Find the minimum sample size. Provide your answer in the integer form. A nurse at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she needs to be 97% confident that the population mean is within 2.9 ounces of the sample mean? The population standard deviation of the birth weights is known to be 6 ounces.

Answer:

729

Step-by-step explanation:

let n be the number , then

\(\frac{n}{12}\) = 60 + \(\frac{9}{12}\) ( multiply through by 12 to clear the fractions )

n = 720 + 9 = 729

Therefore , the solution of the given problem of triangle comes out to be  the equilateral triangle are is 62.28 cm².

In geometry, triangular polygons are ones that have three vertices and a right side. This object in two dimensions has three straight sides. Triangles are examples of three-sided polygons. The sum of a triangle's three angles is 180 degrees. The triangle lies on one plane.

Here,

Given : side = 12cm

Area of an equilateral triangle

=> √3/4 * side²

Side of triangle =12 cm

Area of an equilateral triangle

= >  √3/4 * 12²

=>√3/4 * 12*12

=> 62.28 cm²

Therefore , the solution of the given problem of triangle comes out to be  the equilateral triangle are is 62.28 cm².

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We have the trigonometric identities: cosθ * (1 - sin^2θ) simplifies to cosθ, cotθ + tanθ simplifies to secθ * cscθ, which proves the identity,

cosθ * (1 - sin^2θ) = cosθ

Starting from the left-hand side:

cosθ * (1 - sin^2θ) = cosθ * cos^2θ [using the identity sin^2θ = 1 - cos^2θ]

= cosθ * cosθ * cosθ

= cos^3θ

Using the identity cos^2θ = 1 - sin^2θ:

= (1 - sin^2θ) * cosθ

= cosθ

Therefore, cosθ * (1 - sin^2θ) simplifies to cosθ, which proves the identity.

cotθ + tanθ = secθ * cscθ

Starting from the left-hand side:

cotθ + tanθ = (cosθ / sinθ) + (sinθ / cosθ) [using the definitions of cotθ and tanθ]

= (cosθ * cosθ + sinθ * sinθ) / (sinθ * cosθ)

= (cos^2θ + sin^2θ) / (sinθ * cosθ)

= 1 / (sinθ * cosθ) [using the identity cos^2θ + sin^2θ = 1]

= secθ * cscθ [using the definitions of secθ and cscθ]

Therefore, cotθ + tanθ simplifies to secθ * cscθ, which proves the identity.

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To implement the function f(w1,w2,w3) = Σ m(0, 2, 4, 5, 7) using a 3 to 8 binary decoder and an OR gate, we can connect the input lines w1, w2, and w3 to the A, B, and C inputs of the decoder, respectively.

To implement the given function f(w1,w2,w3) = Σ m(0, 2, 4, 5, 7), we first need to convert it into a truth table as follows:

w1    w2    w3    f

0       0       0     0

0       0        1      1

0        1       0      0

0        1       1       1

1        0       0      0

1        0       1       0

1        1        0       1

1        1       1         1

Here, the binary values of w1, w2, and w3 are listed in the first three columns, and the corresponding value of f is listed in the fourth column. The expression Σ m(0, 2, 4, 5, 7) indicates that the function f should be equal to 1 for the minterms 0, 2, 4, 5, and 7.

We can use a 3 to 8 binary decoder to implement this function as follows:

The input lines of the decoder are w1, w2, and w3.

The outputs of the decoder are eight lines labeled Y0, Y1, Y2, Y3, Y4, Y5, Y6, and Y7, each corresponding to one of the possible input combinations of w1, w2, and w3.

The output line corresponding to each minterm that evaluates to 1 is connected to the input of an OR gate.

The output of the OR gate is the output of the function f.

Specifically, we can connect the input lines w1, w2, and w3 to the decoder as follows:

w1 is connected to the A input of the decoder.

w2 is connected to the B input of the decoder.

w3 is connected to the C input of the decoder.

The eight outputs of the decoder are connected to the inputs of an OR gate as follows:

Y0 is not connected to the OR gate since it corresponds to the input combination 000, which is not a minterm in the function.

Y1 is connected to one input of the OR gate since it corresponds to the input combination 001, which is a minterm in the function.

Y2 is not connected to the OR gate since it corresponds to the input combination 010, which is not a minterm in the function.

Y3 is connected to one input of the OR gate since it corresponds to the input combination 011, which is a minterm in the function.

Y4 is connected to one input of the OR gate since it corresponds to the input combination 100, which is a minterm in the function.

Y5 is connected to one input of the OR gate since it corresponds to the input combination 101, which is a minterm in the function.

Y6 is not connected to the OR gate since it corresponds to the input combination 110, which is not a minterm in the function.

Y7 is connected to one input of the OR gate since it corresponds to the input combination 111, which is a minterm in the function.

The other input of the OR gate is connected to ground (or logic 0).

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Answer:

I believe its A

Step-by-step explanation:

Found the answer and its A, good luck.

The exact value of cos^-1( √3/2) = 30°

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

There are special angles in trigonometry, this angles have exact value and can be obtained without using calculator. Examples of this calculator are; 30°, 60°, 45°

sin30 = 1/2

cos 30 = √3/2

tan 30 = 1/√3

cos 60 = 1/2

sin 60 = √3/2

tan 60 = √3

Therefore, if cos^-1( √3/2) = x

cos x = √3/2

cos 30 = √3/2

cos x = cos 30

therefore x = 30

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The sum of the areas of the stages to infinity of the Sierpinski triangle is 1.333a

The Sierpinski triangle is a fractal pattern made up of smaller triangles recursively.

To determine the sum of the areas of the stages to infinity, we need to use the theory of infinite series.

Specifically, we can use the formula for the sum of an infinite geometric series, which is a/(1-r), where

In this case,

First term, a = Area of the original equilateral triangle

Common ratio = Always 1/4

Thus, the sum of the areas of the stages to infinity is given by

Sum = a/(1-1/4)

Simplifying this expression, we get

Sum = a/(3/4)

Sum = 4a/3.

Evaluate

Sum = 1.333a

Therefore, the sum of the areas is 1.333a

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Answer:

200 students vote in the election

Step-by-step explanation:

We know

120 votes = 60%

1% = 2 votes

To find how many students vote in the election, we take

2 x 100 = 200 votes

So, 200 students vote in the election

Check the picture below.

\(\cfrac{17.5+14}{17.5}~~ = ~~\cfrac{x}{12.5}\implies \cfrac{(17.5+14)(12.5)}{17.5}~~ = ~~x\implies 22.5=x\)

The margin of error for a poll with a sample size of 2050 people is 2.2%.

Margin of error is the measure of the accuracy level of the survey or poll results.

It shows the degree of uncertainty that exists in the polls.

The margin of error for a poll with a sample size of 2050 people is 2.2%.

The margin of error is calculated by the following formula:

Margin of Error = z(α/2) * SQRT(pq/n)

where,z(α/2) = critical value

p = proportion of sample

q = 1 - p

p = sample size

In the above-given question, the sample size is 2050.

To calculate the margin of error, we need to assume a value for p.

Assuming that the proportion of sample is 0.5, we can calculate the margin of error.

Margin of Error = z(α/2) * SQRT(pq/n)

= 1.96 * SQRT(0.5*0.5/2050)

= 1.96 * 0.015

= 0.0294

Therefore, the margin of error is 2.94%. We are asked to round the answer to the nearest tenth of a percent, so we get:

Margin of Error = 2.9% (rounded to the nearest tenth of a percent).

Hence, the margin of error for a poll with a sample size of 2050 people is 2.2%.

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Answer:

Equation Form: x=−2,y=−2

Step-by-step explanation:

Eliminate the equal sides of each equation and combine.

3/2x+1=−x−4

Solve 3/2x+1=−x−4

for x. x=−2

Evaluate y when x=−2.

y=−2

The solution to the system is the complete set of ordered pairs that are valid solutions.

(−2,−2)

The result can be shown in multiple forms.

Point Form:

(−2,−2)

Equation Form:

x=−2,y=−2

Answer:

A=4.5π

The formula for finding a circle is A=πr² so just plug in the value for the radius. Don't forget to divide the entire thing by 2 when you finish, cos it's a semi circle (which is a half circle)

Step-by-step explanation:

Cos Milky Said it.

Answer:

Answer=4.5π

Step-by-step explanation:

you square 3 and then divide it by 2 and then just add pi

A;

5 + 2.5xx = AA

B;

20 + 0.5xx = BB

A: 5 + 2.5 • 11

B: 20 + 0.5 • 11

A = 32.5

B = 25.5

Answer:

2 1/5 ---- 1/10 = 21

10

= 21

10

= 2.1

Step-by-step explanation:

Answer:

  175°

Step-by-step explanation:

Bearing angles are usually measured clockwise from North. Reverse bearing angles differ from forward bearing angles by 180°. These relations and the usual angle sum relation for a triangle can be used to solve this problem.

Angle PQR will be the difference in the bearings from Q to P and Q to R:

  ∠PQR = 124° -46° = 78°

Triangle PQR is isosceles, so the base angle at P will be ...

  ∠QPR = (180° -78°)/2 = 51°

__

The bearing from P to R will be 51° less than the bearing from P to Q. The bearing from P to Q is 180° more than the bearing from Q to P.

  PR bearing = PQ bearing - ∠QPR

  = PQ bearing - 51°

  = (46° +180°) -51° = 175°

The bearing of R from P is 175°.

Answer:

Step-by-step explanation

there are 80 boxes in total

3/4x+10=4

Then solve for x

3/4x = 4 - 10

x = (4-10)/(3/4)

. = -6/3/4

. = -24/3

. = -8

In consecuence , answer IS

x= -8

Answer:

57 feet long

Step-by-step explanation:

Half of 38 is 19. 19+38 is 57

Complete question :

Kaitlin has been given a list of 5 bands and asked to place a vote. Her vote must have the names of her favorite and second favorite bands from the list. How many different votes are possible?

Answer:

20 different votes

Step-by-step explanation:

Total number of bands = 5

To select her favorite ; she chooses 1 from the five ;

Number of bands left = 4

From. The 4 she chooses one ; which is her second favorite

Number of different votes possible :

Favorite selection * second favorite selection

(5 * 4) = 20 different votes.

Answer:

The set of probabilities associated with the values in a random variable's sample space is called the probability distribution. It provides the probability of each possible outcome or value that the random variable can take.

Step-by-step explanation:

The probability distribution can be represented in various forms, depending on the type of random variable. For discrete random variables, the probability distribution is often presented as a probability mass function (PMF), which assigns a probability to each possible value. For continuous random variables, the probability distribution is typically described by a probability density function (PDF), which specifies the likelihood of the variable falling within a certain range of values.

For example, let's consider a random variable X that represents the outcome of rolling a fair six-sided die. The sample space of X consists of the values {1, 2, 3, 4, 5, 6}. The probability distribution or PMF for X would assign a probability to each of these values.

Assuming the die is fair, each outcome has an equal probability of occurring, so the PMF for X would be:

P(X = 1) = 1/6

P(X = 2) = 1/6

P(X = 3) = 1/6

P(X = 4) = 1/6

P(X = 5) = 1/6

P(X = 6) = 1/6

These probabilities sum up to 1, indicating that the probabilities assigned to all possible values of X cover the entire sample space.

The area of the square is 25ft² and the perimeter is 20ft.

It's important to note that the area of a square is calculated as:

= Side ²

The perimeter is calculated as:

= 4 × Side

From the information given, the side is 5ft. The area will be:.

= 5 × 5

= 25ft²

The perimeter will be:

= 4 × Sode

= 4 × 5ft.

= 20 feet

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Answer:

y=720

Step-by-step explanation:

Multiply both sides of the equation by −15.

−675+1y=45

Add 675 to both sides.

1y=45+675

1y=720

--   -----

1      1

y=720

Answer: The median decreases to

Step-by-step explanation: The median without the added 60 degrees is 79.5, which I double checked using a calculator after using the MEAN formulas. All I had to do was then add 60 to the data set and run the calculator again, and it then changed to 77.

Answer

1

\((a + b)^{2} = {a}^{2} + 2ab + {b}^{2} \)

Therefore

Answer:

1

Step-by-step explanation:

SEE IMAGE FOR Solution ...

Answer:

J' (-5, -6)

K' (-7, -7)

L' (-9, -6)

M' (-7, -3)

Step-by-step explanation:

From inspection of the image:

J (6, 5)

K (7, 7)

L (6, 9)

M (3, 7)

y = -x  ⇒  x = -y

So if we reflect the points over the line y = -x then

(x, y) → (-y, -x)

Therefore,

J (6, 5) → J' (-5, -6)

K (7, 7) → K' (-7, -7)

L (6, 9) → L' (-9, -6)

M (3, 7) → M' (-7, -3)

The points are

The rule here is (x,y)=(-y,-x)

Now

new points

Answer:

both of these are not similar

Answer:

  about 0.19 m

Step-by-step explanation:

You want the side of a cube with the same volume as a cuboid of dimensions 0.24 m by 0.19 m by 0.15 m.

The volume of the rectangular prism is ...

  V = LWH = (0.24)(0.19)(0.15) m³

The volume of a cube is ...

  V = s³

So, the side length of a cube is ...

  s = ∛V

For a cube of the same volume as the rectangular prism, the side length is ...

  s = ∛((0.24×0.19×0.15) ≈ 0.19 . . . . meters

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Answer:

there is no solution

Step-by-step explanation:

Answer:

\(2\sqrt{3}\) or 2 square roots of 3

Step-by-step explanation:

The figure shown is a 30 - 60 - 90 degree special right triangle

The image below shows the properties of a 30 - 60 - 90 degree special right triangle

We are asked to find the longer leg (v)

The image tells us that the longer leg is equal to the shorter leg to the square root of 3

so v = 2 to the square of 3

Hence, the answer is the first one