An engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation of all components is 2.2 mm, how many of these components should she consider to be 80% sure of know the mean will be within 0.3 mm? Group of answer choices 1080 126 10 80 Way more than any of these answers

Dave climbed to a height of 4 meters before dropping the object. Note that this assumes that Dave dropped the object straight down and did not throw it horizontally. If he threw it horizontally, then the calculation would be more complicated and would require additional information.

We can use the kinematic equation for vertical motion under constant acceleration due to gravity to solve this problem:

y = yo + voy*t + 1/2*a*t^2

where y is the final height, yo is the initial height (in this case, the height where Dave dropped the object), voy is the initial velocity (which is zero), a is the acceleration due to gravity (-9.8 m/s^2), and t is the time it takes for the object to hit the ground (2 seconds).

Substituting the given values into the equation, we get:

y = yo + 1/2*a*t^2

y = yo + 1/2*(-9.8 m/s^2)*(2 s)^2

y = yo + 19.6 m

Therefore, the height that Dave climbed is equal to the initial height of the object plus 19.6 meters.

To solve for the initial height, we would need more information. However, we can set up a quadratic equation to represent the problem:

-4.9h^2 = -19.6h

where h is the initial height in meters. We can simplify this equation by dividing both sides by -h:

4.9h = 19.6

Solving for h, we get:

h = 4 meters

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Answer:

The answer would be line AB

In the given right triangle, the perimeter is 12 in.

According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the length of the two legs (a and b). Hence,

c^2 = a^2 + b^2

In the given triangle,

c = x in

a = 3 in

b = 4 in

Hence,

x^2 = 3^2 + 4^2

x^2 = 9 + 16

x^2 = 25

x = √25

x = 5

The perimeter of a geometric shape is the sum of all its side. Hence,

Perimeter = 3 + 4 + 5 = 12 in

Note: The question is incomplete. The complete question probability is: Using the Pythagorean theorem, find the perimeter of the triangle.

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Answer:

$17

Step-by-step explanation:

$30/6- 5

$132/6-22

22-5

17

Answer:

Sales goal, S = Q. 10,000

Step-by-step explanation:

Given the following data;

To find his daily sales goal;

\( \frac {20}{100} * S = 2000 \)

\( 0.2 * S = 2000 \)

Dividing both sides by 0.2, we have;

\( S = \frac {2000}{0.2} \)

Sales goal, S = Q. 10,000

9 m, 23 m, and 23 m are the triangle's measurements.

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Therefore, (v - w) is orthogonal to u, which implies that the statement "if proju(v) = proju(w) then (v − w) ⊥ u" is true.

The statement "if proju(v) = proju(w) then (v − w) ⊥ u" is true if and only if u is orthogonal to the projection of (v-w) onto the subspace spanned by u.

Since proju(v) and proju(w) are the projections of v and w onto the subspace spanned by u, we can rewrite the statement as "if the projections of v and w onto the subspace spanned by u are equal, then (v - w) is orthogonal to u".

Let proj_u(v - w) be the projection of (v - w) onto the subspace spanned by u. We know that (v - w) can be decomposed as (v - w) = proj_u(v - w) + (v - w - proju(v - w)).

Note that (v - w - proju(v - w)) is orthogonal to the subspace spanned by u, since proju(v - w) is the closest vector in the subspace to (v - w). Therefore, (v - w) is orthogonal to u if and only if proju(v - w) = 0, which is equivalent to saying that the projection of (v - w) onto the subspace spanned by u is the zero vector.

Assuming that proju(v) = proju(w), we have:

proju(v - w) = proju(v) - proju(w) = proju(v) - proju(w) = 0

Therefore, (v - w) is orthogonal to u, which implies that the statement "if proju(v) = proju(w) then (v − w) ⊥ u" is true.

In conclusion, we have proven that if the projections of v and w onto the subspace spanned by u are equal, then (v - w) is orthogonal to u.

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Answer:

The width is 4

Step-by-step explanation:

the length times the with is the area

since the area is 36

9 times x = 36

so

since 9 x 4 = 36,

the width is 4

a) Compare the populations using measures of center and variation. Mean and MAD of vollyball game attendence are 86, 19.6 respectively. Mean and MAD of basketball game attendence are 185, 17.7 respectively.

b) Difference in the measures of center as a -4.6 to 5.1 multiple of the measure of variation. The difference in the means is about -4.6 to 5.1 times the MAD.

We have two tables consists attendances at volleyball games and basketball games at a school during the year. See the above figure carefully. Now, Compare the populations using measures of center and variation : As we know mean of data is calculated by dividing the sum of data values to the number of data values. Here, Sum of vollyball attendence values, ∑xᵢ = 1720

Number of days = 20

So, mean of vollyball game attendence

= 1720/20 = 86

Sum of basketball ball attendence values, ∑yᵢ = 3700

Number of days = 20

So, mean of basketball ball game attendence = 3700/20 = 185

Now, measure absolute deviations, MAD

MAD of vollyball game attendence is

= [∑( mean of vollyball game attendence - attendance values (i))]/number of days

= 392/20 = 19.6

MAD of basketball ball game attendence is = [∑( mean of basketball ball game attendence - attendance values (i))]/number of days

= 354/20 = 17.7

b) Now, we check the relation between difference in the measures of center as a multiple of the measure of variation.

A : vollyball game attendence

B : basketball game attendence

difference in the measures of center

= Mean (A) - Mean(B) or Mean(B) - Mean (A)

measure of variation, MAD(A) , MAD(B)

[Mean (A) - Mean (B)]/MAD(A)

= ( 86 - 185)/19.6

= -4.643 ~ -4.6

[Mean (B) - Mean (A)]/MAD(B)

= ( 185 - 86)/17.7

= 91/17.7 = 5.1412 ~ 5.1

Hence, difference in the means is about -4.6 to

5.1 times the MAD.

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Complete question :

The above tables show the attendances at volleyball games and basketball games at a school during the year. Volleyball Game Attendance Basketball Game Attendance 112 95 84106 62 68 75 88 93 127 98 117 60176 141 152 181 198 21 49 5485 74 88 132 5 202 190 173 155 169 188 195 4 179 163 186 184207 219 228

a) Compare the populations using measures of center and variation.

b) Express the difference in the measures of center as a multiple of the measure of variation. Round your answers to the nearest tenth. The difference in the means is about (blank) to (blank) times the MAD.

The method for including the garage square footage in the total depends on national standards, with some including it in the total and others excluding it.

When including the garage square footage in the total square footage of a home, there are different ways to do it depending on the national standards used.

Generally speaking, there are two main methods:

Including the garage in the total square footage, or excluding the garage from the total square footage.

If the garage is included in the total square footage, then Bob would add the square footage of the garage (600 square feet) to the square footage of the living spaces in the home (e.g., bedrooms, bathrooms, kitchen, living room, etc.).

This would give him the total square footage of the home, including the garage.

This method is commonly used in some areas of the United States.

On the other hand, if the garage is excluded from the total square footage, then Bob would only count the square footage of the living spaces in the home.

This method is commonly used in other areas of the United States, as well as in other countries.

It is important to note that the method used to calculate the total square footage can affect the perceived value of the home, as well as the taxes and insurance premiums associated with it.

Therefore, it is important for Bob to consult with a local real estate professional or appraiser to determine the most appropriate method for his area.

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\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 30000\\ P=\textit{original amount deposited}\dotfill & \$20000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years \end{cases} \\\\\\ 30000 = 20000[1+(0.09)(t)] \implies \cfrac{30000}{20000}=1+0.09t\implies \cfrac{3}{2}=1+0.09t \\\\\\ \cfrac{3}{2}-1=0.09t\implies \cfrac{1}{2}=0.09t\implies \cfrac{1}{2(0.09)}=t\implies 5.6\approx t\)

Using the Bisector Theorem, the length of DE is 4y + 13 if we bisect (Line Over DE) at point R, DR = 2y + 9, and RE = 3y – 1.

Since l bisects DE at point R, we can use the segment bisector theorem, which states that the ratio of the lengths of the two segments is equal to the ratio of the lengths of the two other segments:

DR/RE = DE/ER

Substituting DR = 2y + 9 and RE = 3y - 1, we get:

(2y + 9)/(3y - 1) = DE/ER

Since R is the midpoint of DE, we have ER = DR = 2y + 9. Substituting this into the equation above, we get:

(2y + 9)/(3y - 1) = DE/(2y + 9)

Cross-multiplying, we get:

DE = (2y + 9)²/(3y - 1)

Expanding the numerator, we get:

DE = (4y² + 36y + 81)/(3y - 1)

Simplifying the expression, we get:

DE = 4y + 13

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The answer is, On  the  interval (-3,-2) to (0,4),  is the graph increasing.

On (0,4) to (3,-2) interval is the graph decreasing.

the graph have a relative maximum at (0,4).

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

from the given graph we get,

On  the  interval (-3,-2) to (0,4),  is the graph increasing.

On (0,4) to (3,-2) interval is the graph decreasing.

the graph have a relative maximum at (0,4).

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X = 40c + 39 = 40(4) + 39 = 199 is the required smallest positive integer.

The smallest positive integer which when divided by 4, 5, 8 and 9 leaves remainder 3, 4, 7 and 8, respectively is 539.

The given equation isx ≡ 3 (mod 4)x ≡ 4 (mod 5)x ≡ 7 (mod 8)x ≡ 8 (mod 9)

By the first condition,x = 4a + 3

where a is any positive integer.

Substituting in the second condition,4a + 3 ≡ 4 (mod 5)⇒ 4a ≡ 1 (mod 5)⇒ a ≡ 4 (mod 5)

Let a = 5b + 4 (where b is any positive integer)

Substituting this in x = 4a + 3, we get

x = 4(5b + 4) + 3 ⇒ x = 20b + 19

Now, substituting this in the third condition,20b + 19 ≡ 7 (mod 8)⇒ 4b ≡ 4 (mod 8)⇒ b ≡ 1 (mod 2)Let b = 2c + 1

Substituting this in x = 20b + 19,x = 20(2c + 1) + 19 ⇒ x = 40c + 39

Finally, substituting this in the fourth condition,40c + 39 ≡ 8 (mod 9)⇒ 4c ≡ 5 (mod 9)

We know that the modular inverse of 4 modulo 9 is 7.

Multiplying both sides by 7,7(4c) ≡ 7(5) (mod 9)⇒ 28c ≡ 35 (mod 9)⇒ c ≡ 4 (mod 9)

Hence,x = 40c + 39 = 40(4) + 39 = 199 is the required smallest positive integer.

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Answer:

\(\sin 2 \theta = -\dfrac{4\sqrt 5}{9}\)

Step-by-step explanation:

\(\text{Given that,}\\\\~~~~~~\sin \theta = \dfrac 23\\\\\implies \sin^2 \theta = \left( \dfrac 23 \right)^2\\\\\implies 1- \cos^2 \theta = \dfrac 49 \\\\\implies \cos^2 \theta = 1 - \dfrac 49 \\\\\implies \cos^2 \theta = \dfrac 59\\\\\implies \cos \theta = \pm\sqrt{\dfrac 59} \\\\\implies \cos \theta = \pm \dfrac{\sqrt 5 }3\\\\\text{Since}~ 90^\circ < \theta < 180^{\circ},~\text{the angle lies in 2nd quadrant}\left(\cos \theta ~\text{is negative}\right).\\\\\)

\(\text{So,}~ \cos \theta = - \dfrac{\sqrt 5 }{3}\\\\\text{Now,}\\\\\sin 2\theta = 2\sin \theta \cos \theta \\\\\\~~~~~~~~=2 \cdot \dfrac 23 \cdot \left( -\dfrac{\sqrt 5}{3} \right)\\\\\\~~~~~~~~=-\dfrac{4\sqrt 5}{9}\)

\(\textbf{Quadrant rule:}\\\\\)

The cross-sectional area will be π*(y^2-x^2) as area of a circle with radius r is π*r^2.

Hence, The cross-sectional area will be π*(y^2-x^2) as area of a circle with radius r is π*r^2.

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Step-by-step explanation:

f(x) = x³ - ax² - 13x + b.

f(1) = 1³ - a(1)² - 13(1) + b = 0

=> 1 - a - 13 + b = 0, b - a - 12 = 0.

f(-3) = (-3)³ - a(-3)² - 13(-3) + b = 0

=> - 27 - 9a + 39 + b = 0, 12 - 9a + b = 0.

Therefore, b - a - 12 = 12 - 9a + b. 8a = 24, a = 3.

=> b - (3) - 12 = 0, b = 15.

To determine if the degree of the function is odd or even we need to look at the extrema of the graph. If both points to the same side, it is, if X goes to positive infinity or to negative infinity, to both direction Y of the graph is going to the same direction, it means that the degree os even. Otherwise, when the extrema are pointing in different directions, it means the degree is odd.

In the present graph, the degree is odd, because the graph has different directions for each extrema.

To determine the signal to the leading coeficient, we check the direction Y is going to increasing values of X. If Y goes positive, the leading coeficient is positive, if it is negative, the leading coeficiente is negative.

In the present graph, the leading coeficient is positive, because for increasing values of X we have increasi

Answer:

Step-by-step explanation:

In conclusion, it can be argued that Abby Sunderland was too young to sail solo. Despite her ambitious and determined nature, her lack of experience and maturity put her at a significant risk during her solo sailing journey. The fact that she had to be rescued twice during her attempt highlights the dangers of attempting such a feat at such a young age. While it is admirable to have the courage to pursue one's dreams, it is important to consider the potential consequences and weigh them against the potential benefits. In this case, it can be argued that the risks far outweighed the potential rewards.

a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

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Answer:

x < 16 ft

Step-by-step explanation:

Perimeter = x

If it is less than 16, the equation is:

x < 16

-Chetan K

Answer:

y = 4x - 2

y = -x + 3

Step-by-step explanation:

Answer: 2 is the probability i think

I want to give a Brainliest to you. Friends??

The area of the shaded region in its simplest form x^2 +23x +49

First, we find the area of the  rectangle as though the small square was not cut out of it

A = (x+10) (2x+5)

Foil

2x^2 +5x+20x+50

2x^2 +25x+50

Then we find the area of the small square

A = (x+1) (x+1)

FOIL

x^2 +x+x+1

x^2 +2x+1

Then we subtract the small square from the large rectangle to find the area of the shaded region

2x^2 +25x+50 - (x^2 +2x+1)

Distribute the minus sign

2x^2 +25x+50 - x^2 -2x-1

x^2 +23x +49

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Answer:

Initial is $26000

It's representing decay.

9.1% change each year.

Answer:

1. x = 8

2. x = 12

3. x = 11

4. x = 6

Step-by-step explanation:

1.

102 + 102 = 204

360 - 204 = 156

156 / 2 = 78

78 = 10x - 2

78 + 2 = 10x

80 = 10x

80 / 10 = x

x = 8

2.

81 = 7x - 3

81 + 3 = 7x

84 = 7x

84 / 7 = x

x = 12

3.

77 = 6x + 11

77 - 11 = 6x

66 = 6x

66 / 6 = x

x = 11

4.

115 + 115 = 230

360 - 230 = 130

130 / 2 = 65

65 = 8x + 17

65 - 17 = 8x

48 = 8x

48 / 8 = x

x = 6