Which term describes a geometric statement that is assumed to be true without proof?

The arithmetic series can be written in summation notation as:

∑_{i=1}⁶ 5i = 5 + 10 + 15 + 20 + 25 + 30 = 105.

What is arithmetic series?

The sum of a series in which each term is computed from the preceding one by adding and subtracting constants is known as an arithmetic series. Alternately, we could say that an arithmetic progression is a set of numbers where, for every pair of successive terms, the second number is obtained by adding a fixed amount to the first.

The common difference in this arithmetic series is 10 - 5 = 5. Therefore, the nth term of the series is given by a_n = 5n.

The first term of the series is 5, which corresponds to n = 1. The last term is 30, which corresponds to n = 6.

The sum of an arithmetic series can be calculated using the formula: S_n = (n/2)(a_1 + a_n), where S_n is the sum of the first n terms, a_1 is the first term, and a_n is the nth term.

Substituting the values of a_1, a_n, and n, we get:

S_6 = (6/2)(5 + 30) = 3(35) = 105

Therefore, the arithmetic series can be written in summation notation as:

∑_{i=1}⁶ 5i = 5 + 10 + 15 + 20 + 25 + 30 = 105.

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As per the given domain and the range, the relation {(-2, 9), (4, 10), (8, 10), (27, 11)} is a function.

Domain and range:

Basically, domain of a function is the set of values that we are allowed to plug into our function where as the range of a function is the set of values that the function assumes.

Given,

function g has a domain of {-2, 4, 8, 27} and the range of {9, 10, 11).

Here we need to find that could g be represented by {(-2, 9), (4, 10), (8, 10), (27, 11)}.

We know that the function means the relation that has two sets and from a set X to a set Y assigns to each element of X exactly one element of Y.

Based on this fact we have to verify that the given relation,

Here in the given relation,

=> {(-2, 9), (4, 10), (8, 10), (27, 11)}.

Each domain value has only one range value.

So, this relation is a function.

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The graph the represents the function f(x) = 3.5ˣ is attached below.

Function:

Basically, the function refers the a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given,

Here we have to find the graph for the function f(x) = 3.5ˣ from the given options.

In order to plot the graph for the function,

We need a table.

The table can derived by applying the sample values.

So, here we have to take the value of x is -2, -2, 0, 1, 2,

Then we get the following table.

And then by using the table, we have to plot the graph like the following.

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Answer:

2*(10^4)

Step-by-step explanation:

Answer:

Expectancy theory

Step-by-step explanation:

We are told that as long as he receives C grades or better, he maintains his current grade point average.

This means that;

There is a large tendency for him to work just hard enough to earn a c grade.

This depicts vrooms expectancy theory of motivation which is defined as a theory whereby a person or persons will act in a particular way just for the sake of what they will gain from exhibiting that particular selected behavior instead of others.

The probability that the first card will be red and the second card will be blue is 4% .

Given: five different colored cards  (red, blue, green, yellow, and black)

First, for any of the five cards being drawn, there is a 1/5 chance, or 20%. So, the probability of a red card being drawn is 1/5. Then, since the card is replaced, it becomes a 1/5, or 20%, chance of any card being drawn (besides red). So, the probability of a blue card being drawn is 1/5.

So , according to the question is asking,

the probability that the first card will be red and the second card will be blue = 1/5 x 1/5 = 1/25

1/25 = 4%

Hence , the probability that the first card will be red and the second card will be blue is 4% .

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Answer:

Step-by-step explanation:

the probability is 4%.

False. The Six Sigma DMAIC approach is a problem-solving methodology used to improve processes and reduce defects, but it is not the only tool available.

Sigma is a statistical measure of dispersion, which is used to measure the variability or spread of a given data set. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. Sigma is commonly used in data analysis and is used to identify outliers and other patterns in data sets.

Depending on the nature of the problem, other problem-solving techniques may be more appropriate. For example, if the goal is to improve customer service, a method such as Lean Six Sigma, which focuses on customer value, may be more effective. Similarly, if the goal is to create new products or services, a design thinking approach could be used. In any case, it is important to assess the situation and choose the best course of action for the specific problem.

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Answer:

b = 5

Step-by-step explanation:

given m = - \(\frac{1}{6}\) , then

y = - \(\frac{1}{6}\) x + b ← is the partial equation

to find b substitute either of the 2 points into the partial equation

using (12, 3 ) , then

3 = - \(\frac{1}{6}\) (12) + b = - 2 + b ( add 2 to both sides )

5 = b

Answer:

78 is the answer

Step-by-step explanation:

because 1 =1

Answer:

Height = 11 inches

Base = 33 inches

Step-by-step explanation:

In this question, we are asked to find the height and base of a parallelogram given the area of the parallelogram.

From the question, we are told that height is 1/3 of base. This means that base is 3 times the height

So if we represent the height with variable h, then the base is 3h

Mathematically the area of a parallelogram can be calculated by the formula

A = bh

Thus ,

363 = h * 3h

3h^2 = 363

divide through by 3

h^2 = 121

h = √121

h = 11 inches

since b = 3h , then b = 3 * 11 = 33 inches

Answer:

a^2 + b^2 = c^2

a^2 + 24^2 = 25^2

a=7

Step-by-step explanation:

The distance between the given points will be 13 square units.

A triangle may be defined as a closed figure having three sides and three interior angles. A right triangle may be defined as a triangle which has one interior angle as 90°. The right triangle consists of a base, an altitude and a hypotenuse. We have the coordinates of the hypotenuse as (-1, 9) and (4, -3). If we plot these points on graph paper, we get the other point as (-1, -3). Also, the distance between the points (-1. 9) and (4, -3) is given by

Distance = √(-3 - 9)² + (4 + 1)²

Distance = √(-12)² + (5)²

Distance = √144 + 25

Distance = √169

Distance = 13 square units.

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Answer:

One

Step-by-step explanation:

6=2(y+2)

Distribute 2

6=2y+4

-4    -4

2=2y

______

2

y=1

Answer:

y = 1

Step-by-step explanation:

First, you need to use the distributive property to simplify:

6 = 2y + 4

Then, subtract 4 from both sides, so you get the numbers on one side and the variables on the other.

2 = 2y

Divide both sides by 2, and . . .

y = 1

Answer: Choice A)   \(9x^2+15x-6\)

=================================================

Work Shown:

\(f(x) = x^2+7x\\\\f(x) = (x)^2+7(x)\\\\f(g(x)) = (g(x))^2+7(g(x)) \ \ \text{ ... replace each x with g(x)}\\\\f(g(x)) = (3x-1)^2+7(3x-1) \ \ \text{ ... plug in } g(x) = 3x-1\\\\f(g(x)) = (3x-1)(3x-1)+7(3x-1)\\\\f(g(x)) = 3x(3x-1)-1(3x-1)+7(3x-1)\\\\f(g(x)) = 9x^2-3x-3x+1+21x-7\\\\f(g(x)) = 9x^2+15x-6\\\\(f \circ g)(x) = 9x^2+15x-6\\\\\)

Answer:

I think the answer is srry if I'm wrong but it's 22 or 42

Step-by-step explanation:

ur welcome srry if I got it wrong

Answer:

D) 408

E) 684

F) 377

Step-by-step explanation:

In these problems, we can simplify the multiplication using these steps:

1. split each number into a tens and ones place

2. multiply each place of the bottom number by both places of the top number (but remember that a digit in the tens place has a zero after it)

3. add the resulting values

D) First, we can split each number into a tens and ones place:

17 = 10 and 7

24 = 20 and 4

Next, we can multiply each digit of the bottom number by both digits of the top number:

(4 × 7)

(4 × 10)

(20 × 7)

(20 × 10)

Finally, we can add all of these values:

(4 × 7) + (4 × 10) + (20 × 7) + (20 × 10)

= 28   +     40    +     140    +     200

= 408

E)

36 = 30 and 6

19 = 10 and 9

Multiplying the places:

(9 × 6)

(9 × 30)

(10 × 6)

(10 × 30)

Adding these values:

(9 × 6) + (9 × 30) + (10 × 6) + (10 × 30)

= 54    +    270    +    60     +    300

= 684

F)

29 = 20 and 9

13 = 10 and 3

Multiplying the places:

(3 × 9)

(3 × 20)

(10 × 9)

(10 × 20)

Adding these values:

(3 × 9) + (3 × 20) + (10 × 9) + (10 × 20)

= 27    +    60      +     90    +    200

= 377

The first-order necessary conditions for the given NLP problem involve the KKT conditions, and a specific solution satisfying these conditions needs further analysis.

(a) The first-order necessary conditions for constrained optimization problems are defined by the KKT conditions. These conditions require that the gradient of the objective function be orthogonal to the feasible region, the constraints be satisfied, and the Lagrange multipliers be non-negative.

(b) Assuming the first Lagrangian multiplier constraint is active means that it holds with equality, while the second one is inactive implies that it does not affect the solution. By incorporating these assumptions into the KKT conditions and solving the resulting equations along with the given constraints, a solution can be obtained.

(c) To determine if the solution satisfies the first-order necessary conditions, one needs to verify if the obtained values satisfy the KKT conditions. This involves checking if the gradient of the objective function is orthogonal to the feasible region, if the constraints are satisfied, and if the Lagrange multipliers are non-negative. Only by performing this analysis can it be determined if the solution satisfies the first-order necessary conditions.

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The rate of Epinephrine drip is37.03 mcg/hr, 2.96 ml/hr, 39.08 mcg/hr, 11.84 ml/hr.

To calculate the rate of Epinephrine drip in mcg/hr, we start with the given rate of 0.07 mcg/kg/min and multiply it by the patient's weight of 74 kg to get 5.18 mcg/min.

We then convert this to mcg/hr by multiplying by 60, resulting in a rate of 310.8 mcg/hr.

To calculate the rate in ml/hr, we consider the concentration of the Epinephrine drip. Using the standard concentration of 2 mg/250 ml, we can convert the rate in mcg/hr to ml/hr by dividing the rate (310.8 mcg/hr) by the concentration (2 mg/250 ml) and then multiplying by 250 ml. This gives us a rate of 2.96 ml/hr.

If the rate is increased by 0.04 mcg/kg/min, we can simply add this increment to the initial rate of 0.07 mcg/kg/min to get the new rate of 0.11 mcg/kg/min. Following the same calculations as before, the new rate in mcg/hr would be 39.08 mcg/hr.

Lastly, if we consider the maximum concentration of 8 mg/250 ml, we can calculate the rate in ml/hr by dividing the new rate in mcg/hr (39.08 mcg/hr) by the concentration (8 mg/250 ml) and then multiplying by 250 ml. This gives us a rate of 11.84 ml/hr.

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Answer:

{ 0, 3, - 3 }

Step-by-step explanation:

f(x) = x(2x - 3)(x + 3)

to find the zeros let f(x) = 0 , that is

x(2x - 3)(x + 3) = 0

equate each factor to zero and solve for x

x = 0

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = \(\frac{3}{2}\)

x + 3 = 0 ⇒ x = - 3

zeros are { 0, \(\frac{3}{2}\) , - 3 }

Answer:

504

Step-by-step explanation:

40%=.40

360*.40=144

original number + increase = x

360+144=504

Answer:

in my opinion you should wear black velvet skinny jeans with oversized rose top and lightly curled hair

Step-by-step explanation:

that is in my opinion

Answer:

8% interest rate

Step-by-step explanation:

step-by-step explanation: intrest = 484

Answer:

a.) Domain: all numbers from 0 to 170   and   d. Range: all numbers from 0 to 60

Step-by-step explanation:

The domain is all of the numbers that the graph is on, over the x-axis. Looking at the x-axis, the graph only spans across 0-170, so the answer would be   a.) Domain: all numbers from 0 to 170.

The range is all of the numbers that the graph is on, over the y-axis. Looking at the y-axis, the graph only spans across 0-60, so the answer would be   d. Range: all numbers from 0 to 60.

The probability is 1/3.

Probability is sincerely how likely something is to show up. whenever we're unsure about the final results of an event, we will communicate about the probabilities of positive consequences—how probably they're. The evaluation of events governed by way of possibility is called information.

Probability is the branch of mathematics concerning numerical descriptions of ways likely an occasion is to arise, or how in all likelihood it's far that a proposition is actual. The opportunity of an event is more than a few among 0 and 1, wherein, kind of talking, zero suggests impossibility of the occasion and 1 shows the truth.

Chance = the wide variety of approaches to achieving achievement. the whole range of viable consequences. as an example, the opportunity of flipping a coin and its being heads are ½ because there may be 1 manner of getting a head and the overall wide variety of feasible results is two (a head or tail). We write P(heads) = ½.

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Answer:=−7

no problem!

Answer:

x= -7

Step-by-step explanation:

3x+15=-2x-20

Step 1 move the variable (x)  to the left hand and change its sign

3x+2x+15=-20

Move the constant (15) and change it's sign

3x+2x=-20-15

5x=-20-15

5x=-35

Divide both sides by 5

x= -7

Answer: the answer would be -7/2

hope this helps :)

Answer:

the cost per liter of the paint is equal to 24 8/liter

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