5. (08.01)
Given the arithmetic sequence an = 2 - 5(n + 1), what is the domain for n? (6 points)
All real numbers
All integers where n > 1
All
integers where n ≥ 2
All integers where n ≥ 1

The normal distribution curve, also known as the Gaussian distribution, is a symmetrical probability distribution that is characterized by a bell-shaped curve. It is commonly used to model random variables in various fields, with many data points concentrated around the mean.

Given data: d = 25 ± 0.05 mmo = 0.025 mm peak position of the curve is 0.01mm to the left of the center of the tolerance zone To draw a normal distribution curve, we use the formula

\(y = \frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{(x - \mu)^2}{2 \sigma^2}}\)

where σ is the standard deviation, μ is the mean and x is the given value. Now, let's calculate the values of μ, x, and σ:

Lower specification limit (LSL) = d - 0.05 = 24.95

Upper specification limit (USL) = d + 0.05 = 25.05

Mean (μ) = (USL + LSL)/2 = (25.05 + 24.95)/2

= 25σ

= 0.025

Peak position of the curve = (LSL + USL)/2 - 0.01 = 25 - 0.01 = 24.99

Now, substituting the values in the formula, we get:

\(y = \frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{(x - \mu)^2}{2 \sigma^2}}\)

To find the area of non-conforming products, we need to integrate the area under the curve from LSL to USL. We can use a calculator or a software program like Excel to find the area. The area comes out to be approximately 0.0668. This means that the percentage of non-conforming products is 6.68%.Therefore, the normal distribution curve is shown below:  Answer: 0.0668

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Answer:

C

Step-by-step explanation:

it is rise over run which means rise 1 over run 4

so the answer is 1/4

Using the two parallel line theorems we proved that ∠8 ≅ ∠4.

In the given question,

Given: f || g

Prove: ∠8 ≅ ∠4

We using given diagram in proving that ∠8 ≅ ∠4

Since f || g, by the Corresponding Angles Postulate which states that "When a transversal divides two parallel lines, the resulting angles are congruent." So

∠8≅∠6

Then by the Vertical Angles Theorem which states that "When two straight lines collide, two sets of linear pairs with identical angles are created."

∠6≅∠4

Then, by the Transitive Property of Congruence which states that "All shapes are congruent to one another if two shapes are congruent to the third shape."

∠8 ≅ ∠4

Hence, we proved that ∠8 ≅ ∠4.

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The reason for ∠8 ≅ ∠4 is alternate exterior angles

The question has to do with finding the proven with the given.

We have been given line f is parallel to line g.

We need to prove angle 8 is congruent to angle 4.

From given figure we observe that line f || line g and these parallel lines are intersected by a transversal.

And the angle 8 are angle 4 are alternate exterior angles.

We know that alternate exterior angles are congruent.

so, ∠8 ≅ ∠4

Therefore, the reason for ∠8 ≅ ∠4 is alternate exterior angles

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The value of x in triangle ABC is 10.

The midsegment theοrem, alsο knοwn as the midline theοrem οr midsegment οf a triangle theοrem, states that the segment cοnnecting the midpοints οf twο sides οf a triangle is parallel tο the third side and half its length.

Since DF is a midsegment οf triangle ABC, it is parallel tο AB and has a length equal tο half the length οf AB. Similarly, FG is a midsegment οf triangle BCD, sο it is parallel tο BC and has a length equal tο half the length οf BC. Finally, GD is a midsegment οf triangle ABD, sο it is parallel tο AD and has a length equal tο half the length οf AD.

Therefοre, we can write the fοllοwing equatiοns based οn the midsegment theοrem:

DF = BC/2 = BG = CG

FG = AC/2 = AD = CD

GD = AB/2 = FA = FB

Now, ∠CAB = ∠DAF

AB/2 = FA  so AB ≅ FA

AC/2 = AD so AC ≅ AD

Thus, ΔABC ≅ ΔAFD

And

CPCT

DF ≅  BC

DF = BC/2

2DF = BC

2DF = x

x = 2DF

x = 2(5)

x = 10

Thus, the value of x in triangle ABC is 10.

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Answer:

donknow

Step-by-step explanation:

Answer:thus the answer is 2

Step-by-step explanation:

Given

The Radius of a solid cylinder (r)=5cm

Height (h)=10cm

Hence

Total surface area =2πrh+2πr

2

=2πr(h+r)

=2π×5(10+5)

=π×10×15

=150πcm

2

Answer:

Yes every square is a rhombus, but not every rhombus is a square

Step-by-step explanation:

Answer:

x=9

Step-by-step explanation:

In a parallelogram, opposite angles are equal.

So that means

2(3x - 4) = x + 37

6x - 8 = x + 37

5x = 45

x = 9

Answer:

x+37=2(3x-4) opposite angle of the parallelogram are equal

x+37=6x-8

37+8=6x-x

45=5x

x=9

the measure of QRS=2(3×9-4)=46

Answer:

The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. For a quadratic function in standard form, y=ax2+bx+c , the axis of symmetry is a vertical line x=−b2a .

Step-by-step explanation:

Answer:

x=-b/2a

Step-by-step explanation:

axis of symmetry is the line that across the vertex from a parabola(ax^2+bx+c).

The expression to find vertex is -b/2a

Thus, x=-b/2a is a vertical line that across the vertex aka the axis of symmetry.

Answer:

Step-by-step explanation:

cost price x .60 = 80

80/.60 = 133.33 was the cost price

Answer:

the answer is 21

because

rt=rs+st

13+8=21

Answer:

To simplify the expression (-3+1)+(-4-i), we can perform the addition operation within the parentheses first:

(-3+1)+(-4-i) = -2 + (-4-i)

Next, we can simplify the addition of -2 and -4 by adding their numerical values:

-2 + (-4-i) = -6 - i

Therefore, (-3+1)+(-4-i) simplifies to -6-i.

Step-by-step explanation:

An = -54 + 6n - 6

An = -60 + 6n

To find the first term and the common difference of an arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:

An = A1 + (n-1)d

where An is the nth term, A1 is the first term, n is the position of the term in the sequence, and d is the common difference.

Given that the 7th term is -18, we can substitute n = 7 and An = -18 into the formula:

-18 = A1 + (7-1)d

Simplifying further:

-18 = A1 + 6d

This gives us equation 1.

Similarly, given that the 16th term is 36, we can substitute n = 16 and An = 36 into the formula:

36 = A1 + (16-1)d

Simplifying further:

36 = A1 + 15d

This gives us equation 2.

We now have a system of two equations:

Equation 1: -18 = A1 + 6d

Equation 2: 36 = A1 + 15d

To solve this system, we can subtract equation 1 from equation 2 to eliminate A1:

36 - (-18) = (A1 + 15d) - (A1 + 6d)

54 = 9d

Dividing both sides by 9, we get:

d = 6

Substituting this value of d back into equation 1, we can solve for A1:

-18 = A1 + 6(6)

-18 = A1 + 36

A1 = -54

Therefore, the first term of the sequence is -54 and the common difference is 6.

The recursive formula for the sequence is:

An = An-1 + 6

The formula for the nth term is:

An = -54 + 6(n-1)

Simplifying further:

An = -54 + 6n - 6

An = -60 + 6n

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Answer:

106

Step-by-step explanation:

180-42-32=

x

Answer:

5 is c 6 is b

Step-by-step explanation:

Answer:

5) C 6) B

Step-by-step explanation:

Yw

Answer:

It should be about 0.1 cups of strawberries to every muffin

Step-by-step explanation:

Answer:  about 15

Step-by-step explanation:

Answer:

15 is the answer

Step-by-step explanation:

Answer:

80-55=25

then

25/2=12.5

he can bye 12.5 balls

Step-by-step explanation:

the distance between the tree and the flagpole is approximately 23.29 feet.

To find the distance between the tree and flagpole, we can use the Pythagorean theorem, which states that the square of the distance between the two points (the hypotenuse of the right triangle) is equal to the sum of the squares of the other two sides.

In this case, the distance between the tree and flagpole (the hypotenuse of the triangle) is equal to the square root of (20^2 + 12^2) = square root of (400 + 144) = square root of 544.

So the distance between the tree and the flagpole is approximately 23.29 feet.

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The probability of getting the exact sequence 65634 when tossing a fair die 5 times is also 1/7776.

i) To find the probability of getting 5 consecutive sixes (66666) when a fair die is tossed 5 times, we can use counting methods.

Since each die toss is independent and has 6 possible outcomes (numbers 1 to 6), the probability of getting a six on any single toss is 1/6.

To calculate the probability of getting 5 consecutive sixes, we multiply the probability of getting a six on each toss:

P(66666) = (1/6) * (1/6) * (1/6) * (1/6) * (1/6) = (1/6)^5 = 1/7776

Therefore, the probability of getting 5 consecutive sixes (66666) when tossing a fair die 5 times is 1/7776.

ii) To find the probability of getting the exact sequence 65634 when a fair die is tossed 5 times, we again use counting methods.

The sequence 65634 consists of specific outcomes for each toss of the die. Since there are 6 possible outcomes for each toss, the probability of obtaining the sequence 65634 is the product of the probabilities of each specific outcome:

P(65634) = (1/6) * (1/6) * (1/6) * (1/6) * (1/6) = (1/6)^5 = 1/7776

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The fact that k≥4≥1 is used in the base case of the inductive proof, not in the inductive step.

In the base case, we need to show that the statement holds for k=4. Since 4≥1, this satisfies the condition. The inductive step assumes that the statement holds for some arbitrary k≥4 and then shows that it holds for k+1. The inductive step of an inductive proof aims to show that if a statement holds true for a certain value, it also holds true for the next value. In the given problem, we need to demonstrate that for k≥4, if 2k≥3k, then 2(k+1)≥3(k+1). The fact that k≥4≥1 is utilized in the base case step of the proof. The base case ensures that the initial condition (k=4) satisfies the given inequality. By showing that the inequality holds true for k=4, we establish a starting point for the inductive step. This allows us to apply the inductive step and generalize the result to all values of k greater than or equal to 4.

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\(\frac{325}{520}\) fraction of the workforce kept their jobs

What is the Percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

What is Percentage change?

The percentage increase is calculated by subtracting the original number from the new number, dividing that result by the original number, and multiplying that result by 100.

where growth in number equals new number minus initial number.

Similar to how a percentage increase is calculated, a percentage reduction is calculated by subtracting a new number from the original number, dividing that new number by the original number, and multiplying that result by 100.

decreasing number where original number - new number

In other words, there is a percentage decline if the response is negative.

Here, It is given:

In January 520 workers were employed;

In the end, 195 employees were redundant;

So, The fraction of the workforce who kept their job:-

The fraction of the workforce who kept their job=\(\frac{520-195}{520}\)

The fraction of the workforce who kept their job=\(\frac{325}{520}\)

Hence,

The fraction of the workforce who kept their job=\(\frac{325}{520}\)

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Answer:

36.6 meters

Step-by-step explanation:

1 yard is .9144 meters so 40 yards is 36.576 meters. (i rounded it)

The value of the determinant is -39. Therefore, the correct option is O.

The given determinant is \(|23 25 0|31 32 0|42 47 01|\)

We can calculate the determinant value by evaluating the cross-product of the first two columns.

We get: \(|23 25 0|31 32 0|42 47 01| = (23×32×1) + (31×0×47) + (0×25×42) - (0×32×42) - (25×31×1) - (23×0×47) \\= 736 + 0 + 0 - 0 - 775 - 0 \\= -39\)

Hence, the value of the determinant is -39.

Therefore, the correct option is O.

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Answer:

Plug it in.

y = -1, y1 = 1

x = 3, x1 = 1

-1 - 1 = m( 3 - 1)

-2 = 2m

m = -1

The slope is -1

y = -x +b

-1 = -3 +b

b = 2

The equation is y = -x + 2

Hope this helps.

Step-by-step explanation:

The another equivalent expression of total liquid is (x+2)/4.

Expressions that perform similarly but differ in appearance are said to be equivalent expressions. When the same value for the variable is entered, two algebraic expressions that are equivalent will have the same result.

x quarts liquid in the container 3/4 part of liquid is removed

Then remaining liquid in container = X - \(\frac{3}{4}X\)

Then remaining liquid in container = x/4quarts

Another 1/2 quart is poured into container

Then total liquid = \(X-\frac{3}{4}X+\frac{1}{2}\) quarts

total liquid = \(\frac{X+2}{4}\) quarts

So, then the another equivalent expression of total liquid is (x+2)/4.

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The total amount the mechanic will need in retirement savings to meet their retirement income goal is $880,000.

Option A.

The total amount the mechanic will need in retirement savings to meet their retirement income goal is calculated as follows;

80% of  $44,000 = ?

= 0.8 x  $44,000

= $35,200

The amount needed to generate $35,200 annually at a 4% withdrawal rate is calculated as follows;

Let the amount = x

0.04x = $35,200

x = $35,200/0.04

x = $880,000

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Answer:

B

Step-by-step explanation:

because when you divide all the answers their hours of training its all different answers

The equivalent annual devaluation rate of this stock (rounded to the nearest tenth of a percent) is 27.6% and its worth (rounded to the nearest ten dollars) after 1 year is $138,000.

Devaluation rate:

Basically, the devaluation rate refers the deliberate downward adjustment of the value of a country's money relative to another currency, group of currencies, or currency standard.

Given,

In a recent stock market downturn, the value of a $5,000 stock is decreasing at 2. 3% per month. This situation can be modeled by the equation A(t) = 5,000(0. 977)^12t, where A(t) is the final amount and t is time in years.

Here we need to find the equivalent annual devaluation rate of this stock (rounded to the nearest tenth of a percent) and what is it worth (rounded to the nearest ten dollars) after 1 year.

While we looking into the given question,

We have identified that, the decreasing percent per month is 2.3%.

So, for 1 year, the decreasing percent is,

=> 12 x 2.3 = 27.6%

Similarly, devaluation rate after one is year calculated by applying the value of t as 1, in the given equation, then we get,

=> A(1) = 5,000(0.977)¹²ˣ¹

=> A(1) = 5,000(0.977)¹²

=> A(1) = 5000 x 276

=> A(1) = 138000

Therefore, the annual devaluation rate is 138,000.

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