3.5[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

For a loan value of 1, the monthly payment on a 30 year loan at 7% is ...

  A = (0.07/12)/(1 -(1 +0.07/12)^(-12·30)) ≈ 0.00665302495

Then the amount repaid after 360 payments is ...

  360A = 2.39508898 . . . times the principal amount

__

a) For a monthly payment of $1050, the principal can be ...

  $1050/0.00665302495 ≈ $157,823

__

b) The amount repaid to the loan company is ...

  $157,823×2.39508898 ≈ $378,000

__

c) The amount that is interest is ...

  $378,000 -157,823 = $220,177

Answer:

$50 dollars saved

Step-by-step explanation:

Given

[tex]y = 10x[/tex]

Required

The amount saved after 5 weeks

We have:

[tex]y = 10x[/tex]

Substitute 5 for x

[tex]y = 10*5[/tex]

[tex]y = 50[/tex]

Answer:

The domain of a function is the input numbers that, when plugged into a function, the result is defined. In simple words, we can define the domain of a function as the possible values of x that will make an equation true.

The range of a function is defined as a set of solutions to the equation for a given input. In other words, the range is the output or y value of a function. There is only one range for a given function.

hope this helps!

Step-by-step explanation:

Answer: lil t j

Step-by-step explanation:

I’m not a goat but I fit the description we walk around with then bands in my pocket

Answer:

1) x = -17 +6y + 2z/3

2) x= -13 - 4y - 5z/6

3) x= -22 +4y + 3z/3

Step-by-step explanation:

1) 3x-6y-2z=-17

3x- 6y -2z- (-6y -2z)= - 17 - ( 6y -2z )

3x=-17+6y+2z

3x/3= -17/3 +6y/3 + 2z/3

x = -17 +6y + 2z/3

2) −6x+4y+5z=13

-6x+4y+5z- ( 4y + 5z )= 13 - ( 4y + 5z )

-6x=13-4y-5z

-6x/-6= 13/-6 - 4y/-6 - 5z/-6

x= -13 - 4y - 5z/6

3) −3x−4y−3z=22

-3x=22+4y+3z

-3x/-3 = 22/-3 + 4y/-3 +3z/-3

x= -22 +4y + 3z/3

9514 1404 393

Answer:

  (x, y) = (1, -3)

Step-by-step explanation:

The x-term has a coefficient of 1 in the first equation, making it easy to write and expression that can be substituted for x:

  x = -3y -8

Using this in the second equation, we have ...

  4(-3y -8) -3y = 13

  -15y -32 = 13

  -45 = 15y

  -3 = y

Then the value of x is ...

  x = -3(-3) -8 = 1

The solution is (x, y) = (1, -3).

Answer:

Step-by-step explanation:

Area = [tex]Area = \pi r^2 = \pi(3)^2 = 9\pi = 28.27\\Circumference = 2\pi r = 2\pi 3 = 6\pi = 18.85[/tex]

Answer:

[tex]area = 28.27 {m}^{2} \\ c = 18.84m[/tex]

Explanation is attached to the picture

Hope this helps you.

Answer:

The function is as follows:

def count_bases(DNA_str):

   retDNA = {}

   for i in DNA_str:

       if i in retDNA:

           retDNA[i]+=1

       else:

           retDNA[i] = 1

   return retDNA

Step-by-step explanation:

This defines the function

def count_bases(DNA_str):

This initializes a dictionary

   retDNA = {}

This iterates through the dictionary

   for i in DNA_str:

If an item exists in the dictionary

       if i in retDNA:

The count is updated by 1

           retDNA[i]+=1

Otherwise

       else:

The count is set to 1

           retDNA[i] = 1

This returns the DAN

   return retDNA

Answer:

Choose 1 ball from a bag with 1 red ball and 4 white balls. Record the color, replace the ball and repeat the experiment 20 times.

Step-by-step explanation:

Given

[tex]Cups = 5[/tex]

[tex]Ball=1[/tex]

[tex]Trials = 20[/tex]

See attachment

Required

Simulate the above experiment (fill in the gaps)

The probability of choosing a ball correctly in each trial are independent, and each probability is calculated as:

[tex]P(Correct) = \frac{Ball}{Cups}[/tex]

This gives:

[tex]P(Correct) = \frac{1}{5}[/tex]

The number of times (i.e. 6) he chose correctly is not a factor in his simulation

So, a correct simulation of the experiment is as follows:

Choose 1 ball from a bag with 1 red ball and 4 white balls. Record the color, replace the ball and repeat the experiment 20 times.

The selected ball represents the number of balls hidden (i.e. 1 ball).

The total number of balls (5 balls; i.e. 1 red and 4 white) represent the number of cups (5 cups)

The 20 times represent the number of times the experiment is repeated.

Answer:

The x-intercept is the value of the variable x when the value of the function is equal to zero

so

In the table we have

(-1, 0)(−1,0) is a x-intercept, because

For x=-1x=−1 the value of the function is equal to zero

(-6, 0)(−6,0) is a x-intercept, because

For x=-6x=−6 the value of the function is equal to zero

therefore

the answer is

the continuous function in the table has two x-intercepts

(-1, 0)(−1,0)

(-6, 0)(−6,0)

Answer:

L = 295ft

W = 95ft

Step-by-step explanation:

Perimeter of a rectangle = 2(L+W)

If the length is 200 ft more than the width, then:

L = 200+W

Substitute

P = 2(200+W+W)

780 = 2(200+2W)

780 = 400+4W

4W = 780-400

4w = 380

W = 380/4

W = 95ft

Since L = 200+w

L = 200+95

L = 295ft

Answer:

45 miles in 1 hour

Step-by-step explanation:

1 hour is 60 minutes

22.5 miles / 30 minutes  * 2/2 = 45 miles / 60 minutes = 45 miles in 1 hour

Answer:

He drove 22.5 miles in 60 min. He drove 45 miles in 1 hour

Step-by-step explanation:

22.5 miles in 30 min

1 hour= 60 min

30+30=60

22.5+22.5=45 miles

The number of times that the band played an encore at 7 out of the next 14 shows.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The band should do an encore at a rate of 2 out of every 4 gigs, or 2/4 = 1/2 shows, according to the available statistics.

We may use the following percentage to determine how many of the following 14 performances will likely have an encore:

1/2 = x/14

14 = 2x

x = 7

Therefore, we can expect the band to play an encore at 7 out of the next 14 shows.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

Answer:

Surface area = 850 cm²

Volume = 1000 cm³

Step-by-step explanation:

Applying,

A = h(a+b+c+d)................ Equation 1

Where A = Surface area of the trapezoidal prism, a, b, c, d = length of the four sides the trapezium respectively, h = height of the prism.

From the diagram in the question,

Given: h = 25 cm, a = 6 cm, b = 14 cm, c = 7 cm, d = 7 cm

Substitute these values into equation 1

A = 25(6+14+7+7)

A = 25(34)

A = 850 cm²

From the volume,

V = A'h...................... Equation 2

Where A' = Area of the base.

From the diagram,

A' = 1/2(6+14)4

A' = 40 cm²

Therefore,

V = 40×25

V = 1000 cm³