What is the 5th term of the sequence defined by f(n) = 3(n-3)

The system of equations as an augmented matrix is \(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

From the question, we have the following parameters that can be used in our computation:

x                  = 100

   -5m  - 7c  = 350

   -5m  - 9c  = 200

The above means that the variables in the system of equations are

x, m and c

So, we have the following representation

x    m     c        

1    0      0        100

0   -5    -7        350

0   -5    -9        200

When represented as an augmented matrix, we have

\(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

Hence, the augmented matrix is \(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

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Answer:

2

Step-by-step explanation:

If two people shared three hamburgers then each person would get one hamburger and a half. Since there are two people and three hamburgers, both people can get one hamburger and split the third. In decimal form, It would be 1.5

Answer:

The answer is 3 because 6÷2 which equal 3 which is represent the three hameburgers and 6÷2=3 because there would be 6 hamburgers to share between two people.

Answer:

The singers can finish first through fifth in 360360 ways.

Step-by-step explanation:

The order of the singers is important, because they are ranked by positions. So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

\(P_{(n,x)} = \frac{n!}{(n-x)!}\)

In this question:

Top five singers, from 15 finalists. So

\(P_{(15,5)} = \frac{15!}{(15-5)!} = 360360\)

The singers can finish first through fifth in 360360 ways.

Answer:

Step-by-step explanation:

Represent the equation as follows:

\(a * b = c\)

Where a,b and c are decimal numbers

To solve further, we make use of trial by error method

Let

\(a = 2.52\)

\(b = 0.6\)

Such that

\(2.5 * 0.6 = c\)

\(1.512 = c\)

\(c = 1.512\)

This set of digits do not follow the rule in the question

Let

\(a = 2.55\)

\(b = 1.6\)

\(2.55 * 1.6 = c\)

\(4.08 = c\)

\(c = 4.08\)

The result has only 2 non zeros (4 and 8)

Hence

\(2.55 * 1.6 = 4.08\) answers the question.

However, there are other set of numbers that can be used too

One of the equation which illustrates and meets the conditions given is :

First number, x = 1.25

First number, x = 1.25 Second number, y = 0.2

Result = first Number × second number

Result = 1.25 × 0.2

Result = 1.25 × 0.2 Result = 0.25

Evaluating the result : 0.25

Number of digits = 3

Non - zero digits = 2

There are several values of x and y which will satisfy the 3 conditions given.

Therefore, the product of the values 1.25 and 0.2 gives the required output.

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Enola needs to contribute $4,330.68 per month to the account.

Let's denote the monthly contribution as X.

The interest rate is 0.4% per month.

Since Enola plans to save for 3 years, the total number of months is:

= 3 * 12

= 36 months.

Using formula for compound interest: Future value = Present value * (1 + interest rate)^number of periods

We will plug values:

$5,000 = X * (1 + 0.004)^36

X = $5,000 / (1 + 0.004)^36

X = $5,000 / (1.004)^36

X = $4,330.68248

X = $4,330.68.

Answer:

35 mph

Step-by-step explanation:

time = distance / speed

210 miles and has an average of a certain speed

t = 210 / s

If the average speed had been 3mph more, he could have traveled 228 miles in the same length of time

t = 228 / (s + 3)

Set equal

210 / s = 228 / (s + 3)

Cross multiply

210s + 630 = 228s

Subtract 210s from both sides

630 = 18s

Divie both sides by 18

35 = s

35 mph

Sorry this took so long.....

Had to get some help from the internet

Have a great day!!!!!

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

To get the volume of a prims, we do the products of the base times its height.

Being a rectangular prims, the area of its base is the product of its dimesions, so the volume of a rectangular prism is simply the product of its three dimensions:

Since the volume is equal to 0.728 yd³, we have:

So, the measure of c is 0.4 yards.

Answer:

w independant a dependant

Step-by-step explanation:

The probability of getting at least 6 heads is3/256 or 0.0117

Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution.

Probability is a measure of how likely something is to occur. Calculating probability involves dividing the total number of outcomes by the number of possible ways an event may occur.

Given that,

A fair coin is tossed = 8 time.

We have to find the probability of getting at least 6 heads.

Since, the probability of getting head, when one coin is tossed = 1/2

And the probability of getting tale = 1/2  

The probability of getting head at least  6 times when coin is tossed 8 times can be given as,

The head can come 6 times, then probability = \((1/2)\x^{6} (1/2)\x^{2}\) =  (1/2)⁸

The head can come 7 times, then probability = (1/2)⁷(1/2) = (1/2)⁸

The head can come 8 times, then probability = (1/2)⁸

The probability of getting head at least 6 times

= (1/2)⁸ + (1/2)⁸ +  (1/2)⁸ = 3(1/2)⁸ = 3/256 = 0.0117

The probability of getting at least 6 heads is3/256 or 0.0117

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Answer:

45

Step-by-step explanation:

Mark me brainliest plzzz

Answer:

see explanation

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

a hexagon has 6 sides , then

sum = 180° × (6 - 2) = 180° × 4 = 720°

12

the polygon has 5 sides , so

sum = 180° × (5 - 2) = 180° × 3 = 540°

sum the interior angles and equate to 540

y + 90 + 120 + 90 + 110 = 540

y + 410 = 540 ( subtract 410 from both sides )

y = 130

13

the polygon has 7 sides , so

sum = 180° × (7 - 2) = 180° × 5 = 900°

sum the interior angles and equate to 900

p + 90 + 141 + 130 + 136 + 123 + 140 = 900

p + 760 = 900 ( subtract 760 from both sides )

p = 140

Answer:

Please attach a photo to this so I can better answer your question

Answer:

Step-by-step explanation:

Point: 10,-9

k=-2

y=-2x+b

So: 9, -7

8,-5

7,-3

6,-1

5,1

4,3

3,5

2,7

1,9

0,11

y=-2x+11

Answer:

y + 9 = - 2(x - 10)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - 2 and (a, b ) = (10, - 9 ) , then

y - (- 9) = - 2(x - 10) , that is

y + 9 = - 2(x - 10)

It will take 18.9 years for your investment to reach $1,500

From the question, we have the following parameters that can be used in our computation:

Initial deposit = 500 dollars

Rate of growth = 6% per year

The above implies that the growth follows an exponential path

An exponential function that represents a growth function is represented as

A(n) = a * (1 + r)ⁿ

Where

A(n) = value of investment after nth year

a = Initial deposit = 500

r = rate of growth = 6%

Substitute the known values in the above equation, so, we have the following representation

A(n) = 500 * (1 + 6%)ⁿ

Evaluate the sum

A(n) = 500 * 1.06ⁿ

When the investment is 1500 grams, we have

500 * 1.06ⁿ = 1500

Divide both sides by 500

1.06ⁿ = 3

So, we have

n = log(3)/log(1.06)

Evaluate

n = 18.9

Hence, the number of years is 18.9

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Answer:

The answer is actually 18.3 Years

Step-by-step explanation:

I got it correct on the test :D

The ball reached a maximum height of approximately 39 feet.

To find out how high the ball went, we'll first need to determine its initial velocity. We can use the following kinematic equation to do this:

y = y₀ + v₀t + (1/2)at²

where

Since the ball is in the air for 3 seconds, it takes half that time (1.5 seconds) to reach its maximum height, and another 1.5 seconds to fall back to the initial height. When the ball reaches its maximum height, its final velocity (v) will be 0. We can use another kinematic equation to find the initial velocity (v₀):

v = v₀ + at

where

Plugging in the values, we get:

0 = v₀ - (32.2 ft/s²)(1.5 s)

Solving for v₀, we find:

v₀ = (32.2 ft/s²)(1.5 s) = 48.3 ft/s

Now that we have the initial velocity, we can use the first kinematic equation to find the maximum height (y):

y = y₀ + v₀t + (1/2)at²

Plugging in the values, we get:

y = 3 ft + (48.3 ft/s)(1.5 s) - (1/2)(32.2 ft/s²)(1.5 s)²

y ≈ 3 ft + 72.45 ft - 36.225 ft

y ≈ 39.225 ft

To determine how the surface area of a rectangular prism changes when all dimensions are quadrupled, we need to compare the original surface area to the new surface area.

The original surface area of the rectangular prism is given by:

SA_original = 2lw + 2lh + 2wh

where l, w, and h represent the length, width, and height of the prism, respectively.

In this case, the dimensions of the original box are:

Length (l) = 3 ft

Width (w) = 6 ft

Height (h) = 5 ft

Substituting these values into the formula, we have:

SA_original = 2(3)(6) + 2(3)(5) + 2(6)(5)

            = 36 + 30 + 60

            = 126 square feet

Now, if we quadruple all the dimensions of the box, the new dimensions would be:

Length (l_new) = 4(3) = 12 ft

Width (w_new) = 4(6) = 24 ft

Height (h_new) = 4(5) = 20 ft

The new surface area of the enlarged box is given by:

SA_new = 2(l_new)(w_new) + 2(l_new)(h_new) + 2(w_new)(h_new)

       = 2(12)(24) + 2(12)(20) + 2(24)(20)

       = 576 + 480 + 960

       = 2016 square feet

Comparing the original surface area (SA_original = 126 sq ft) to the new surface area (SA_new = 2016 sq ft), we can see that SA_new is 16 times greater than SA_original.

Therefore, the correct answer is:

1. The new surface area would be 16 times the original surface area.

The value of m<RQS as required to be determined in the task content is; 70°.

It follows from the task content that the measure of angle RQS is to be determined as required.

Recall, the measure of the central angle subtended by an arc is twice that which it subtends at any point on the circumference.

Therefore, m<RPS = 2 • m<RQS.

m<RQS = 140°/2

m<RQS = 70°.

Ultimately, the measure of angle RQS are; 70°.

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Answer:
3/2

Step-by-step explanation:

the answer is 3/2 because you take the slope by using the equation y/x. I did this problem by starting prop the point (0,-6). I then counted for how many points I went up, how many did I go to the right or left. If it went to the right it’s positive, to the left it is negative. In this case it went to the right 2 times every time it went up 3. Meaning 3/2

An equation which you can use to represent the relationship shown in the table is y = 4.5x.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Based on the information provided in the table (see attachment), we can logically deduce the following data points on the line:

Points on x-axis = (4, 5).

Points on y-axis = (18.0, 22.5).

At point (4, 18.0), a linear equation of this line in slope-intercept form can be calculated by using the point-slope form as follows:

y - 18.0 = (22.5 - 18.0)/(5 - 4)(x - 4)

y - 18.0 = 4.5(x - 4)

y = 4.5x - 18 + 18.0

y = 4.5x.

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Answer:

C. y= -5/2x+8.

Step-by-step explanation:

if to substitute the given coordinates into every given equation, then option 'C' is correct only: 3= -5/2 *2+8 and -2= -5/2*4+8.

Answer:

y=-5/2x+8

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-2-3)/(4-2)

m=-5/2

y-y1=m(x-x1)

y-3=-5/2(x-2)

y=-5/2x+10/2+3

y=-5/2x+5+3

y=-5/2x+8

The 99% confidence interval for the true population mean backpack weight is approximately (68.15, 71.85) ounces, rounded to two decimal places.

To construct a 99% confidence interval for the true population mean backpack weight, we can use the formula:Confidence Interval = Sample Mean ± (Critical Value * Standard Deviation / √Sample Size).

Since the population standard deviation is known, we can use the z-distribution and find the critical value corresponding to a 99% confidence level. The critical value for a 99% confidence level is approximately 2.576.

Given that the sample mean weight is 70 ounces, the population standard deviation is 6.4 ounces, and the sample size is 48, we can calculate the confidence interval:

Confidence Interval = 70 ± (2.576 * 6.4 / √48).

Simplifying the expression, we get:

Confidence Interval ≈ 70 ± 1.855.

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Therefore, sin(0) = -√305/41 when 0 is an angle in quadrant IV.

Trigonometry is a branch of mathematics that deals with the study of relationships between the angles and sides of triangles. It is used to solve problems in many fields, including engineering, physics, astronomy, and architecture. Trigonometry involves the use of functions such as sine, cosine, and tangent to relate the angles and sides of a right triangle. It also includes the study of trigonometric identities, equations, and graphs, as well as applications of trigonometry in real-world situations.

Here,

If 0 is an angle in quadrant IV, then cosine is positive and sine is negative. We can use the Pythagorean identity to find the value of sin(0):

sin²(0) + cos²(0) = 1

sin²(0) = 1 - cos²(0)

sin(0) = -√(1 - cos²(0))

substituting the given value of cos(0):

sin(0) = -√(1 - (4√47/41)²)

sin(0) = -√(1 - (16*47/41))

sin(0) = -√(1 - 736/41)

sin(0) = -√(305/41)

sin(0) = -(√305)/√(41)

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To find the measure of the geometry-big circle, we need to sum up the measures of all the arcs around the circle.

We are given the following measures:

\(\sf\:m\angle AB = 56 \\\)

\(\sf\:m\angle BC = 59 \\\)

\(\sf\:m\angle CD = 63 \\\)

\(\sf\:m\angle DE = 63 \\\)

\(\sf\:m\angle EF = 31 \\\)

To find the measure of the geometry-big circle, we add up these measures:

\(\sf\:m\angle AB + m\angle BC + m\angle CD + m\angle DE + m\angle EF \\\)

Substituting the given values:

\(\sf\:56 + 59 + 63 + 63 + 31 \\\)

Simplifying the expression:

\(\sf\:272 \\\)

Therefore, the measure of the geometry-big circle is 272.

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♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

7. \((f+g)(x) = 6x - 2\)

8. \((f-g)(x) = 2x + 8\)

Step-by-step explanation:

We are given two function, f(x) and g(x).

We want to find their addition and their subtraction, and we do this combining like terms.

The functions are:

\(f(x) = 4x + 3\)

\(g(x) = 2x - 5\)

7. Find (f+9) (x)

\(4x + 3 + 2x - 5 = 4x + 2x + 3 - 5 = 6x - 2\)

So

\((f+g)(x) = 6x - 2\)

8. Find (f - g) (x)

\(4x + 3 - (2x - 5) = 4x + 3 - 2x + 5 = 4x - 2x + 3 + 5 = 2x + 8\)

So

\((f-g)(x) = 2x + 8\)

The expression 2y² - 2 + 4x - 2x + 3 - 2x + 5y² solved by collecting like terms is 7y² + 2x + 1

2y² - 2 + 4x - 2x + 3 - 2x + 5y²

= 2y ² + 5y² + 4x - 2x - 2 + 3

= 7y² + 2x + 1

Therefore, the expression 2y² - 2 + 4x - 2x + 3 - 2x + 5y² solved by collecting like terms is 7y² + 2x + 1

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