Use the Distributive Property to write each expression as an equivalent algebraic expression.

(7 + a)3

The sum of the first four terms of the arithmetic series 4+8+12+... is calculated using the sum formula for arithmetic series, resulting in a sum of 40.

The question seeks the expression for the sum of the first four terms of the arithmetic series 4+8+12+... To solve this, we utilize the formula for the sum of the first n terms of an arithmetic series, which is Sn = n/2 [2a + (n-1)d], where Sn is the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms.

For the series 4+8+12+..., the first term a = 4, the common difference d = 4, and the number of terms n = 4. Plugging these values into the formula gives us:

S4 = 4/2 [2(4) + (4-1)4] = 2 [8 + 12] = 2 × 20 = 40.

Therefore, the sum of the first four terms of the arithmetic series 4+8+12+... is 40.

This expression sums from [tex]\( (k-1)^4 \) to \( 4n \),[/tex] which doesn't represent the arithmetic series either.

None of the given expressions seem to represent the arithmetic series [tex]\(4 + 8 + 12 + ... \)[/tex] for four terms correctly.

An arithmetic series is a sequence of numbers in which the difference between any two consecutive terms is constant. In this case, the series given is:

[tex]\[ 4 + 8 + 12 + ... \][/tex]

The common difference between consecutive terms is (8 - 4 = 4).

The general formula for the sum of an arithmetic series is:

[tex]\[ S_n = \frac{n}{2}(a_1 + a_n) \][/tex]

Where:

[tex]- \( S_n \)[/tex] is the sum of the first ( n ) terms,

[tex]- \( a_1 \)[/tex]is the first term,

[tex]- \( a_n \) is the \( n \)[/tex]-th term.

To find the sum of the first four terms, we can use this formula.

Now, let's look at each option:

[tex]a. \( \sum\limits_{(a-1)^4}^{(2n+4)} \)[/tex]

[tex]b. \( \sum\limits_{(s=1)}^{4} (1+4n) \)[/tex]

[tex]c. \( \sum\limits_{(k=1)}^{4} (n+4) \)[/tex]

[tex]d. \( \sum\limits_{(k-1)^4}^{4n} \)[/tex]

We need to choose the expression that correctly represents the sum of the arithmetic series.

Using the formula for the sum of an arithmetic series, we have:

[tex]\[ a_1 = 4 \][/tex]

[tex]\[ a_n = 4 + (4 \times (n-1)) \][/tex](since the common difference is 4)

Now, let's plug these values into the formula:

[tex]\[ S_4 = \frac{4}{2}(4 + (4 + 4 \times (4-1))) \][/tex]

[tex]\[ S_4 = \frac{4}{2}(4 + 4 + 16) \][/tex]

[tex]\[ S_4 = \frac{4}{2}(24) \][/tex]

[tex]\[ S_4 = 2 \times 24 \][/tex]

[tex]\[ S_4 = 48 \][/tex]

So, the sum of the first four terms of the series is 48.

Now, let's see which expression correctly represents this sum.

a. [tex]\( \sum\limits_{(a-1)^4}^{(2n+4)} \)[/tex]

  - This expression doesn't seem to represent an arithmetic series.

b. [tex]\( \sum\limits_{(s=1)}^{4} (1+4n) \)[/tex]

  - This expression doesn't seem to represent an arithmetic series either.

c.[tex]\( \sum\limits_{(k=1)}^{4} (n+4) \)[/tex]

  - This expression sums[tex]\( n+4 \) for \( k = 1 \) to \( k = 4 \)[/tex], but it doesn't seem to correctly represent the arithmetic series.

d. [tex]\( \sum\limits_{(k-1)^4}^{4n} \)[/tex]

  - This expression sums from [tex]\( (k-1)^4 \) to \( 4n \),[/tex] which doesn't represent the arithmetic series either.

None of the given expressions seem to represent the arithmetic series [tex]\(4 + 8 + 12 + ... \)[/tex] for four terms correctly. If none of the options are correct, it's possible that there might be a typo or a mistake in the options provided.

2. Which expression defines the arithmetic series 4+8+12+.. for four terms? a.sumlimits _(a-1)^4(2n+4)

b.sumlimits _(s=1)^4(1+4n)

c.sumlimits _(k=1)^4(n+4)

d.sumlimits _(k-1)^44n

Answer:

Opposite sides of parallel are just like diagonal and the other diagonal going the other way.

Step-by-step explanation:

To show Lin's elevation at 3:00 p.m on a graph, mark a point below her starting altitude at 2:00 p.m, given that she was climbing downwards. The exact placement will depend on her descent rate, for which we have no data.

The question refers to Lin climbing downwards in the period from 2:00 p.m. to 3:00 p.m. In order to plot Lin's movement on a graph, we need to define the vertical axis as her altitude and the horizontal axis as time. Since Lin was moving downward, her altitude at 3:00 p.m. should be less than her altitude at 2:00 p.m.

For example, if she started at an altitude of 4,000 meters at 2:00 p.m., when adding a point to the graph at 3:00 p.m., it should be below the 4,000-meter altitude point, since Lin was descending. The exact point will depend on the speed of her descent, which we don't have information on, but it would be somewhere below the starting point.

It's similar to the thrown rock example where the rock rises and then falls. Lin, like the rock, started at a higher point (instead of airborne, she was high on a cliff or a hill), but then moved downwards, decreasing her altitude over time.

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The point is placed at -50 feet to represent a possible elevation halfway between 0 feet and -100 feet. However, it is important to note that her actual elevation could be anywhere within this range.

Assuming Lin started climbing from an elevation of 0 feet at 2:00 p.m., she could have reached a negative elevation at 3:00 p.m. This is because the graph shows that she was descending at a constant rate.

To determine her possible elevation, we need to consider the following:

The slope of the graph represents the rate of change in elevation. A negative slope indicates that Lin is descending.

The y-intercept of the graph represents Lin's elevation at 2:00 p.m. Since she started at 0 feet, the y-intercept is 0.

The time interval from 2:00 p.m. to 3:00 p.m. is one hour.

Using this information, we can determine that Lin's elevation at 3:00 p.m. could be anywhere from 0 feet to -100 feet. This is because the slope indicates that she is descending at a rate of -100 feet per hour.

Answer:

361x ÷ 19 = 19x

Answer:

18/x = 19

18=19x

Step-by-step explanation:

ANSWER

108°

EXPLANATION

The measure of each interior angle of a regular polygon is given by

[tex] \theta = \frac{(n - 2) \times 180}{n} [/tex]

where n refers to the number of sides of the polygon.

From the question we have n=5 in this case.

We substitute to obtain;

[tex]\theta = \frac{(5 - 2) \times 180}{5} [/tex]

[tex]\theta = \frac{3\times 36}{1} [/tex]

This simplifies to:

[tex]\theta = 108 \degree[/tex]

Hence each interior angles of a regular polygon with 5 - sides is 108°

Final answer:

To solve the equation 4x = -4r + 2d for x, isolate x by performing the same mathematical operations on both sides of the equation.

Explanation:

To solve the equation 4x = -4r + 2d for x, we need to isolate x on one side of the equation. We can do this by performing the same mathematical operations on both sides of the equation. Let's start by moving the terms containing r and d to the other side:

4x + 4r - 2d = 0

Next, we can factor out the common factor of 4:

4(x + r - 0.5d) = 0

Finally, we divide both sides of the equation by 4 to solve for x:

x + r - 0.5d = 0

The solution for x is x = -r + 0.5d.

Answer:

[tex]R^{2}=0.7744[/tex]

Step-by-step explanation:

r represents the correlation coefficient between two sets of data. It is a measure of the degree of association between the two sets of data and gives insight into the strength and direction of the relationship.

On the other hand, [tex]R^{2}[/tex] is the coefficient of determination for a given data set. It is a measure of the predictive power of a linear model.

Given r, [tex]R^{2}[/tex] is simply the square of r;

in this case we are given, r = 0.88. Therefore, [tex]R^{2}=0.88^{2}\\\\R^{2}=0.7744[/tex]

Answer:

A= 10.5

Step-by-step explanation:

Answer:10.5 yards

Step-by-step explanation:3 x 7 / 2

7776pi since the volume of a sphere can be found by V=4/3pi(r)^3

V=4/3pi(18)^3

V=7776pi

Answer:

[tex]\large\boxed{972\pi\ cm^3}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a sphere:}\\\\V=\dfrac{4}{3}\pi R^3\\\\R-radius\\\\\text{We have the diameter of the sphere.}\ D=18cm.\\\\D=2R\to R=\dfrac{18}{2}\ cm=9cm.\\\\\text{Substitute:}\\\\V=\dfrac{4}{3}\pi(9^3)=\dfrac{4}{3}\pi(729)=(4)\pi(243)=972\pi\ cm^3[/tex]

Answer:

C. 9

Step-by-step explanation:

Matrix is an arranged array of rows and columns. The number of rows are represented by m and number of columns by n. Hence the elements of matrix is denoted by small letter with it's row number and column number in subscript.

Like elements belonging to A matrix will be written as:

[tex]a_{mn}[/tex]

In the given matrix, we have to tell the element b_23 which means we have to point out the element in row 2 and column 3.

Looking at the matric we can see that the number at the position of 2nd row and third column is 9.

Hence Option C is the correct answer ..

Answer:

$15116.28

Step-by-step explanation:

Given data:

interest rate, r= 4%

time, t= 18 years

Final investment, A= $26000

Principle investment, P=?

As per the formula of interest

A= P (1+rt)

Putting the values:

26000= P(1+ 0.04(18))

P= 26000/(1+ 0.04(18))

P= 15116.28 !

The square root of f(x) is ±(x + 12) and the square root of g(x) is not defined.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable).

f(x) = x^2 + 24x + 144

f(x) = x^2 + 2(12)x + 12^2

f(x) = (x + 12)^2

Square root of f(x) is ±(x + 12)

g(x) = x^3 - 216

g(x) = (x - 6)(x^2 + 6x + 36)

Here, (x^2 + 6x + 36) does not have real roots hence it is not possible to find the square root of g(x).

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Answer:

[tex]\frac32 \pi[/tex]

Step-by-step explanation:

If you realize that the sin is actually the y coordinate of a (unit) circle when you travel around it, you will know that it is -1 when you are 3 quarters round, assuming you started at (1,0).

The circumference is measured in radians, where one round is 2π.

So 3/4 of 2π is 3/2 π.

In degrees, the answer is 3/4 of 360°, which is 270°.

Answer:

C

Step-by-step explanation:

Answer:

of the number is X, 16 = 1 + (2/10)×X - 8

Answer:

16 = [tex]\frac{6x}{5}[/tex] - 8

Step-by-step explanation:

Topic: One Unkown equation, mixed numbers

first we have to establish our variables, we only have one so we call

x = "a number"

and we start building our one unknown equation part by part by reading

"Sixteen is the same" means in math that "x ="

"one and two tenths"  1 [tex]^{2/10}[/tex]

this means we have (remember how to sum fractions?)

1 + 2 / 10 = 10/10 + 2/10 = 12/10 = 6/5

so " one and two tenths times a number added to negative 8" become [tex]\frac{6x}{5}[/tex] + (-8)

so we have our equation

16 = [tex]\frac{6x}{5}[/tex]  + (-8) or 16 = [tex]\frac{6x}{5}[/tex]  - 8

Answer:

y=36°

z=54°

Step-by-step explanation:

3y+2y -> 5y=180 y=36

90-36= 54

Answer:

[tex]\large\boxed{z=\dfrac{15\sqrt3}{2}}[/tex]

Step-by-step explanation:

We have the right triangle 30° - 60° - 90°. The sides are in ratio

1 : √3 : 2. Look at the picture.

[tex]15=2x\to2x=15[/tex]         divide both sides by 2

[tex]\dfrac{2x}{2}=\dfrac{15}{2}\\\\x=\dfrac{15}{2}[/tex]

[tex]z=x\sqrt3\to z=\dfrac{15}{2}\sqrt3=\dfrac{15\sqrt3}{2}[/tex]

Answer:

l = 65 – 15d; discrete

Step-by-step explanation:

15 is the centimeters he cuts off every day, you have to multiply that by D that´s the nomber of days, in order to calculate how much baguette does he have left.

If 4 days have passed, the anser would be 5 centimeters:

I=65- 15(4)= 65-60= 5

Answer:

[tex]l=65-15d[/tex]; discrete.

Step-by-step explanation:

Let d represent number of days.

We have been given that for lunch every afternoon, Diep cuts 15 centimeters of bread for his  sandwich. The length of loaf cut in d days would be [tex]15d[/tex].

Diep bought a baguette loaf of bread 65 centimeters long. The length of loaf of bread after d days would be initial length minus amount of loaf cut in d days that is:

[tex]65-15d[/tex]

Since [tex]l[/tex] represents length of bread, so our equation would be: [tex]l=65-15d[/tex]

Therefore, the expression [tex]l=65-15d[/tex] represents the given scenario.

The variable d represents number of days and days cannot be fractional. We can take only whole number of days, therefore, the graph of the equation would be discrete.

Answer:

-15

Step-by-step explanation:

(-2/7) = 5

(5/-8) = -3

5 x -3 = -15

Answer:

0.17 or 5/28

Explanation:

(-2/7)=-0.28

(5/-8)=-0.62

(-0.28)(5/-8)=0.17

Hello There!

To find the mean, add up all the numbers and divide according to how many numbers there are. The mean for this set would be "9"

To find the median, place the numbers in value order and find the middle. if there is no middle, add up the two numbers in middle and divide by 2. In this set, the median would be "8.5"

To find the mode or modal value, it is best to put the numbers in order. Then count how many of each number. A number that appears most often is the mode. In this set, there would be no mode.

The range of a set of data is the difference between the highest and lowest values in the set. In this set, the range would be "12"

heres your answer in a picture

The answer is:

According to the picture, the angle that the boat should head upstream is 19° north of west.

From the figure, we can see that there is a right triangle formed, and since we know its hypothenuse and its opposite side, we can use the following trigonometric relation:

[tex]Sin(\alpha)=\frac{opposite}{hypothenuse}[/tex]

We are given that:

[tex]opposite=6\\hypothenuse=18[/tex]

So, substituting and calculating, we have:

[tex]Sin(\alpha)=\frac{6}{18}[/tex]

[tex]Arcosin(Sin(\alpha))=Arcsin(\frac{6}{18})\\\\\alpha =19.47\°[/tex]

Therefore the angle that the boat should head upstream is 19°, but since speeds and direction and involved, we need to look for the direction, we can see that the vertical speed is due to north, and the horizontal speed is due to west, knowing that, we can conclude that the resultant speed will be due to north of west.

Hence,  according to the picture, the angle that the boat should head upstream is 19° north of west.

Have a nice day!

Answer:

20 and 56

Step-by-step explanation:

76/2 = 38

38 - 18 = 20

38 + 18 = 56

20 + 56 = 76

ANSWER

Quadrant IV

EXPLANATION

The given point have the x-coordinate to be positive and the y-coordinate to be negative.

In general, the point P(x,-y) lies in the fourth quadrant.

The reason is that, this quadrant contains the positive x-axis and the negative y-axis.

See attachment for diagram.

Answer: II and IV

Step-by-step explanation:

Answer:

Approximately  31.42

Step-by-step explanation:

You use the Distance Formula

d= √( x2 - x1 )^2 + ( y2 - y1 )^2

substitute

r=  √(3-3)^2 + (6-1)^2

    √0^2 + 5^2

r = √25

r = 5

Now you can use the equation for  finding the circumference

2πr

2π5

≈ 31.42

Answer:

p=m/v

v=9 x 4 x 4=144cm

m=1267.2g

p=1267.2/144

p=8.8 g/cm^3

Answer:

8.8

Step-by-step explanation:

Density = Mass / Volume

Volume = 9 × 4 × 4  = 144

Mass = 1267.2

Density = 1267.2 / 144 = 8.8

Answer:

a. 84 students

b. 12

Step-by-step explanation:

a.

From the information given, we see that 7 out of 12 practice every day. Now we want to know how many (let it equal x) would we expect to practice everyday given there are total 144 martial artists?

we set up a ratio and cross multiply and solve for x:

[tex]\frac{7}{12}=\frac{x}{144}\\7*144=12*x\\1008=12x\\x=\frac{1008}{12}=84[/tex]

So 84 students practice everyday

b.

The sample size is a "proportion" of the whole population. Here, there are a total of 144 martial artists. And we took 12 of them to figure out how many practice everyday (from these 12). So , clearly, the sample size is 12

14 + 7 + 10 = 31 marbles total

7/31 = 0.23 or 23%

The probability of drawing a black marble from a bag containing 14 gray, 7 black, and 10 white marbles is 7/31, which, as a decimal rounded to the nearest hundredth, is 0.23.

The theoretical probability of drawing a black marble from a bag containing 14 gray, 7 black, and 10 white marbles can be calculated by dividing the number of black marbles by the total number of marbles in the bag.

To find the total number of marbles, we add up the counts for each color: 14 gray + 7 black + 10 white = 31 marbles in total.

Next, we calculate the probability by taking the number of black marbles and dividing it by the total number of marbles: Probability = (Number of black marbles) / (Total number of marbles) = 7 / 31.

Converting that probability into a decimal gives us approximately 0.2258. However, rounding this to the nearest hundredth, as asked in the question, gives us 0.23. So, the probability of drawing a black marble is 0.23.

Answer:

x<-1

Step-by-step explanation:

6x-3 <-9

Add 3 to each side

6x-3+3 <-9+3

6x < -6

Divide by 6

6x/6 < -6/6

x < -1

Answer:

x<-1

Step-by-step explanation:

6x-3<-9

Add 3

6x<-6

-6/6=-1

x<-1

5/8 paper chains used more than 2 containers but less than 2 3/4 containers of glitter.

To calculate the area Tia needs to waterproof, find the perimeter of the triangular base and multiply it by the height of the prism.

To find the area Tia will waterproof, we need to calculate the lateral surface area of the triangular prism. The lateral surface area is given by the formula:

Lateral Surface Area = Perimeter of Base × Height

First, find the perimeter of the triangular base by adding up the lengths of all three sides. Then, multiply this perimeter by the height of the prism. This will give you the area Tia needs to waterproof.

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To determine the area Tia needs to waterproof for her triangular prism tent with base dimensions 14 ft, 8 ft, and side lengths 8 ft, the total area is calculated as the sum of the areas of the two triangular bases.

To find the area that Tia needs to waterproof, we can calculate the surface area of the triangular prism. The formula for the surface area of a triangular prism is given by:

A = 2B + Ph

where:

- B is the area of the triangular base,

- P is the perimeter of the base, and

- h is the height of the prism.

First, calculate the area of one triangular base (either base 1 or base 2). The area B of a triangle is given by:

[tex]\[ B = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

For base 1:

[tex]\[ B_1 = \frac{1}{2} \times 14 \times 8 = 56 \, \text{ft}^2 \][/tex]

Now, find the perimeter P of the base, which is the sum of the three sides:

[tex]\[ P = \text{side}_1 + \text{side}_2 + \text{side}_3 \][/tex]

[tex]\[ P_1 = 8 + 8 + 14 = 30 \, \text{ft} \][/tex]

Now, substitute these values into the formula for the surface area:

[tex]\[ A_1 = 2 \times 56 + 30 \times h \][/tex]

Similarly, calculate the area [tex]\( A_2 \)[/tex] for base 2.

Tia needs to waterproof both bases, so the total area to be waterproofed is [tex]\( A_1 + A_2 \).[/tex]

Answer:

1: It's I think 2+2

2: If I got your accent right then it's 4

3: count 2 and 2 makes 4

4: YAYYY YOU GOT IT PRACTICE MORE

Step-by-step explanation:

PLZZZZ MARK BRAINLIST!! REALLY FUNNY QUESTION AND MADE MY DAY!!!