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The probablity that the sample's mean length is greate than 6.3 inches is0.8446.

Given mean of 6.5 inches,standard deviation of 0.5 inches and sample size of 46.

We have to calculate the probability that the sample's mean length is greater than 6.3 inches is 0.8446.

Probability is the likeliness of happening an event. It lies between 0 and 1.

Probability is the number of items divided by the total number of items.

We have to use z statistic in this question because the sample size is greater than 30.

μ=6.5

σ=0.5

n=46

z=X-μ/σ

where μ is mean and

σ is standard deviation.

First we have to find the p value from 6.3 to 6.5 and then we have to add 0.5 to it to find the required probability.

z=6.3-6.5/0.5

=-0.2/0.5

=-0.4

p value from z table is 0.3446

Probability that the mean length is greater than 6.3inches is 0.3446+0.5=0.8446.

Hence the probability that the mean length is greater than 6.3 inches is 0.8446.

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The diameter of circle O in the image given is: AB.

The diameter of a circle can be referred to as the largest chord in a circle which is the line segment that passes through the center of a circle with both ends on the circle.

In the image given, AB is the largest chord and also passes through the center of the circle, O.

Thus, the diameter is: AB.

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The mean could be used to describe a data set by itself, while interquartile range would almost never be used to describe a data set by itself.

Brief Description of Mean and Interquartile Range

While interquartile range only assesses the middle half of the data, mean and range deal with the entire set of data. The mean is significant in statistics because it helps us determine where a dataset's "center" is. The mean contains information from each observation in a dataset as a result of how it is calculated.

The interquartile range in descriptive statistics reveals the spread of your distribution's middle half. Any distribution that is sorted from low to high is divided into four equal portions using quartiles. The second and third quartiles, or the center half of your data set, are contained in the interquartile range (IQR).

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Answer: x² + 4x +3=0

Step-by-step explanation:

Add 4x to both sides.

Length of each side is 176 feet ² .

each side of house = 22 feet long

Perimeter of octagon = 8 × sides

Length of each side of house = 8 × 22 ⇒ 176 feet²

Therefore, length of each side is 176 feet ² .

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Answer:

Step-by-step explanation:

Evaluate 5 - 3(a3 – b2)2 when a = 3 and b = 5.

5 - 3 × (a³-b²)²                           a=3 and b=5

5 - 3 × (3³ - 5²)² =

5 - 3 × (27  - 25)² =

5 - 3 × (2)² =

5 - 3 × 4 =

5 - 12 =

-7

20 years is the answer.

A= R(1+r)^ t

A-415    

R=230

r=3%

415=230 (1+3%)^ t

t=log1.03  315/230

t=19.89 (use calculator)

David will invest at least 20 years.

An investment is a dedication of an asset to achieve an increase in value over a period of time. Investing requires the sacrifice of current assets such as time, money and effort. In finance, the purpose of an investment is to generate a profit on the invested asset

The most common example of an investment type. Investment is generally what you want to use in the future with the aim of generating regular cash flow or increasing the value of something over time so that you can sell it at a higher price than you purchased.

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Considering the critical points of the function, we have that:

The critical points of a function are the values of x for which:

[tex]f^{\prime}(x) = 0[/tex]

In this problem, the function is:

[tex]f(x) = 3x^3 - 16x + 2[/tex]

The derivative is:

[tex]f^{\prime}{x} = 6x^2 - 16[/tex]

The critical points are given as follows:

[tex]6x^2 - 16 = 0[/tex]

[tex]x^2 = \frac{16}{6}[/tex]

[tex]x = \pm \sqrt{\frac{16}{6}}[/tex]

[tex]x = \pm 1.63[/tex]

For x < -1.63, one example of the derivative is:

[tex]f^{\prime}{-2} = 6(-2)^2 - 16 = 8[/tex]

Positive, hence increasing.

For -1.63 < x < 1.63, one example of the derivative is:

[tex]f^{\prime}{0} = 6(0)^2 - 16 = -16[/tex]

Negative, hence decreasing.

For x > 1.63, one example of the derivative is:

[tex]f^{\prime}{2} = 6(2)^2 - 16 = 8[/tex]

Positive, hence increasing.

Hence:

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Range of values of the variable p is  [tex]0\leq p\leq \frac{10}{3}[/tex]

Step-by-step explanation:

From general quadratic equation [tex]ax^{2} +bx+c[/tex], for imaginary case-

[tex]D\leq 0\\b^2-4ac\leq 0[/tex]

In given question, [tex]a= p+2[/tex], [tex]b=2p[/tex], [tex]c= 5-p[/tex]

using above condition-

[tex]b^2-4ac = 4p^2-4(2p)(5-p)\leq 0\\4p^2 - 40p+8p^2\leq 0\\12p^2-40p\leq 0\\4p(3p-10)\leq 0[/tex]

Here, [tex]4p\leq 0, p\leq 0[/tex]

and

[tex]3p-10\leq 0\\p\leq \frac{10}{3}[/tex]

Therefore, range of values of the variable p is  [tex]0\leq p\leq \frac{10}{3}[/tex].

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The total amount of manufacturing overhead cost is closest to $ 29,500.

In business, overhead or overhead rate refers to an ongoing fee for working in a commercial enterprise. Overheads are the expenditure that can not be quite simply traced to or recognized with any unique revenue unit, not like running fees which include uncooked cloth and exertions.

Overhead fees, frequently referred to as overhead or working prices, confer with those expenses associated with running a commercial enterprise that cannot be connected to creating or producing a product or service. they're the prices the business incurs to live in the enterprise, irrespective of its success degree.

Examples of overhead encompass hire, administrative expenses, or worker salaries. Overhead fees may be observed on a business enterprise's income assertion, wherein they are subtracted from its profits to reach at the internet profits discern.

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The statement that correctly describes the horizontal asymptote of g(x) is:

Limit of g (x) as x approaches plus-or-minus infinity = 6, so g(x) has an asymptote at y = 6.

In this problem, the function is:

[tex]g(x) = \frac{42x^3 - 15}{7x^3 - 4x^2 - 3}[/tex]

The horizontal asymptote is given as follows:

[tex]y = \lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} \frac{42x^3 - 15}{7x^3 - 4x^2 - 3} = \lim_{x \rightarrow \infty} \frac{42x^3}{7x^3} = \lim_{x \rightarrow \infty} 6 = 6[/tex]

Hence the correct statement is:

Limit of g (x) as x approaches plus-or-minus infinity = 6, so g(x) has an asymptote at y = 6.

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The points on the graph of (-4, 0), (-2.5, -12), and (0, -3), gives;

From the description of the graph, we have;

Furthest point left of the graph = (-4, 0)

The furthest point right on the graph = (0, -3) = The maximum point

The minimum point = (-2.5, -12)

F(x) < 0 at the minimum point

The minimum point is to the right of x = -4

The point the graph crosses the y-axis = (0, -3)

Therefore;

The interval of the graph where F(x) is larger than 0 is to the left of (-4, 0), is the interval (-∞, -4)

The true statement is therefore;

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The value of the angle will be C. 20°

From the information given, it was stated that the protractor showed an angle going through the tenth tick mark after ten degrees.

This means the value of the angle will be:

= 10° + 10°

= 20°

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i. The number of people who like banana only is 20.

ii. The number of people who like none of the fruits is zero.

iii. The number of people who like at most one fruit is 30.

The question has to do with sets.

A set a collection of well ordered items

Since we have 55 people, 3x + 5 people like banana and x + 5 people like apple. If all the people who like apple also like banana and if 2x + 15 people like at least one of fruit then, we have that

3x + 5 + x + 5 + 2x + 15 = 55

3x + 2x + x + 5 + 5 + 15 = 55

6x + 30 = 55

6x = 55 - 25

6x = 30

x = 30/6

x = 5

Since the number of people who like banana only is 3x + 5.

So, number of people who like banana only is n = 3x + 5

= 3(5) + 5

= 15 + 5

= 20

So, the number of people who like banana only is 20.

Since from the question, a person likes at least one fruit, either banana, apple or both. No one likes none of the fruits.

So, the number of people who like none of the fruits is zero.

To like at most one fruit, the person either likes apple or banana.

So, their sum is n = 3x + 5 + x + 5

= 4x + 10.

Since x = 5, we have n = 4x + 10.

= 4(5) + 10

= 20 + 10

= 30

So, the number of people who like at most one fruit is 30.

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The correct option is A. hot water moving through a pipe.

Electrical current passing through a metal wire is similar to hot water moving through a pipe.

Electrical charge carriers, often electrons or atoms deficient in electrons, travel as current. The capital letter I is a typical way to represent current. The ampere, denoted by the letter A, is the common unit.

The method of flowing of electrical current in metal wire is-

Comparison of flow of electricity with flow of water in pipe-

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The complete question is-

which of the following situations would be mist similar to an electrical current passing through a metal wire in a closed circuit?

A. hot water moving through a pipe

B. an automobile traveling through a tunnel

C. an airplane flying through clouds

D. a flying pan heating up on a hot plate

E. a bird building a nest

Answer:

Step-by-step explanation:

dddfykb

The equation can be used to find other combinations of x and y is  y^2 = (1/16)x^3

The direct variation from the square of y to the cube of x is represented as:

y^2 = kx^3

Where k represents the variation constant.

When x = 4, y = 2.

So, we have:

2^2 = k * 4^3

This gives

4 = 64k

Divide both sides by 64

k = 1/16

Substitute k = 1/16 in y^2 = kx^3

y^2 = (1/16)x^3

Hence, the equation can be used to find other combinations of x and y is  y^2 = (1/16)x^3

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The resulted integral is [tex]I=\frac{8}{3} \times \frac{5 \pi}{16}=\frac{5 \pi}{6}[/tex].

In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or just an added to the initial, the derivative of which is initial function (indefinite integral).

Computation of the integrals:

Step 1: We employ the equations in cylindrical coordinates.

[tex]x=r \cos \theta, y=r \sin \theta, z=z[/tex]

Thus, in cylindrical coordinate system,

E lies above the paraboloid [tex]z=r^{2}[/tex] and below the plane [tex]z=2 r \sin \theta[/tex] .

Therefore, the top part E is  [tex]z=2 r \sin \theta[/tex] is the cross-section between paraboloid and the plane.

Now, at the cross-section use, [tex]r^{2}=2 r \sin \theta[/tex] and  [tex]z=2 r \sin \theta[/tex] .

Thus, the limits are given as ;

[tex]r^{2} \leq z \leq 2 r \sin \theta \quad 0 \leq r \leq 2 \sin \theta[/tex]

Apply the limits as compute the integration;

[tex]\begin{aligned}I=\iiint_{E} z d V &=\int_{0}^{\pi} \int_{0}^{2 \sin \theta} \int_{\tau^{2}}^{2 r \sin \theta} z r d r d z d \theta \\&=\int_{0}^{\pi} \int_{0}^{2 \sin \theta}\left[\frac{z^{2}}{2}\right]_{r^{2}}^{2 r \sin \theta} r d r d \theta \\&=\frac{1}{2} \int_{0}^{\pi} \int_{0}^{2 \sin \theta}\left[4 r^{2} \sin ^{2} \theta-r^{4}\right] r d r d \theta\end{aligned}[/tex]

                       [tex]\begin{aligned}&=\frac{1}{2} \int_{0}^{\pi} \int_{0}^{2 \sin \theta}\left[4 r^{3} \sin ^{2} \theta-r^{5}\right] d r d \theta \\&=\frac{1}{2} \int_{0}^{\pi}\left[r^{4} \sin ^{2} \theta-\frac{r^{6}}{6}\right]_{0}^{2 \sin \theta} d \theta \\&=\frac{8}{3} \int_{0}^{\pi} \sin ^{6} \theta d \theta\end{aligned}[/tex]

Step 2: Now, calculate for the [tex]I_{1}=\int_{0}^{\pi} \sin ^{6} \theta d \theta[/tex].

 [tex]\begin{aligned}\sin ^{6} \theta &=\left(\sin ^{2} \theta\right)^{2} \times \sin ^{2} \theta \\&=\left[\frac{1-\cos 2 \theta}{2}\right]^{2} \times\left[\frac{1-\cos 2 \theta}{2}\right] \\&=\frac{1}{8}\left(1-2 \cos 2 \theta+\cos ^{2} 2 \theta\right)(1-2 \cos 2 \theta) \\&=\frac{1}{8}\left(1-2 \cos 2 \theta+\frac{1+\cos 4 \theta}{2}\right)(1-2 \cos 2 \theta)\end{aligned}[/tex]

         [tex]\begin{aligned}&=\frac{1}{16}(3-4 \cos 2 \theta+\cos 4 \theta)(1-2 \cos 2 \theta) \\&=\frac{1}{32}(10-15 \cos 2 \theta+6 \cos 4 \theta-\cos 6 \theta)\end{aligned}[/tex]

Further compute the value of

   [tex]\begin{aligned}I_{1} &=\int_{0}^{\pi} \sin ^{6} \theta d \theta \\&=\frac{1}{32} \int_{0}^{\pi}(10-15 \cos 2 \theta+6 \cos 4 \theta-\cos 6 \theta) d \theta \\&=\frac{1}{32}\left[10 \theta-\frac{15 \sin 2 \theta}{2}+\frac{3 \sin 4 \theta}{2}-\frac{\sin 6 \theta}{6}\right]_{0}^{\pi} \\&=\frac{5 \pi}{16}\end{aligned}[/tex]

Therefore, the obtained integral is  [tex]I=\frac{8}{3} \times \frac{5 \pi}{16}=\frac{5 \pi}{6}[/tex].

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The complete question is -

Use cylindrical or spherical coordinates, whichever seems more appropriate. Evaluate ∫∫∫E z dV, where E lies above the paraboloid

z = x² + y²

and below the plane z = 2y. Use either the Table of Integrals or a computer algebra system to evaluate the integral.

Using an exponential function, it is found that Mary's initial investment was of $3,030.

An exponential function is modeled by:

[tex]y = ab^x[/tex].

In which:

Her investment model, in thousands of dollars, is:

[tex]M(x) = 3.03(1.28)^{2x}[/tex]

Then a = 3.03, since we measure the amount in thousands of dollars, Mary's initial investment was of $3,030.

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The two odd numbers are 43 and 37.

Whole numbers are positive numbers belonging to the set W ∈ {1, 2,3, 4, ...}

The two odd numbers can be represented as (2m-1) and (2n-1) respectively sum=80 and difference = 6

Let m and n be two whole numbers

Therefore

,[tex]2m-1) + (2n-1)= 80\\(2m-1) - (2n-1)= 6\\\\2(m+n-1)=80\\2(m-n)=6\\\\m+n = 41\\m-n=3\\[/tex]

Adding the two equations

[tex](m+n)+(m-n)=2m=44\\m=22\\n=m-3=19\\[/tex]

so m=22 ad n=19. our two odd numbers are 2m-1 = 43 and 2n-1 = 37

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Answer:

14.35 ft

Step-by-step explanation:

We can use the pythagorean theorem to find the distance between the poles since both triangles are right triangles.

a^2 + b^2 = c^2

a^2 + 12^2 = 14^2

a^2 + 144 = 196

a^2 = 52

a = 7.21 ft

a^2 + b^2 = c^2

a^2 + 7^2 = 10^2

a^2 + 49 = 100

a^2 = 51

a = 7.14 ft

7.21 + 7.14 = 14.35 ft

Brainliest, please :)

Answer: c; 14.35

Step-by-step explanation: I need help on this and i saw this guy asked for brainlist and i think two people need to anser so please give him brainlist.

None of the expressions is an identity

The expressions are given as:

I. y=x

II. 4 = 3x^2 + 2

III. x=x

In algebra, there are three identities; and they are

None of the given expression take the above forms

Hence, none of the expressions is an identity

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Taking a quotient, we will see that she can make 7 bowls of cereal (and some leftover milk).

We know that for each bowl, she needs 1/2 cups of milk.

And we also know that she has a total of (3 + 3/5) cups of milk.

To know how many bowls she can make, we need to take the quotient between the total that she has and the amount that she needs for each bowl:

(3 + 3/5)/(1/2)

We can rewrite the total as:

3 + 3/5 = 15/5 + 3/5 = 18/5

Then the quotient becomes:

(18/5)/(1/2) = (18/5)*2 = 36/5 = 35/5 + 1/5 = 7 + 1/5

So she can make 7 bowls of cereal (and some leftover milk).

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The value of t based on the information about the sphere is 1.3π.

It should be noted that the volume of a sphere is 4/3πr³. In this case, it's divided into 8 equal parts.

Volume of each part = 1/8 × 4/3πr³

= 1/8 × 4/3 × π × 8

= 4/3π

= 1.3πin³

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Answer:

Step-by-step explanation:

The distance between the two stations is 360km.

Speed is the rate of change of distance.

Rate is a measure of one quantity against another in this case distance and time.

Analysis:

time at station A = 12:24

time at station B = 14:12

time spent = 14:12 - 12:24 = 1 hour 48 minutes = convert 48 minutes to hour

we divide 48 by 60 = 0.8

Total time = 1.8 hours

Distance = speed x time = 200 x 1.8 = 360 km

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The linear inequality of the given graph is: D. y < -2x + 3.

First, using two points on the line, (0, 3) and (1.5, 0), find the slope (m).

Slope (m) = change in y / change in x = (3 - 0) / (0 - 1.5)

Slope (m) = 3/-1.5 = -2.

Next, substitute (x, y) = (0, 3) and m = -2 into y = mx + b to find the value of b.

3 = -2(0) + b

3 = 0 + b

b = 3

Substitute m = -2 and b = 3 into y < mx + b (the shaded part is at the left, so we use the "<" sign)

y < -2x + 3

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https://brainly.com/question/68367When two lines intersect at a point, angles are formed. Some of these angles formed are vertically opposite and thus are equal.

Therefore, the required proof and answer to the question are stated below:

a) m< TRV = 60° (given)

   m<TRS = 4x° (given)

Thus, it can be concluded from the diagram that:

<TRV ≅ m<BRW  (vertically opposite angle property)

Also,

m<TRS ≅ m<VRW (vertically opposite angle property)

But,

m<VRW = m<VRZ + m<ZRW

Thus,

m<TRV ≅ m<BRW = 60°

m<TRV + m<BRW + m<TRS + m<VRW = [tex]360^{o}[/tex]

60° + 60° + m<TRS + m<VRW = [tex]360^{o}[/tex]

m<TRS + m<VRW =   [tex]360^{o}[/tex] - [tex]120^{o}[/tex]

                             = [tex]240^{o}[/tex]

2m<TRS = [tex]240^{o}[/tex] (since m<TRB = m<VRW )

m<TRS = 120

4x = 120

x = [tex]\frac{120}{4}[/tex]

  = [tex]30^{o}[/tex]

Thus, x = [tex]30^{o}[/tex]

b) The missing reason in step 3 is the angle addition postulate.

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