We want to obtain a sample to estimate a population mean. Based on previous evidence, researchers believe the population standard deviation is approximately
σ
=
24.4
. We would like to be 99.5% confident that the estimate is within 0.5 of the true population mean. How large of a sample size is required?

n
=

Using equivalent angles, the solutions are given as follows:

a) [tex]x = \frac{15\pi}{23}[/tex].

b) [tex]x = \frac{9\pi}{62}, x = \frac{53\pi}{62}[/tex].

c) [tex]x = \frac{3\pi}{8}, \frac{11\pi}{8}[/tex]

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

For item a, we have to find the equivalent angle on the 2nd quadrant, where the sine is also positive.

Hence:

[tex]\pi - \frac{8\pi}{23} = \frac{23\pi}{23} - \frac{8\pi}{23} = \frac{15\pi}{23}[/tex]

Hence [tex]x = \frac{15\pi}{23}[/tex].

For item b, if two angles are complementary, the sine of one is the cosine of the other.

Complementary angles add to 90º = 0.5pi, hence:

[tex]x + \frac{11\pi}{31} = \frac{\pi}{2}[/tex]

[tex]x = \frac{31\pi}{62} - \frac{22\pi}{62}[/tex]

[tex]x = \frac{9\pi}{62}[/tex]

The equivalent angle on the second quadrant is:

[tex]\pi - \frac{9\pi}{62} = \frac{62\pi}{62} - \frac{9\pi}{62} = \frac{53\pi}{62}[/tex]

Hence the solutions are:

[tex]x = \frac{9\pi}{62}, x = \frac{53\pi}{62}[/tex]

For item c, the angles are also complementary, hence:

[tex]x + \frac{\pi}{8} = \frac{\pi}{2}[/tex]

[tex]x = \frac{4\pi}{8} - \frac{\pi}{8}[/tex]

[tex]x = \frac{3\pi}{8}[/tex]

The tangent is also positive on the third quadrant, hence the equivalent angle is:

[tex]x = \pi + \frac{3\pi}{8} = \frac{8\pi}{8} + \frac{3\pi}{8} = \frac{11\pi}{8}[/tex]

Hence the solutions are:

[tex]x = \frac{3\pi}{8}, \frac{11\pi}{8}[/tex]

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Answer:

46

Step-by-step explanation:

Answer:

46

According to question,

10% × x = 20

x = 20 ÷ 10%

x = 20 ÷ 0.1

x = 200

Now find 23% of x

23% × 200

0.23 × 200

46

Using linear functions, the inequality that represents when Gilberta has more wallpaper left in her room than María has in hers is: t < 5.

A linear function is modeled by:

y = mx + b

In which:

For this problem, we consider:

Hence the amounts Gilberta and Maria have left after t hours are given by:

Gilberta has more papers when:

G(t) > M(t).

Hence:

35 - 4.3t > 30.5 - 3.4t

-0.9t < -4.5

Multiplying by -1:

0.9t < 4.5

t < 4.5/0.9

t < 5.

Hence the inequality is:

t < 5.

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Answer:

t < 5

Step-by-step explanation:

Other dude is right but here's the version without explanation

Answer:

47

Step-by-step explanation:

3068 - 1266 - 1755 = 47

Answer:

The third number is 47.

Step-by-step explanation:

The sum of three numbers is 3068 - this can be expressed mathematically as:

[tex]\displaystyle{x + y + z = 3068}[/tex]

Given that two of the numbers are 1266 and 1755 (in order) then substitute x = 1266 and y = 1755:

[tex]\displaystyle{1266 + 1755 + z = 3068}[/tex]

Find the third number - solve for z-variable:

[tex]\displaystyle{3021 + z = 3068}\\\\\displaystyle{z = 3068-3021}\\\\\displaystyle{z = 47}[/tex]

Therefore, the third number is 47.

In order to make 3 dimensional object to 4 dimensional object, it's important to draw the 4 dimensional shape in a way that gives the illusion of the 3 dimensional object.

It should be noted that shapes play an important part in geometry.

Here, to make make 3 dimensional object to 4 dimensional object, it's important to draw the 4 dimensional shape in a way that gives the illusion of the 3 dimensional object.

Also, it should be noted that a 4D tesseract can be used to project the image.

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The answers to the service charge rate are:

This is the number of calls for the help desk

160000/3200 = 50per call

For the network center

735000/9800

= 75 per device that was monitored

For the Electronic mail

100000/10000 =

10 for the mail account

For local voice support

124600/8900

= 14 per phone extension

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Using the z-distribution, a sample of 142,282 should be taken, which is not practical as it is too large of a sample.

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

The margin of error is:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

Assuming an uniform distribution, the standard deviation is given by:

[tex]S = \sqrt{\frac{(4 - 0)^2}{12}} = 1.1547[/tex]

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The sample size is found solving for n when the margin of error is of M = 0.006, hence:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.006 = 1.96\frac{1.1547}{\sqrt{n}}[/tex]

[tex]0.006\sqrt{n} = 1.96 \times 1.1547[/tex]

[tex]\sqrt{n} = \frac{1.96 \times 1.1547}{0.006}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 1.1547}{0.006}\right)^2[/tex]

n =  142,282.

A sample of 142,282 should be taken, which is not practical as it is too large of a sample.

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Answer:

Step-by-step explanation:

t(-7)= 3(-7)= -21

s(-21)= 2-(-21)= 2 + 21= 23

Answer:12002/9987

Step-by-step explanation:

The constant of proportionality between the cost and the number of pounds is: A. 0.59.

The constant of proportionality of a relationship between two variables X and Y can be defined as the ratio between of X and Y at a constant value. This means that the ratio or product of X and Y will give us a constant if both are in a proportional relationship.

Thus, the constant of proportionality for the  relationship between two variables X and Y would be calculated as:

Constant of proportionality (k) = Y/X. [this is the proportional between the two quantities, X and Y].

Given the table of values, using a pair of points on the table, say, (5, 2.95), we can calculate the constant of proportionality as:

X = 5

Y = 2.95

Constant of proportionality (k) = Y/X = 2.95/5

Constant of proportionality (k) = 0.59 pounds per dollar.

Therefore, the constant of proportionality between the cost and the number of pounds is: A. 0.59.

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The number 0.22 represents the population proportion and the correct way to represent it is p = 0.22.

Statistics is a mathematical tool defined as the study of collecting data, analysis, understanding, representation, and organization. Statistics is described as the procedure of collecting data, classifying it, displaying that in a way that makes it easy to understand, and analyzing it even further.

It is given that:

It is given that:

The Department of Motor Vehicles reports that the proportion of all vehicles registered in California that are imported is 0.22.

The number 0.22 represent the population proportion.

The population proportion can be represented by the letter p:

p = 0.22

Thus, the number 0.22 represents the population proportion, and the correct way to represent it is p = 0.22.

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Answer:

  $711.23

Step-by-step explanation:

We assume the entire closing cost went to reducing the principal of the loan. Then the amount borrowed was $147,192.

The amortization formula tells you the monthly payment.

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

P is the principal, r is the annual rate, and t is the number of years.

The monthly payment is ...

  A = $147,192(0.041/12)/(1 -(1 +0.041/12)^-360) ≈ $711.23

Jeff's monthly payment is $711.23.

Solution:

Let x be the number

Triple the number=3x

According to the question,

3x+5=50

⇒3x+5−5=50−5          [Subtract 5 from both sides]

⇒3x=45

⇒ x = 45/3

​           [Divide 3 from both sides]

⇒x=15

∴15 is the required number. When it is tripled and increased by 5, we get 50.

Answer:

15√3

Step-by-step explanation:

after grouping and adding them to get 15√9

then you apply Surds

Answer:

43

Step-by-step explanation:

I would see a pattern like this

1 4 6 2 5 7 8 9 7 15 41 ?

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

start pattern key

then

15 = 8 × 2 - 1

a10 = a7 × a4 - a1

41 = 9 × 5 - 4

a11 = a8 × a5 - a2

? = 7 × 7 - 6 = 43

a12 = a9 × a6 - a3

Answer:

[tex]21 \sqrt{2} [/tex]

Step-by-step explanation:

See attached image.

Step-by-step explanation:

4x-2y = 9 ...1

2x-y = -6 ...2

if ...2 × 2

4x-2y = -12

9 is not equal to -12

The contract price is $8,750,000

What is contract price?

Contract price means the amount Lao Construction Company charged the customer for total contract's execution.

We need to ascertain the percentage completion of the project first and foremost, which is the total costs incurred to date divided by the contract's total costs.

cost incurred to date=$ 1,500,000

total contract's cost=cost incurred to date+ expected future costs

total contract's cost=$1,500,000+$6,000,000

total contract's cost=$7,500,000

% completion=$1,500,000/$7,500,000

% completion=20%

gross profit recognized=(contract price*% completion)-costs incurred till date

gross profit recognized=$250,000

contract price=unknown(assume it is X)

% completion=20%

cost incurred to date=$ 1,500,000

$250,000=(20%*X)-$1,500,000

$250,000+$1,500,000=0.20X

$1,750,000=0.20X

X=$1,750,000/0.20

X=$8,750,000

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Jet 1 moves with a speed of  672 mi/h, while jet 2 moves with a speed of  672 mi/h + 80mi = 752 mi/h.

Let's say that the rate (or speed) of the slower jet is R, then the rate of the faster jet is:

R + 80mi/h

Now, if we step on any of the two jets (such that we view it as if it doesn't move) the other jet will move with a speed equal to:

S = R + R + 80mi/h

We know that after 8 hours, the to jets are 11,392 mi apart, then we know that:

(R + R + 80mi/h)*8h = 11,392 mi

Now we can solve that for R:

2*R + 80mi/h = 11,392 mi/8h = 1,424 mi/h

R = 1,424 mi/h - 80mi/h)/2 = 672 mi/h

So Jet 1 moves with a speed of  672 mi/h, while jet 2 moves with a speed of  672 mi/h + 80mi = 752 mi/h.

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The equation for the reflected function is:

g(x) =  (1/2)*(3)^(-x)

Here we know that function g(x) is a reflection of f(x) across the y-axis.

Remember that the reflection is written as:

g(x) = f(-x)

Here we know that:

f(x) = (1/2)*(3)^x

Then, replacing that in the equation for g(x), we get:

g(x) =  f(-x) = (1/2)*(3)^(-x)

g(x) =  (1/2)*(3)^(-x)

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Due to length restrictions, we kindly invite to check the explanation herein for further details of the hyperbola.

Herein we have an hyperbola whose axis of symmetry is parallel to the y-axis and the major semiaxis length is in the y-direction. By analytical geometry, we know that eccentricities of hyperbolae are greater than 1.

a) The formula for eccentricity is:

e = √(a² + b²) / a      (1)

Where:

If we know that a = 4 and b = 3, then the eccentricity of the hyperbola is:

e = √(4² + 3²) / 4

e = 5 / 4

b) The coordinates of the two vertices of the hyperbola are:

V(x, y) = (h, k ± a)      (2)

Where (h, k) are the coordinates of the center of the hyperbola.

V₁ (x, y) = (0, 4), V₂ (x, y) = (0, - 4)

The coordinates of the foci of the hyperbola are:

F(x, y) = (h, k ± c), where c = √(a² + b²).     (3)

c = √(4² + 3²)

c = 5

F₁ (x, y) = (0, 5), F₂ (x, y) = (0, - 5)

The equations of the asymptotes of the hyperbola are:

y = ± (a / b) · x

y = ± (4 / 3) · x      (4)

And the equations of the directrices of the hyperbola are:

y = k ± (2 · a - c)

y = 0 ± (8 - 5)

y = ± 3     (5)

The graph is presented in the image attached below.

c) The parametric equations for the hyperbola are the following formulae:

y = ± a · cosh t   →   y = ± 4 · cosh t      (6)

x = b · sinh t   →   x = 3 · sinh t     (7)

d) First, we determine the slopes of the two tangent lines by implicit differentiation:

m = (16 · x) / (9 · y)

m = (16 · 2.3) / [9 · (± 4.807)]

m = ± 0.851

Second, we find the intercept of each tangent line:

(x, y) = (2, 4.807)

b = 4.807 - 0.851 · 2

b = 3.105

y = 0.851 · x + 3.105      (8)

(x, y) = (2, - 4.807)

b = - 4.807 - (- 0.851) · 2

b = - 3.105

y = - 0.851 · x - 3.105      (9)

e) The definite integral of the arc length of the hyperbola is presented below:

[tex]s = \int\limits^{2}_{1} {\sqrt{\left(\frac{dx}{dt} \right)^{2}+\left(\frac{dy}{dt} \right)^{2}}} \, dt[/tex]

If we know that dx / dt = a² · sinh² t and dy / dt = b² · cosh² t, then the definite integral for the arc length is:

[tex]s = \int\limits^2_1 {\sqrt{a^{2}\cdot \sinh ^{2}t +b^{2}\cdot \cosh^{2}t}} \, dt[/tex]      (10)

f) We apply the following substitutions on (1): x = r · cos θ, y = r · sin θ. Then, we have the polar form by algebraic handling:

r(θ) = (a · b) / (b² · sin² θ - a² · cos² θ)     (11)

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The angles and length of the triangle area as follows:

The sum of angles in a triangle is 180 degree.

Therefore,

∠DBC = 180 - 29 - 90 = 61°

Hence,

∠A = 180 - 29 - 61 - 55 = 35°

∠CBD = 61°

Using trigonometric ratios,

sin 55 = opposite / hypotenuse

sin 55 = AD / 40

AD = 40 sin 55

AD = 32.7660817716

AD = 32.77 units

cos 55 = adjacent / hypotenuse

cos 55 = BD / 40

BD = 40 cos 55

BD = 22.943057454

BD = 22.94 units

sin 29 = 22.94 / BC

BC = 22.94 sin 29

BC = 11.1215326885

BC = 11.12 units

cos 29 = CD / 11.12

CD = 11.12 cos 29

CD = 9.72577114339

CD = 9.73 units

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Answer:

40 + 10 + 30 = 50 + 30 = 80

Step-by-step explanation:

40 + 10 + 30 = 50 + 30 = 80

Answer:

10(4+3+1)

Step-by-step explanation:

Expand 40+30+10 by the distributive property:: 10(4+3+1)

The equation of the line that passes through the given points is

y = 1/3x + 5.

The formula for the equation of a line passing through two points (x1, y1) and (x2, y2) is

[tex](y-y1) = \frac{(y2-y1)}{(x2-x1)} (x-x1)[/tex]

Where the fraction (y2 - y1)/(x2 - x1) is the slope of the line denoted by 'm'.

It is given that, a line passes through the points (-3,4) and (6,7).

So, the equation of the line is

[tex](y-y1) = \frac{(y2-y1)}{(x2-x1)} (x-x1)[/tex]

On substituting x1 = -3, y1 = 4, x2 = 6, and y2 = 7

(y - 4) = [(7 - 4)/(6 + 3)](x + 3)

⇒ (y - 4) = (3/9)(x + 3)

⇒ (y - 4) = 1/3(x + 3)

⇒ y- 4 = 1/3x + 1

⇒ y = 1/3x + 1 + 4

∴ y = 1/3x + 5

Thus, the equation of the line passing through the points (-3,4) and (6,7) is y = 1/3x + 5. Where the slope m = 1/3.

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Esto significa que debemos tener 58 páginas de plástico para contener las 517 tarjetas.´

Sabemos que cada página puede almacenar hasta 9 cartas.

Entonces queremos ver cuantos grupos de 9 cartas hay en el conjunto de 517, para ver esto tomamos el cociente entre 517 y 9.

N = 517/9  = 57.44

Y no podemos tener un numero racional, así que debemos redondear al proximo número entero, que es 58.

Esto significa que debemos tener 58 páginas de plástico para contener las 517 tarjetas.

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Answer:

y=1/4x-1/2

Step-by-step explanation:

The value of cos(L) in the triangle is Five-thirteenths

Right triangles are triangles whose one of its angle has a measure of 90 degrees

The value of a cosine function is calculated as:

cos(L) = Adjacent/Hypotenuse

The hypotenuse is calculated as

Hypotenuse^2 = Opposite^2 + Adjacent^2

So, we have:

Hypotenuse^2 = 12^2 + 5^2

Evaluate

Hypotenuse^2 = 169

Take the square root of both sides

Hypotenuse = 13

So, we have

Adjacent = 5

Hypotenuse = 13

Recall that

cos(L) = Adjacent/Hypotenuse

This gives

cos(L) = 5/13

Hence, the value of cos(L) in the triangle is Five-thirteenths

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