Write an explicit formula for a_na n ​ , the n^{\text{th}}n th term of the sequence 34, 26, 18, ...34,26,18

Answer:

$19.43

Step-by-step explanation:

when 5.5 pounds cost $14.74 then 1 pound costs $2.68

because 14.74 divided by 5.5 equals 2.68

To calculate the price of 7.25 you multiply the price for 1 pund by 7.25

7.25 * 2.68 = 19.43

To find the coefficient of the z⁴q¹² term in the expansion of (2z+q)¹⁶, we can use the binomial formula. The coefficient can be determined by applying the formula and identifying the appropriate combination of terms.

The binomial formula, also known as the binomial theorem, allows us to expand the expression (2z+q)¹⁶. The formula states that for any positive integer n, the expansion of (a+b)ⁿ can be represented as the sum of terms with coefficients determined by the combination formula.

In this case, we are interested in the term with z⁴q¹². The binomial formula is given by: (a+b)ⁿ = C(n, k) * a^(n-k) * b^k, where C(n, k) represents the combination of choosing k terms from a set of n terms.

For the term with z⁴q¹², we need to find the coefficient C(16, k) where k represents the power of q. Since we want q¹², we set k = 12. Plugging these values into the binomial formula, we can calculate the coefficient of the desired term.

To learn more about binomial formula click here:

brainly.com/question/30100288

#SPJ11

Answer:

4^8

Step-by-step explanation:

If you are multiplying two bases that are the same with different exponents, the exponents get added and the base stays the same:

\(x^a*x^b=x^{a+b}\\\\4^3*4^5=4^{3+5}\\\\4^3*4^5=4^8\)

Therefore, 4^3 * 4^5 = 4^8

Lexi, this is the solution:

1. The line AB is dividing the angles: all the angles above AB add up to 180 degrees, and all the angles below AB also add up to 180 degrees.

2. Angles FED and CEG are vertical angles, because they are opposite to each other when two lines cross, and they are equal. Therefore, FED = CEG and both measure 130 degrees.

3. Angles DEB and AEC are also vertical angles. Therefore, DEB = AEC and both measure 20 degrees.

4. Now, we can solve for x. As you can see in the graph, x is the sum of angles AEC and CEG, therefore, x = AEC + CEG.

x = AEC + CEG

x = 20 + 130

x = 150 degrees :=)

To determine the number of gallons of paint needed to cover office 143, we need to know the square footage of the office.

Once we have that information, we can divide the square footage by the coverage rate per gallon to calculate the required amount of paint.

Let's assume the square footage of office 143 is 800 square feet.

Number of gallons needed = Square footage / Coverage rate per gallon

Number of gallons needed = 800 square feet / 50 square feet per gallon

Number of gallons needed = 16 gallons

Therefore, you would need approximately 16 gallons of paint to cover office 143, assuming each gallon covers 50 square feet.

Learn more about square feet here : brainly.com/question/30678567

#SPJ11

Zeros of numerator

Zeros of denominator

Option A

Answer:

\(p\leq 56\)

Step-by-step explanation:

Plz mark brainliest!

The ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is (2, -1).

option C.

The ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is determined as follows;

The four points include;

A = (1, 2)

B = (2, - 3)

C = (-2, - 2)

D = (-3,  1)

The  ordered pair that can be plotted together with these four points, must fall withing these coordinates. Going by this condition we can see that the only option that meet this criteria is;

(2, - 1)

Thus, the ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is (2, -1).

Learn more about ordered pairs here: https://brainly.com/question/30467126

#SPJ1

Working in certain industries or environments can lead to various injuries, including sprains, muscle pains, severe fatigue, falls, burns, chemical exposure, machinery malfunctions, and even explosions.

In certain industries or work environments, employees may face a higher risk of injuries due to the nature of their tasks and the surrounding conditions.

Severe fatigue is another concern, especially in occupations that involve long hours or physically demanding work. Fatigue can impair judgment and coordination, increasing the likelihood of accidents and injuries

Additional injuries can result from falls, which can happen due to slippery surfaces, uneven ground, or inadequate safety precautions. Burns may occur when working with hot objects, open flames, or chemicals without proper protective measures. Chemical exposure can lead to injuries ranging from skin irritation to more severe health issues.

Machinery malfunctions pose a significant risk, especially if safety features are not in place or not properly maintained. Accidents involving machinery can cause serious injuries, such as fractures, amputations, or even fatalities. In some cases, explosions may occur in work environments where hazardous materials or volatile substances are present.

To know more about workplace injuries, visit:
brainly.com/question/31184578
#SPJ11

Answer:

1 1/4

Step-by-step explanation:

(7) The volume of the square base pyramid is 122.5 in³.

(8) The volume of the equilateral base pyramid is 311.8 cm².

(9)  The volume of the square base pyramid is 2,880 ft³.

The volume of the pyramids is calculated by applying the following formula as follows;

(7) The volume of the square base pyramid is calculated as;

V = ¹/₃Bh

where;

V = ¹/₃ x (7 in x 7 in ) x 7.5 in

V = 122.5 in³

(8) The volume of the equilateral base pyramid is calculated as;

V = ¹/₃Bh

V = ¹/₃ x (a²√3/4) x h

V =  ¹/₃ x (12²√3/4) x 15

V = 311.8 cm²

(9)  The volume of the square base pyramid is calculated as;

V = ¹/₃Bh

where;

V = ¹/₃ x (24 ft x 24 ft ) x 15 ft

V = 2,880 ft³

Learn more about volume of pyramid here: https://brainly.com/question/21510592

#SPJ1

Answer:

d

Step-by-step explanation:

the corresponding angles are described by 2 parallel lines and a line that cross them all

The opposite side of the right triangle (x) is approximately 6.888 inches long.

To solve this problem, we can use the trigonometric ratio for the sine function, which is opposite/hypotenuse. We have the hypotenuse as 12 inches and the opposite angle as 35 degrees, so we can set up the equation:

sin(35) = opposite/12

To solve for the opposite, we can multiply both sides by 12:

opposite = 12 * sin(35)

sin(35) as approximately 0.574:

opposite = 12 * 0.574

opposite ≈ 6.888

Therefore, the opposite side of the right triangle (x) is approximately 6.888 inches long.

More on right-angle triangles can be found here: https://brainly.com/question/3772264

#SPJ1

Convert the inequality to interval notation: a > 10:

(10, ∞)

Answer:

56

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

got it from person above me have nice day

So, here we are to factor the polynomials :

\(\\ 1. \sf \qquad5a^2b^2 + 10ab +25a\\ \\\)

\( \longrightarrow\sf \qquad5a(ab^2 + 2b +5)\\ \\\)

\(\\ 2. \sf \qquad 8m^2n^2 - 24mn^3 +16mn\\ \\\)

\( \longrightarrow\sf \qquad 8mn(mn - 3n^2 +2)\\ \\\)

\(\\ 3. \sf \qquad 9xz^3 + 18yz^2 + 24z^2\\ \\\)

\(\longrightarrow \sf \qquad 3z(3xz^2 + 6yz+ 8z)\\ \\\)

\(\\ 4. \sf \qquad 16x^6y + 16x^2y^4 + 32x^3y^2\\ \\\)

\( \longrightarrow \sf \qquad 16 {x}^{2} y(x^4 + y^3 + 2xy)\\ \\\)

Some points to know :

The value of x that satisfies the equation is x = 15/8, which is equivalent to 1.875.

To solve the equation (2/3)x - (1/5)x = x - 1 and find the value of x, we can follow these steps:

Combine like terms on the left side of the equation:

(2/3 - 1/5)x = x - 1

Find a common denominator for the fractions on the left side. The common denominator for 3 and 5 is 15, so we rewrite the equation as:

(10/15 - 3/15)x = x - 1

Simplify the left side of the equation:

(7/15)x = x - 1

To eliminate the fraction, we can multiply both sides of the equation by the denominator of the fraction, which is 15:

15 * (7/15)x = 15 * (x - 1)

This simplifies to:

7x = 15x - 15

Subtract 15x from both sides of the equation to isolate the x term:

7x - 15x = -15

Simplifying further:

-8x = -15

Divide both sides of the equation by -8 to solve for x:

x = (-15) / (-8)

Simplifying the division:

x = 15/8

For more such question on equivalent . visit :

https://brainly.com/question/2972832

#SPJ8

Hi! I'd be happy to help you write the sum in sigma notation. Given the sum: 3 - 3x + 3x^2 - 3x^3 + , + (-1)^n * 3x^n, the sigma notation would be:

Σ[(-1)^k * 3x^k] from k=0 to n

Here's a step-by-step explanation:

1. Identify the pattern in the sum: It alternates between positive and negative terms, and each term has a power of x multiplied by 3.
2. Assign the variable k for the index of summation.
3. Determine the range of k: The sum starts with k=0 and goes up to k=n.
4. Represent the alternating sign using (-1)^k.
5. Combine all components to form the sigma notation: Σ[(-1)^k * 3x^k] from k=0 to n.

The sum can be written in sigma notation as:

\($\displaystyle\sum_{n=1}^\infty (-1)^n 3x^n$\)

The given series is:

\(3 - 3x + 3x^2 - 3x^3 + ...\)

To write it in sigma notation, we first notice that the terms alternate in sign, and each term is a power of x multiplied by a constant (-3). We can write the general term of the series as:

\((-1)^n * 3 * x^n\)

where n is the index of the term, starting from n = 0 for the first term.

Using sigma notation, we can express the sum of the series as:

\($\displaystyle\sum_{n=1}^\infty (-1)^n 3x^n$\)

where the summation is over all values of n starting from n = 0.

Learn more about sigma notation

brainly.com/question/27737241

#SPJ11

\(\large{\underline{\underline{\pmb{\sf{\color{yellow}{Answer:}}}}}}\)

The value of x is 3

Step-by-step explanation:

\( \textsf{\underline{\large{To find :-}}} \)

The value of x

\( \textsf{\underline{\large{Given :-}}} \)

4 : 9 = (5x + 13) : 63

\(\textsf{\underline{\underline{\large{Solution :-}}}} \)

we can write this as

\( \sf \frac{4}{9} = \frac{(5x + 13)}{63} \)

Now we will cross multiply the values

\( \sf 4 \times 63 = 9(5x + 13) \\ \\ \sf 252 = 45x + 117 \\ \\ \sf 252 - 117 = 45x \\ \\ \sf 135 = 45x \\ \\ \sf \frac{135}{45} = x \\ \\ \sf \orange {3 = x}\)

Answer:

7

Step-by-step explanation:

The annual economic order quantity for GM Electronics is approximately 240 alarm systems.

To calculate the annual economic order quantity (EOQ), we need the following information:

Expected monthly sales: 800 alarm systems

Selling price per alarm system: R4,000

Cost price per alarm system: R2,000

Inventory holding cost: 1% of the unit cost price

Cost of placing an order: R60

The formula to calculate EOQ is:

EOQ = √[(2 * Annual Demand * Cost per Order) / Holding Cost per Unit]

First, we need to calculate the annual demand:

Annual Demand = Monthly Sales * 12

Annual Demand = 800 * 12 = 9,600 alarm systems

Next, we can calculate the holding cost per unit:

Holding Cost per Unit = Unit Cost Price * Inventory Holding Cost

Holding Cost per Unit = R2,000 * 0.01 = R20

Now we can plug these values into the EOQ formula:

EOQ = √[(2 * 9,600 * 60) / 20]

EOQ = √(1,152,000 / 20)

EOQ = √57,600

EOQ ≈ 240 alarm systems

To know more about economic order refer to-

https://brainly.com/question/28347878

#SPJ11

The tree has 11 vertices with degree 1.

To find the number of vertices with degree 1 in a tree with degree sequence (6,6,6,6,4,...), we can use the Handshaking Lemma. This lemma states that the sum of all vertex degrees in a graph is twice the number of edges. In a tree, the number of edges is one less than the number of vertices, so we can write:

6+6+6+6+4+...+2+2+1+1 = 2n-1

where n is the number of vertices. Simplifying this equation gives:

n = (6+6+6+6+4+...+2+2+1+1+1)/2 + 1

The term inside the parentheses is the sum of all vertex degrees, which we know from the degree sequence. Plugging in the values and simplifying, we get:

n = 18

So the tree has 18 vertices. Since we know that the rest of the vertex degrees are either 2 or 1, we can subtract the six vertices with degree 6 and the one vertex with degree 4 to get:

18 - 6 - 1 = 11

For more about vertices:

https://brainly.com/question/31502059

#SPJ11

The given statement: The standard deviation is a resistant measure of spread is true.

Standard deviation is the measure of how spread out numbers are. It is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability. When data points are closely spaced from the mean, there is a little variation, and when they are far spaced from the mean, there is a large variation. The standard deviation determines how much the data deviate from the mean.

When outliers are included, resistant statistics don't change (or vary very little). Resistance does not imply that anything is immobile; that would be "immovable." It implies that your results could fluctuate a bit, but not much.

Learn more about Standard deviation:

https://brainly.com/question/8290584

#SPJ4

A) when the diameter of the balloon is 1.2 feet, the diameter is increasing at a rate of approximately 0.853 feet per minute .

B) when the top of the ladder is 12 feet above the ground, the foot of the ladder is moving away from the wall at a rate of approximately 0.8817 ft/s.

To find the rate at which the diameter of the balloon is increasing, we can use the relationship between the volume and the diameter of a sphere. The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. Since the diameter is twice the radius, we have d = 2r.

Given that the volume is increasing at a rate of 2.4 cubic feet per minute, we can differentiate the volume equation with respect to time t to find the rate of change of volume with respect to time:

dV/dt = (4/3)π(3r²)(dr/dt)

Since we are interested in finding the rate at which the diameter (d) is increasing, we substitute dr/dt with dd/dt:

dV/dt = (4/3)π(3r²)(dd/dt)

We also know that r = d/2, so we substitute it into the equation:

dV/dt = (4/3)π(3(d/2)²)(dd/dt)

= (4/3)π(3/4)d²(dd/dt)

= πd²(dd/dt)

Now we can substitute the given values: d = 1.2 ft and dV/dt = 2.4 ft³/min:

2.4 = π(1.2)²(dd/dt)

Solving for dd/dt, we have:

dd/dt = 2.4 / (π(1.2)²)

dd/dt ≈ 0.853 ft/min

Therefore, when the diameter of the balloon is 1.2 feet, the diameter is increasing at a rate of approximately 0.853 feet per minute.

For the second question, we can use similar reasoning. Let h represent the height of the ladder, x represent the distance from the foot of the ladder to the wall, and θ represent the angle between the ladder and the ground.

We have the equation:

x² + h² = 16²

Differentiating both sides with respect to time t, we get:

2x(dx/dt) + 2h(dh/dt) = 0

We are given that dx/dt = 2 ft/s and want to find dh/dt when h = 12 ft.

Using the Pythagorean theorem, we can find x when h = 12:

x² + 12² = 16²

x² + 144 = 256

x² = 256 - 144

x² = 112

x = √112 ≈ 10.58 ft

Substituting the values into the differentiation equation:

2(10.58)(2) + 2(12)(dh/dt) = 0

21.16 + 24(dh/dt) = 0

24(dh/dt) = -21.16

dh/dt = -21.16 / 24

dh/dt ≈ -0.8817 ft/s

Therefore, when the top of the ladder is 12 feet above the ground, the foot of the ladder is moving away from the wall at a rate of approximately 0.8817 ft/s.

To know more about diameter click here :

https://brainly.com/question/29844000

#SPJ4

The standard error of the mean 0.79

The margin of error  1.55

The standard error of the mean is one of the components of the margin of error.

The margin of error is the multiplication of standard error of the mean and critical value. Margin of error is denoted by E

sample size, n= 40,

Sample mean,   = 25 and

population standard deviation, \(\alpha\)= 5

\(SE_{x}\)

The standard error of the mean, \(SE_{x}\)

\(SE_{x}\) = \(\alpha\)/√n

\(SE_{x}\) = 5/√40

\(SE_{x}\) = 5/6.3246

\(SE_{x}\) = 0.79

We have to find the critical value  

\(\alpha\)/2 = 0.05/2 = 0.025 is ± 1.96

The margin of error, E

E =  \(Z_{\alpha /2 }\) * \(SE_{x}\)

E= 1.96×0.79

E= 1.55

The standard error of the mean 0.79

The margin of error  1.55

To know more about standard error visit brainly.com/question/29296846

#SPJ4

The following equation's linear components have no solutions.

Because they contain the same variable term on one side of the equation but distinct constant values on the other, 5-4x-7-10x=-8x-4-6x-10.

A linear polynomial over a field with zero coefficients can be used to create a linear equation. The answers to such an equation are the numbers that, when the unknowns are replaced, make the equality true.

This particular situation, in which the variable is accurately referred to as the unknown, is commonly referred to as a "linear equation."

In the case of two variables, each solution can be thought of as a point's Cartesian coordinates on the Euclidean plane. The answers to a linear equation result in a line.

Given is an equation that reads 5-4x-7-10x=-8x-4-6x-10 and 14x-2=14x-14.

A linear equation has no solutions if both sides of the equation have different constant values but the same variable term.

To know more about linear equation, visit:

https://brainly.com/question/21835898

#SPJ1

Answer:

A. (1,2,3,4,...)

Step-by-step explanation:

Becuase continous numbers are numbers that keep going forever going forward.

Answer:

a is countuse because of this (...) that means it keeps going

Step-by-step explanation:

In a basket holding 35 pieces of fruit with an apple-to-orange ratio of 2:5, there are 10 apples.

To find the number of apples in the basket, we need to determine the ratio of apples to the total number of fruit pieces.

Given that the ratio of apples to oranges is 2:5, we can calculate the total number of parts in the ratio as 2 + 5 = 7.

To find the number of apples, we divide the total number of fruit pieces (35) by the total number of parts (7) and multiply it by the number of parts representing apples (2):

Apples = (2/7) * 35 = 10.

Therefore, there are 10 apples in the basket of 35 pieces of fruit.

Learn more about Ratio:

brainly.com/question/13419413

#SPJ11