What is 2. 314 repeating as a fraction in simplest form

The historical rate of defective widgets produced by ACME Corporation was 7%. Approximately, 91.2 is the standard deviations is the point estimate from 7%.

In statistics, standard deviation is a measure of the amount of variation or distribution of a set of values. A low standard deviation indicates that the values ​​tend to be close to the ensemble mean (also called the expected value), while a high standard deviation indicates that the values ​​are spread over a wider range.

The standard deviation can be abbreviated SD, and is most commonly used in mathematical texts and equations with the lowercase Greek letter σ (sigma) for the population standard deviation, or the Latin letter s for the standard deviation of the sample.

The standard deviation of a random variable, sample, population, data set, or probability distribution is the square root of its variance. It is algebraically simpler than the mean absolute deviation, although less robust in practice. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same units as the data.

According to the Question:

Given that:

Defective widgets produced by ACME corporation was 7%

Total sample was 856 widgets.

Therefore, the Standard Deviation estimates from 7% is:

856 of 7% = 91.2

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Answer:

285 cm²

Step-by-step explanation:

Area of square = 15² = 225 cm²

Area of triangle = bh/2 = 15*8/2 = 60 cm²

Area of composite figure = 225+60 = 285 cm².

Answer:

See image.

Step-by-step explanation:

Each value is grouped into one of three ranges, 0-15, 15-30, 30-45, once we know how many values are in each group, we can graph it.

3 and 10 fall in 0-15, so thats 2 values
17, 23, and 28 fall in 15-30, so thats 3 values,

33 and 42 fall in 30-45, so thats 2 values.

The function has a local maximum at x = 1/3 and a local minimum at x = -4/3.

A quadratic equation is a second-order polynomial equation in a single variable x

ax²+bx+c=0

with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots x can be found by completing the square,

ax²+bx+c=0

To analyze the function F(x) = -2x² - 6x³ + 4x + 1, we can begin by finding its derivative:

F'(x) = -4x - 18x² + 4

Then, we can find the critical points of the function by setting F'(x) equal to zero and solving for x:

-4x - 18x² + 4 = 0

Using the quadratic formula, we get:

x = (-(-4) ± ((-4)² - 4(-18)(4))) / (2(-18))

Simplifying, we get:

x = (-(-4) ± (400)²) / (-36)

x = (-(-4) ± 20) / (-36)

x = 1/3 or x = -4/3

So the critical points of the function are x = 1/3 and x = -4/3.

To determine the nature of these critical points, we can use the second derivative test.

F''(x) = -4 - 36x

Plugging in x = 1/3, we get:

F''(1/3) = -4 - 36(1/3) = -16 < 0

So x = 1/3 is a local maximum.

Plugging in x = -4/3, we get:

F''(-4/3) = -4 - 36(-4/3) = 40 > 0

So x = -4/3 is a local minimum.

Therefore, the function has a local maximum at x = 1/3 and a local minimum at x = -4/3.

complete question  F(X) = 6x³ - 4x² + 1. Find The Equation Of The Tangent Line To F(X)When X = 2.

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Complete question:

Find the local maximum and minimum of f(x) = -2x² - 6x³ + 4x + 1.

the percentage 68% value is calculated by adding 85 and 20, or 70; the 95% value is calculated by adding 85 and 40, or 115; and the 99.7% value is calculated by adding 85 and 60, or 150.

68%: 70

95%: 115

99.7%: 150

The 68-95-99.7 rule is used to estimate the percentage of a population that falls within a certain range of values when the data is normally distributed. The rule states that 68% of the population falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. To find the percentages, we subtract the mean (85) from the corresponding standard deviation (20, 40, and 60, respectively) and add the result to the mean. Thus, the 68% value is calculated by adding 85 and 20, or 70; the 95% value is calculated by adding 85 and 40, or 115; and the 99.7% value is calculated by adding 85 and 60, or 150.

the complete question is :

Assume the resting heart rates for a sample of individuals are normally distributed with a mean of 85 and a standard deviation of 20. Use the 68-95-99.7 rule to find the following quantities:

1.The percentage of individuals with resting heart rates between 65 and 105.

2.The percentage of individuals with resting heart rates above 125.

3.The range of resting heart rates that includes the middle 95% of the individuals in the sample.

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Answer:

x² + y² = 16

Step-by-step explanation:

the circle has its centre at the origin (0, 0 )

the equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

the radius r of the circle is 4 , then

x² + y² = 4² , that is

x² + y² = 16

If a delivery truck is transporting boxes of two sizes: large and small. there are 70 large boxes and 65 small boxes in the truck.

Let's assume that x represents the number of large boxes, and y represents the number of small boxes.

We know that there are 135 boxes in total, so:

x + y = 135

We also know that the total weight of the boxes is 5475 pounds, so:

55x + 25y = 5475

Now we have a system of linear equations with two variables. We can use substitution or elimination to solve for x and y. Let's use substitution:

From the first equation, we can solve for x in terms of y:

x = 135 - y

Substitute this expression for x into the second equation:

55x + 25y = 5475

55(135 - y) + 25y = 5475

Simplify and solve for y:

7425 - 55y + 25y = 5475

30y = 1950

y = 65

Now we can use the first equation to solve for x:

x + y = 135

x + 65 = 135

x = 70

Therefore, there are 70 large boxes and 65 small boxes in the truck.

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The optimal speed for the delivery minivan to minimize the cost of an 80 mile delivery for the gift shop considering only the cost of fuel and wages is approximately 126 mph.

Let's first determine the total cost of the delivery as a function of the speed of the minivan. The cost consists of two parts: the cost of fuel and the cost of the driver's wages. Since the driver's rate is $20 per hour and the delivery is 80 miles, the cost of the driver's wages is:

W = $20 × (80/V) = $1600/V

The cost of fuel is given by the formula C = [tex]0.005V^2[/tex], where V is the speed of the minivan in mph. The total cost of the delivery is therefore:

C(V) = [tex]0.005V^2 + 1600/V[/tex]

To find the speed that minimizes the cost of the delivery, we need to find the value of V that makes the derivative of C(V) equal to zero:

C'(V) = [tex]0.01V - 1600/V^2[/tex]

0 = [tex]0.01V - 1600/V^2[/tex]

0 = [tex]V^3 - 160000[/tex]

[tex]V^3[/tex] = 160000

V = cuberoot(160000) = 40√10

The exact speed that minimizes the cost of the delivery is V = 40√10 mph. Rounded to the nearest whole number, the answer is 126 mph (since 40√10 ≈ 126.49).

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The measure of the unknown angle is 93°

First we should get the interior angles of the triangle in the right side.

The angle in the left side is given by:

x  + 127° = 180°

x = 180° - 127°

x = 53°

While the angle in the right side is:

y + 146° = 180°

y = 180° - 146°

y = 34°

Now remember that the sum of the interior angles of a triangle must be 180°, then if the angle at the top is z we can write:

z + 34° + 53° = 180°

z = 180° - 34° - 53°

z = 93°

And this angle is a vertical angle of the one we want to find, so the measure of the unknown angle is also 93°.

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Answer:

3(x^2+3x-1)

Step-by-step explanation:

3x^2+9x-3

3(x^2+3x-1)

Answer:

Step-by-step explanation:

Answer: A. You cannot use any theorem along with option A. For B, you can use SAS. For option C, you can use SAS. For option D, you can use SSS. For option D, you can use ASA. So, the answer is A.

Answer:

The problem is the answer to your equation

Step-by-step explanation:

Im sorry to disappoint but these questions don't really have a name.

Answer:

$20.64

Step-by-step explanation:

When you take 40% of 33, you are left with 19.8. You then translate the sales tax into 84 cents and add it to 19.8. That will give you $20.64 as the after tax price.

The right choice is Choice D: Lines AC and RS are skew lines. Skew lines are two lines that never cross and are not equal moreover.

A line is characterized as a bunch of focuses that broaden endlessly in one or the other heading. A line is the briefest distance between any two focuses.

What are skew lines?

Skew lines are two lines that never cross and are not equal moreover. Thus we can say that the two lines can not exist in a similar plane.

From the figure obviously

Line AC and RS are in various planes and they are likewise not crossing one another, subsequently, as per the meaning of skew lines, they are skew lines.

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the complete question is:

Lines AC and RS are:

Coplanar

Parallel

Perpendicular

Skew

Answer:

----------------------------

Since diagonals of a kite are perpendicular to each other, the triangles AED and CED are right triangles.

Find the length of ED:

Find the length of legs AE and CE using Pythagorean theorem:

Find the length of AC:

Answer:

AC = 12.7 cm

Step-by-step explanation:

To find:-

Answer :-

We are here given a kite in which AC ⊥ DB and DE = EB = 4cm . We are interested in finding out the length of AC .

[tex]\rule{200}2[/tex]

D I A G R A M : -

[tex]\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){$\sf A$}\put(0.5,-0.3){$\sf B $}\put(5.2,-0.3){$\sf D $}\put(1,0){\line(1,-2){2}}\put(5,0){\line(-1, - 2){2}}\put(2.9,-4.4){$\sf C $}\put(3,3){\line(0, - 1){7}}\put(4,2){$\sf 7cm $}\put(4.5,- 2){$\sf 8cm $}\put(3.4,0.2){$\sf 4cm $}\put(2,.2){$\sf 4cm $}\put(3.2, - .5){$\sf E $}\multiput(2,0.2)(2.2,0){2}{\line(0,-1){0.4}}\multiput(1.9,0.2)(2.2,0){2}{\line(0,-1){0.4}}\put(5,-4){$\boxed{\bf \textcopyright Tony Stark}$}\put(3.01,0.01){\framebox(0.25,0.25)}\end{picture}[/tex]

[tex]\rule{200}2[/tex]

We can see that,

[tex]\sf:\implies AC = AE+EC\\[/tex]

We can seperately find AE and EC and then add them up to find AC . We can see that due to the diagonals intersecting each other at right angles , there is formation of 4 right angled triangle, the triangles which we will be using are ∆AED and ∆CED .

We can use Pythagoras theorem here according to which

[tex]\sf:\implies h^2 = a^2 + b^2 \\[/tex]

In two triangles AED and CED hypotenuse are 7cm and cm respectively.

So that , in ∆AED ,

[tex]\sf:\implies 7^2 = AE^2 + DE^2 \\[/tex]

[tex]\sf:\implies AE^2 = 7^2 - DE^2 = 7^2 - 4^2 \\[/tex]

[tex]\sf:\implies AE^2 = 49 - 16 \\[/tex]

[tex]\sf:\implies AE = \sqrt{ 33} \\[/tex]

[tex]\sf:\implies\red{ AE = 5.74} \\[/tex]

Similarly, in ∆CED ,

[tex]\sf:\implies 8^2 = CE^2 + DE^2 \\[/tex]

[tex]\sf:\implies CE^2 = 8^2 - DE^2 = 8^2 - 4^2 \\[/tex]

[tex]\sf:\implies CE^2 = 64- 16 \\[/tex]

[tex]\sf:\implies CE = \sqrt{ 33} \\[/tex]

[tex]\sf:\implies\red{ CE = 6.93} \\[/tex]

Now add them up to find AC , as ;

[tex]\sf:\implies AC = AE + CE\\[/tex]

[tex]\sf:\implies AC = 5.74 + 6.93 \\[/tex]

[tex]\sf:\implies AC = 12.67 \\[/tex]

Rounding off to nearest tenth, will give us,

[tex]\sf:\implies \red{ AC = 12.7 \ cm } \\[/tex]

Hence the length of AC is 12.7 cm.

All the given options applies to the statement. A related-samples design reduces problems due to individual differences; can have an order effect; have less sample variance, increases the likelihood of rejecting the null hypothesis; needs few participants for same degree of power.

1. A related-samples design decreases or eliminates problems that is caused by individual differences such as age, IQ, gender, or personality.

2. Related samples (specifically, one sample of participants with repeated measures) can have an order effect such that a change observed between one measurement and the next might be attributable to the order in which the measurements were taken rather than to a treatment effect.

3. Related samples have less sample variance, which increases the likelihood of dismissing the null hypothesis if it is false (that is, increasing power).

4. Related samples (specifically, one sample of participants with repeated measures) needs very less participants for the same degree of power.

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The formula NEXT = NOW - 8 is neither recursive or explicit.

In a recursive fοrmula, we can find the value οf a term in the sequence using the value οf the previοus term. Hοwever, in an explicit fοrmula, we can find the value οf a term in the sequence using its pοsitiοn. Hence, this is anοther difference between recursive and explicit.

Recursive formula = [tex]\rm a_{n}=a_{n-1}+ d[/tex]

Explicit formula = [tex]\rm a_n= a_1 + (n - 1) d[/tex]

Here, NEXT = NOW - 8 resembles Recursive formula, but the value of Next isn't given. Even if it starts at 50, The value of n isn't specified.

Therefore, The formula NEXT = NOW - 8 is neither recursive or explicit.

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Complete question:

Is the formula recursive, explicit, or neither?

NEXT = NOW - 8, starting at 50.

Step-by-step explanation:

For the second triangle, you can find X by subtracting 32+85 from 180, which leaves X as 63.

Next, since Y is the same as X, it means that Z is equal to 180-(45+63)

X=63

Y=63

Z=72

Therefore, the value of the investment after 3.5 years is $2325.28.

Percent is a unit of measurement that represents a fraction of 100. It is often used to express a proportion or rate in relation to a total of 100. For example, if a sales tax is 7%, that means that for every $100 spent, $7 goes towards the tax. The symbol used to represent percent is %.

Here,

The formula for the value of the investment after t years is:

[tex]A = P(1+r/n)^{nt}[/tex]

where:

A is the amount of money after t years

P is the principal investment (initial amount invested)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time in years

Using this formula, we can plug in the values given in the problem:

P = 2000

r = 0.04

n = 12 (monthly compounding)

t = 3.5

A = [tex]2000(1 + 0.04/12)^{12*3.5}[/tex]

A = [tex]2000*(1.003333)^{42}[/tex]

A = 2000(1.162641)

A = $2325.28

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Answer:

384 cm^2

Step-by-step explanation:

Let the lengths of the sides of the right-angled triangle be 6x, 8x, and 10x, where x is a constant.

Since the perimeter of the triangle is 96 cm, we have:

6x + 8x + 10x = 96

24x = 96

x = 4

Therefore, the lengths of the sides of the triangle are 24 cm, 32 cm, and 40 cm.

The area of a right-angled triangle is given by the formula:

Area = (1/2) * base * height

where the base and height are the two shorter sides of the triangle.

Using the Pythagorean theorem, we can determine that the base and height of the triangle are 24 cm and 32 cm, respectively.

Therefore, the area of the triangle is:

Area = (1/2) * base * height

Area = (1/2) * 24 cm * 32 cm

Area = 384 cm^2

Therefore, the area of the right-angled triangle is 384 cm^2.

After seven years, the yearly sales are 855,355.65.

A relation is any subset of a Cartesian product.

As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."

A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.

Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).

A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).

Every function, as you can see from these definitions, is a relation from X.

the following parameters

a = 650000

r = 4% = 0.04

t = 7

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The 8th term of the given geometric sequence is -156250.

A sequence of numbers is called a geometric sequence if each term, except for the first term, is obtained by multiplying the previous term by a constant factor, which is called the common ratio.

The given sequence is a geometric sequence where each term is obtained by multiplying the previous term by -5.

So, the common ratio (r) between any two consecutive terms is -5.

To find the 8th term, we can use the formula for the nth term of a geometric sequence:

[tex]an = a1 * r^{(n-1)[/tex]

where,

an = 8th term

a1 = first term = 2

r = common ratio = -5

n = 8 (since we want to find the 8th term)

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

[tex]a8 = 2 * (-5)^{(8-1)}\\\\a8 = 2 * (-5)^7\\\\a8 = 2 * (-78125)\\\\a8 = -156250[/tex]

Hence, the 8th term of the given geometric sequence is -156250.

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Answer:109-6b degrees + P but we do not know P yet.

Step-by-step explanation:

Answers:

Explanation:

An integer is any positive or negative whole number. Zero is also an integer. Examples include 12, 15, and -27.

Non-integer values are anything with a fractional or decimal part. An example is 2.47; another example is 2/3 (since it turns into roughly 0.667).

1. The center of circle is (5, -10)

2. The new center of circle is (4, -12)

3. Equation is [tex](x-4)^2+(y+12)^2 = 64[/tex]

The Circle identities defines a set of fundamental identities in trigonometry that depends on the six trigonometric functions of an angle in a right-angled triangle.

Given circle equation is [tex](x-5)^2+(y+10)^2 = 64[/tex]

after translated 1 left and 2 down, by simply add 1 in x and add 2 in y axis, So, the new circle equation will be,

[tex](x-4)^2+(y+12)^2 = 64[/tex]

1. The center of the given circle [tex](x-5)^2+(y+10)^2 = 64[/tex]

Generally the equation of circle is [tex](x-h)^2 +(y-k)^2 =r^2[/tex]

where, (h, k)is center of circle and r is radius.

by comparing the given equation, we get, h = 5, k = -10

So, the center of circle is (5, -10)

2. New center after translation

equation is [tex](x-4)^2+(y+12)^2 = 64[/tex]

comparing the given equation, we get, h = 4, k = -12

So, the new center of circle is (4, -12)

3. Equation of the resulting circle is [tex](x-4)^2+(y+12)^2 = 64[/tex]

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Answer: The answer is 286.4! (Not rounded: 286.391)

Step-by-step explanation:

I hope this helped you! <333

The amount of filter paper that you need to line the funnel is given as follows:

125.6 cm³.

The volume of a cone of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height, and then divided by 3.

V = πr²h/3.

The parameters for the cone in this problem are given as follows:

Hence the amount of filter paper that you need to line the funnel is given as follows:

V = 3.14 x 4² x 7.5/3

V = 125.6 cm³.

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Answer:

12pi

Step-by-step explanation:

circumfrence : 2*pi*r

the radius is found by dividing the diameter in half so, 12/2 or 6

now multiply 6 with 2 and pi and you get 12pi

~lmk if you got Qs

The difference between the amount of money she will have in Euros and the amount she will have in British pounds will be zero.

Kathy needs to exchange half of her US dollars into British pounds and half of her US dollars into euros. Since it is given that pound is equal to USD and euro is also equal to USD, when she withdraws half of her US dollars as British pounds and half of it as euros, she will have the same amount of pounds and euros. Thus, the difference between the amount of money she will have in Euros and the amount she will have in British pounds will be zero. Therefore, she will have the same amount of money in both currencies, and the answer to the question is 0 (rounded to the nearest whole number).

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