A consumer wishes to estimate the proportion of processed food items that contain genetically modified (GM) products.


(a) If no preliminary study is available, how large a sample size is needed to be 99 percent confident the estimate is within 0. 03 of ?



(b) In a preliminary study, 210 of 350 processed items contained GM products. Using this preliminary study, how large a sample size is needed to construct a 99% confidence interval within 0. 03 of ?

The sample size needed to obtain a margin of error of 0.05 for the estimation of a population proportion is 384.

Given margin of error of 0.05 and confidence interval of 95%.

We have to find the sample size needed to obtain a margin of error of 0.5 with confidence level of 95%.

Margin of error is the difference between real values and calculated values.

The formula of margin of error is as under:

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

where

z is the critical value of z for given confidence level

n is sample size

σ is population standard deviation

We have not given population standard deviation so we will use the following formula:

Margin of error=z*[tex]\sqrt{p(1-p)}[/tex]/[tex]\sqrt{n}[/tex]

We have to find z value for 95% confidence level.

z value=1.96

We know that [tex]\sqrt{p(1-p)}[/tex]<=1/2

put [tex]\sqrt{p(1-p)}[/tex]=1/2

Margin of error=1.96*1/2/[tex]\sqrt{n}[/tex]

0.05=1.96*0.5/[tex]\sqrt{n}[/tex]

[tex]\sqrt{n}[/tex]=0.98/0.05

[tex]\sqrt{n}[/tex]=19.6

squaring both sides

n=384.16

After rounding off we will get

n=384.

Hence the sample size needed to obtain a margin of error of 0.05 is 384.

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Applying the trigonometric ratios, the equations that can be used are:

sin 45 = BC/9

cos 45 = BC/9

In the given image below, to find the unknown lengths of the triangle, we would apply the following trigonometric ratios:

To find AC, use the cosine ratio, CAH.

To find BC, use the sine ratio, SOH.

sin 45 = opp/hyp = BC/9

sin 45 = BC/9

cos 45 = adj/hyp = BC/9

cos 45 = BC/9

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Answer: A, E

Step-by-step explanation: Sin(45)=BC/9 ; cos(45)=Bc/9

[tex]ac {}^{2} = cb {}^{2} + ba {}^{2} - 2(cb)( ba)(cos \alpha ) \\ ac {}^{2} = 21 {}^{2} + 26 {}^{2} - 2(21)(26)(cos112) \\ ac {}^{2} = 441 + 676 - 1092(cos112) \\ ac {}^{2} = 1526.07 \\ ac = 39.065[/tex]

Answer:

Step-by-step explanation:

Answer:

2/x

Step-by-step explanation:

Step-by-step explanation:

400 is the whole = 100%

20% (= 20 out of 100 equal parts of 100%) are red.

how many are that ?

well, again, 400 = 100%

1% = 100%/100 = 400/100 = 4

20% = 20×1% = 20×4 = 80

when you combine these 2 steps, you see you get 20% by multiplying the 100% by 20/100 or 0.20.

400 × 0.2 = 80

now,

35% are yellow.

35% = 35×1% = 35×4 = 140

or

400×0.35 = 140

red + yellow = 80 + 140 = 220

the rest are green

400 - 220 = 180

we would get this also by seeing that

red + yellow = 20% + 35% = 55%.

so, green has then the remaining 100-55 = 45%

and again

45% = 45×1% = 45×4 = 180

or

400×0.45 = 180

The measurement of angle C in the given figure is 118°.

Given that are two lines intersecting at a point making 4 angles, 118°, C, D and B.

B and D are opposite to each other and C and 118° are opposite to each other.

We need to find the measurement of angle C.

To find the measurement of angle C, we can use the concept of vertical angles.

Vertical angles are a pair of non-adjacent angles formed when two lines intersect.

They are always congruent, meaning they have the same measure.

In this case, angle 118° and angle C are vertical angles. So, their measures are equal:

Angle C = 118°

Therefore, the measurement of angle C is 118°.

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If the function is

[tex]y = 4 e^x \cos(3x)[/tex]

then we have derivatives

[tex]Dy = 4 e^x \cos(3x) - 12 e^x \sin(3x)[/tex]

[tex]D^2y = -32 e^x \cos(3x) - 24 e^x \sin(3x)[/tex]

Now consider the linear ODE

[tex]aD^2y + bDy + cy = 0[/tex]

Substituting [tex]y[/tex] and its derivatives reduces the equation to

[tex](-32a + 4b + 4c) \cos(3x) + (-24a - 12b) \sin(3x) = 0[/tex]

Now,

[tex]-24a - 12b = 0 \implies b = -2a[/tex]

[tex]-32a + 4b + 4c = 0 \implies c = 10a[/tex]

Then the minimal ODE with the given solution is

[tex]aD^2y -2a Dy + 10ay = 0[/tex]

or

[tex]\boxed{D^2y  -2 Dy + 10y = 0}[/tex]

table 1, and table 2 are the answers.

we know that any function is increasing when for an increase in x-values, y-value should also increase

we will verify each table

table-1:

we can see that

x increase as -3, -2, -1 , 0, 1,2

y is also increasing -6,-3,-1,1,3,6

so, this is increasing

table-2:

we can see that

x increase as -3, -2, -1 , 0, 1,2

but it is asking between -2 to 1

y-values are -4,-1,1,4.....which is increasing

so, this is  increasing

table-3:

we can see that

x increase as -3, -2, -1 , 0, 1,2

but y changes from -3 to -5 .....which is decreasing

so, this is not increasing

table-4:

we can see that

x increase as -3, -2, -1 , 0, 1,2

but y changes from 7 to 1 .....which is decreasing

so, this is not increasing

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Answer:

[tex]\huge\boxed{\sf x = 65 \textdegree}[/tex]

Step-by-step explanation:

Using trigonometric ratio cos.

Here,

[tex]\displaystyle cos \theta =\frac{adjacent}{hypotenuse} \\\\cos \ x =\frac{12}{28} \\\\cos \ x = 0.43\\\\x = cos^{-1} 0.43\\\\x = 65 \textdegree\\\\\rule[225]{225}{2}[/tex]

Using proportions, it is found that each farmer bought 68,008 kg.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Each t has 1000 kg, hence the amount of maize seeds in kg is given as follows:

6460 x 1000 + 760 = 6,460,760 kg

The amount per farmer is:

6,460,760/95 = 68,008 kg.

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Based on the angle of the seesaw and the height off the ground, the maximum length of the seesaw is 2 meters.

This can be found as:

Sin 30° = 1 / Maximum length

Solving gives:

Sin 30° = 1 / Maximum length

Ml = 1 / Sin 30°

= 1 / 0.5

= 2 meters

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The formula is illustrated below:

It should be noted that a cylinder simply means a three dimensional solid which holds two parallel bases that are joined by a curved surface.

In this case, it can be seen that the formula that can be used to calculate the volume and the surface area of the cylinder is illustrated above.

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For the function g(x) we have:

The function g(x) is given by applying transformations to f(x), the transformations are:

The function is:

[tex]g(x) = -(x + 2)^2 + 5[/tex]

The graph is the one you can see below:

There you can see that the vertex is at (-2, 5), then the line of symmetry is:

x = -2.

And we have a maximum at the vertex, which is y = 5.

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Answer:

$ 51.36

Step-by-step explanation:

To find the sales tax multiply the tax rate by the cost of the product and then add to the cost.

Sales tax = tax rate * cost price

              = 7% * 48

              = 0.07 * 48

              = $ 3.36

Cost price = cost of product + sales tax

                 = 48 + 3.36

                 = $ 51.36

The measure of the length BP and BC are 6 and 10 respectively

The given figure is a circle containing two chords AD and BC. From the given diagram, the following are true

AP = PC

BP = PD

BC = BP + PC

Circle theorem includes the concept of tangents, sectors, angles, the chord of a circle and proofs. A circle is the locus of all points in a plane which are equidistant from a fixed point.

Given the following parameters

AP = 3.5,

PD = 6,

PC = 4

According to the expression above;

BP = PD = 6

BC =  BP + PC

BC = 6 + 4

BC = 10
Hence the measure of the length BP and BC are 6 and 10 respectively

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Step 1

Using the points (2,0) and (-2, -3), we get the slope is

[tex]\frac{-3-0}{-2-2}=\frac{3}{4}[/tex]

Step 2

Using the point (2,0), the equation is

[tex]y=\frac{3}{4}(x-2)[/tex]

Step 3

Using the distributive property, we get [tex]y=\frac{3}{4}x-\frac{3}{2}[/tex].

Answer:

Associative Property

For multiplication, the rule is "a(bc) = (ab)c"; in numbers, this means 2(3×4) = (2×3)4.

Answer:
3rd Option!

Step-by-step explanation:

EDGE 2022; good luck

The figure with the new side length if Yasmin changed the scale factor to 1 inch : 3 and two-thirds feet is a square with side lengths of 7 and one third feet.

From the information given, the actual length of each side was 4 feet and the scale factor was 1 inch : 2 feet.

The new length will be:

= 2 × 3 2/3

= 7 1/3

Therefore, the new length is 7 1/3 feet.

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Answer: $18.51

Step-by-step explanation:
1015cm^3/7.95cm^3/g = 127.67g

127.67g/1000g = .128

.128*$.29 = $.037

$.037*500 = $18.51

Answer:

$1170

Step-by-step explanation:

1. We know that each steel part has a volume of 1015 cubic centimeters, and the machinist wants to make 500 of these. Then the total volume of the steel part the machinist will make will be 1015 x 500.

--> 1015 x 500

--> 507500 cubic centimeters.

2. The density of the steel part is 7.95 grams per one cubic centimeter. Then the total density of the 500 steel parts will be 507500 x 7.95.

--> 507500 x 7.95

--> 4,034,625 grams.

3. For every kilo of steel part, the cost is $0.29. We should first change the 4,034,625 gram to kilo. Since 1000 grams is a kilo, we divide 4,034,625 by 1000.

--> 4,034,625 grams / 1000 = 4034.625 kilograms.

Now we multiply 4034.625 by 0.29 to find the total cost.

--> 4034.625 x 0.29

--> 1170.04125.

Since the question specifically asked to round it to the nearest dollar, our final answer becomes $1170.

Answer:

Step-by-step explanation:

40 por ciento

The profit Mrs karki made from the Sari she sold at RS 11300 was 28.25%

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

VAT = 13% = 0.13 * 8000 = 1040

Selling price - VAT = 11300 - 1040 = 10260

Profit = [(10260 - 8000)/8000] * 100% = 28.25%

The profit Mrs karki made from the Sari she sold at RS 11300 was 28.25%

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The value of y from the given figure is 6√3

From the given figure, according to the theorem;

H² = 6² - 3²

H² = 36 - 9

H²  = 27

H = 3√3

Determine the value of y using the same theorem;

y² = 9² + ( 3√3)²

y² = 81. + 27

y = √108

y = 6√3

Hence the value of y from the given figure is 6√3

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The equation in slope intercept form is y = -4x/3 + 10

The representations are given as:

So, we have:

2 * x + 1.5 * y = 15

Evaluate the product

2x + 1.5y = 15

Subtract 2x from both sides

1.5y = -2x + 15

Divide through by 1.5

y = -4x/3 + 10

Hence, the equation in slope intercept form is y = -4x/3 + 10

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The length of the wall = 125m

The area of the Playground = 10000[tex]m^{2}[/tex]

What is geometry?

A branch of mathematics that broadly deals with the measurement, properties, and connections of points, lines, angles, surfaces, and solids: the investigation of qualities of given elements that hold true even after being subjected to predetermined transformations.

Given data:

Perimeter of the playground=410m

length of the wall = 80m

The playground's width can be calculated as follows if its length is 80 meters:

(Formula of Perimeter of a rectangle)

P=2(L+B)              

410=2(80 +B)

410= 160 + 2B

2B= 410-160

2B= 250

B= 125 m

This results in a 125 m length for the playground.

The area of playground.

Area = Length x Width

Area = 80 x 125

area = 10000[tex]m^{2}[/tex]

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The statement best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers is a polynomial

Polynomial expression are equation that has a leading degree of 2 and above. For instance the following expressions are polynomials.

ax^2+bx+c and;

mx^2+nx+p

Take the sum of the polynomials

P(x) =. ax^2+bx+c

f(x) = mx^2+nx+p

Since both expressions are quadratic in nature, hence the sum will result in a polynomial that is quadratic in nature.

Based on the explanation above, we can conclude that the statement best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers is a polynomial

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Answer: -x

Apply Multiplicative Distribution Law:- 1/5 * 5x - 1/5 * 20 - 1/2 * 4x - 1/2 *(-8)

Determine the sign for multiplication or division: 1/5 * 5x - 1/5 * 20 - 1/2 * 4x + 1/2 * 8

Cross out the common factor: x - 1/5 * 20 - 1/2 * 4x + 1/2 * 8

Cross out the common factor: x - 4 - 1/2 * 4x + 1/2 * 8 - 4 - 2x + 1/2 * 8

Cross out the common factor: x - 4 - 2x + 1/2 * 8

Cross out the common factor:  x - 4 - 2x + 4

Reorder and gather like terms: (x - 2x) + (- 4 + 4)

Collect coefficients for the like terms: (1 - 2) * x + (- 4 + 4)

Calculate the sum or difference :  - x + (- 4 + 4)

The sum of two opposites equals 0: -x

Answer: -x

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Answer:

D) Substitute 5 into each expression and evaluate them.

Step-by-step explanation:

Given that the distance and angle of elevation of the tree from P are 50 m. and 32°, and Q is 100 m. from P, we have;

a. The height of the tree is approximately 31.2 m.

b. i. The distance of Q from the base of the tree is 50•√5 m.

ii. The angle of elevation of the top of the tree from Q is approximately 15.6°

iii. The bearing of the tree from Q is 296.565°

a. tan(32°) = Height/50

Height = 50 × tan(32°) = 31.243 m.

b. i. The distance, d, of Q from the base of the tree is given by Pythagorean theorem as follows;

d = √(100² + 50²) = 50•√5

ii. The angle of elevation is given by trigonometric ratios as follows;

[tex]tan (\theta) = \frac{31.243}{50 \cdot \sqrt{5} } [/tex]

Which gives;

[tex]\theta= arctan \left( \frac{31.243}{50 \cdot \sqrt{5} } \right) \approx 15.6 ^{ \circ} [/tex]

iii. The angle formed at Q by the lines from Q to the point P and Q to the tree is found as follows;

Angle = arctan(50/100) ≈ 26.565°

The angle between the direction north of Q and a line from Q to the tree is therefore;

90° - 26.565° = 63.435°

The bearing, which is the angle described clockwise from the direction north of Q and the direction from Q to the tree, is therefore;

Bearing = 360° - 63.435° = 296.565°

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The point F as described in the task content is at point; 0.6 on the number line.

Since it follows from.tge task content that; point D is at -3, and point E Is at 6, it follows that the length of segment, DE is; |-3-6| = 9.

Consequently, since the ratio of Df to FE ls 2:3

It follows that point F is at -3 + (2/5) × 9.

Point F is therefore at 0.6 on the number line.

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Answer:

if I am sick, then I will not come to school.

Step-by-step explanation:

The total number of bars of kitkat Mr hassell had in total is 3 1/2 bars

Total bars of KitKat = 6 × 3/4

= (6×3)/4

= 18/4

= 9/2

= 4 1/2 bars

Number of bar remaining after eating 1 bar = 4 1/2 - 1

= 3 1/2 bars

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