Two complementary angles are in the ratio 5 to 7 find the angles

The mean and standard deviation for the number of boys in the 950 babies are 475 and 15.41, respectively

From the complete question, we have:

P(boy)= 0.5

Sample size = 950

The mean is then calculated as:

[tex]\bar x = np[/tex]

This gives

[tex]\bar x = 950 * 0.5[/tex]

Evaluate

[tex]\bar x = 475[/tex]

The standard deviation is calculated as:

[tex]\sigma = \sqrt{np(1 - p)[/tex]

This gives

[tex]\sigma = \sqrt{950 * 0.5(1 - 0.5)[/tex]

Evaluate

[tex]\sigma = 15.41[/tex]

Hence, the mean and standard deviation for the number of boys in the 950 babies are 475 and 15.41, respectively

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The probability that exactly 800 chips are acceptable is less than 0.000001

The given parameters are:

The binomial probability is represented as:

[tex]P(x) = ^nC_x * p^x * (1- p)^{n - x}[/tex]

So, we have:

[tex]P(300) = ^{3000}C_{800} * (72\%)^{800} * (1- 72\%)^{3000 - 800}[/tex]

The data values are large.

So, we use a statistical calculator to evaluate the expression

Using the calculator, we have:

P(300) < 0.000001

Hence, the probability that exactly 800 chips are acceptable is very small i.e. less than 0.000001

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The triangle: α = 40°, β = 35°, and a = 10. is b = 8.9, γ = 105°, c = 15.0

If A, B, and C are the measurements of the angles of an oblique triangle, and a, b, and c are the lengths of the sides opposite of the corresponding angles, then the ratios of the a side’s length to the sine of the angle opposite the side must all be the same.

a/ sin A = b/ sin B = c/ sin C

Using Angle sum property in a triangle we have,

α+β+ γ = 180

40+35+ γ=180

γ= 180-75

γ= 105°

Now,

c/ sin γ= a/ sin α

c/ sin 105= 10/ sin 40

c/ 0.96592 = 10 /0.6427

c = 15

again,

b/ sin  β=  a/ sin α

b/ sin 35=  10/ sin 40

b/0.5737= 15.559

b= 8.92

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Answer:

436.6

Step-by-step explanation:

3700×0.118=436.6

The parameters of an Exponential Distribution is D. a > 0

This refers to the distribution of probability with respects to time taken in a Poisson point process.

Hence, we can see that from the previous knowledge of exponential distributions, it is stated that λ > 0 is the parameter of the distribution, and is supported on the interval [0, ∞).

Therefore, option D is correct.

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[tex]20^{\tfrac 52}\\\\=(20^5)^{\tfrac 12}\\\\=\left(20^4 \cdot 20 \right)^{\tfrac 12}\\\\=20^{\tfrac 42} \cdot 20^{\tfrac 12}\\\\=20^2 \sqrt{20}\\\\=400\sqrt{4 \times 5}\\\\=400 \times 2\sqrt 5\\\\=800\sqrt 5[/tex]

Answer:

[tex]800\sqrt{5}[/tex]

Step-by-step explanation:

Given: [tex]\large (20)^\text{$ \dfrac{5}{2} $}[/tex]

Properties of Exponents:

Rational Exponent Property: [tex]\large x^\text{$ \dfrac{m}{n} $} = \large \text{$ \sqrt[n]{x^m} $}[/tex]

Product of Powers Property:

1. Convert into a radical:

[tex]\sqrt[2]{20^5} \implies \sqrt{20^5}[/tex]

2. Simplify the expression:

[tex]\sqrt{20^2\times20^2\times20^1}\\\\\implies \sqrt{20^4\times20}\\\\\implies 20^2\sqrt{20}\\\\\implies 20^2\sqrt{4\times5}\\\\\implies 20^2\times2\sqrt{5}[/tex]

3. Evaluate the power:

[tex]20\times20\times2\sqrt{5}\\\\\implies 400\times2\sqrt{5}[/tex]

4. Multiply:

[tex](400\times2)\sqrt{5}\\\\\implies800\sqrt{5}[/tex]

Triangles 3 and 4 are isosceles right angles because they have same length.

It should be noted be noted that the square has all right angles equal. The largest angle of the triangle is the right angle m.

Here, the triangles are isosceles right angles as both the legs and the acute angles are congruent.

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Answer:

33,75 clients(huh?)

Step-by-step explanation:

75 / 100 = 0,75(1% of all clients)

0,75 * 45 = 33,75(number of business clients)

answer:

1769.344983 or 1769.34 (depends on what you’re rounding to)

explanation:

- the equation for a cylinder‘s surface area is: (2 π r h)+(2 π r^2)

so 2 just means x2

π is just pi

r is your radius and for this equation your radius is 8 cm

and h is your height so for this equation your height is 27.2 cm

- so the equation filled in is:

(2 x π x 8 x 27.2) + (2 x π8^2) = 1769.344983 or 1769.34

(2 x π x 8 x 27.2) = 1367.221123

(2 x π8^2) = 402.1238597

1367.221123 + 402.1238597 = 1769.344983

hope this helps :)

Answer:

68.27%

Step-by-step explanation:

By the Empirical Rule, as 65% and 75% are both one standard deviation apart from the mean of 70%, then this represents 68.27% of the data.

Answer:

4 x y ^2

Step-by-step explanation:

4 x y^2    would be the GFC

3(5x+7)-6(4-2x) - given

15x+21-24+12x - distributive property

27x-3 - combine like terms

[tex]x^3=216\\x=\sqrt[3]{216}=6[/tex]

This is a simple example. You (should) know that [tex]6^3=216[/tex].

But you can solve it like this:

[tex]\begin{array}{r|l}216&2\\108&2\\54&2\\27&3\\9&3\\3&3\\1\end{array}[/tex]

Therefore

[tex]\sqrt[3]{216}=\sqrt[3]{2^3\cdot3^3}=\sqrt[3]{2^3}\cdot\sqrt[3]{3^3}=2\cdot3=6[/tex]

Hi student, let me help you out! :)

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We are asked to find the value of x in the equation [tex]\pmb{x^3=216}[/tex].

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Is x by itself? No, it's cubed, or multiplied times itself three times.

So we need to use the opposite operation.

The opposite of cubing is taking the cube root, so we take the cube root of both sides:

[tex]\star~\large\pmb{\sqrt[3]{x^3}=\sqrt[3]{216}}[/tex]

On the left, the cube root sign and the cube cancel, because they're opposite, and we're left with x.

On the right, we take the cube root of 216, which gives us:

[tex]\star~\large\pmb{x=6}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students :)

Answer:

x=2

Step-by-step explanation:

axis of symmetry is

x-2=0

or

x=2

Answer:

Graph B. On a coordinate plane, a vertical dashed line at (2, 0) is parallel to the y-axis.

Answer:

2/5

Step-by-step explanation:

The equation connecting C,A and n is  C = 25A - [tex]\frac{49990000}{n}[/tex]

Variation is a mathematical term used to show how a quantity behaves when one quantity increases or decreases.

Analysis:

C = AK + M/n

where K and M are constants

when n = 1000, A = 5000, C = 75010

75010 = 5000K + M/1000-----------1

50004 = 10000k + M/200-------------2

solving simultaneously,  K = 25, M = -49990000

C = 25A - 49990000/n

In conclusion, the equation connecting C,A and n is C = 25A - 49990000/n

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x²+3x

= x×x+3×x

= x(x+3)

The mean, median, and midrange of the given that are 66, 66 and 66 respectively.

Option D) Mean = 66, median = 66, midrange = 66 is the correct answer.

Mean is the sum total of the number divided by number of terms

Median is the middle number when arranged in ascending or descending order.

Midrange is the average of the sum of the maximum number and the minimum number.

Given that;

First, we arrange in ascending order.

60, 62. 64, 66, 68, 70, 72

Mean = ( 60 + 62 + 64 + 66 + 68 + 70 + 72 ) / 7

Mean = 462 / 7

Mean = 66

Median = 66

66 is the middle number.

Range = ( Max + Min ) / 2

Range = ( 72 + 60 ) / 2

Range = 132 / 2

Range = 66

Therefore, the mean, median, and midrange of the given that are 66, 66 and 66 respectively.

Option D) Mean = 66, median = 66, midrange = 66 is the correct answer.

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Answer:

15400 in² :)))!

Step-by-step explanation:

Input Data:

Radius = 70 in

Objective:

Find the area of the circle.

Solution:

Area = πr2

= 3.14 x (70) ^2

= 3.14 x (4900)

Area = 15400 in²

Answer:

9 feet, 108 inches, 274.32 cm, 2.7432 meters

Step-by-step explanation:

Not enough information is given to answer.

You didn't provide the list of "these" to choose from, but I can just list some potential answers I could see being an option.

3 yards = 9 feet [1 yard = 3 feet. 3 yards = 9 feet]

             9 feet is also 108 inches [1 foot = 12 inches. 9 feet = 108 inches]

3 yards = 108 inches

{There are 91.44 cm in a yard} (1 yard = 91.44 cm. 3 yards = 274.32 cm),

3 yards = 274.32 cm

3 yards = 2.7432 meters (1 yard = 0.9144 meters; 3 yards = 2.7432 meters)

Answer:

4 times

Step-by-step explanation:

If the smaller container only holds 2 liters, you would have to divide 8 by 2 which is 4.

Answer:

4 times

Step-by-step explanation:

Its 4 times cause 8/2=4

The simplest form of the given ratios are : 10:3 , 1:3 , and 12:1

A ratio indicates how many times one number contains another.

Here, for given ratio

2 litres : 600 ml    = 2000 ml : 600 ml

                             = 20 : 6

                            = 10 : 3

8 h : 1 day       =  8 hrs : 24 hrs

                        = 8:24

                       = 1 : 3

3 km : 250 m = 3000 m : 250 m

                      = 3000 : 250

                      = 300 : 25

                     = 12 : 1

Thus, the simplest form of the given ratios are : 10:3 , 1:3 , and 12:1.

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Answer:

Its A

Step-by-step explanation:

Answer:

AC ≈ 17.3 , BC ≈ 5.3

Step-by-step explanation:

using the tangent ratio in right triangle ACD

tan51° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{AD}[/tex] = [tex]\frac{AC}{14}[/tex] ( multiply both sides by 14 )

14 × tan51° = AC , then

AC ≈ 17.3 ( to the nearest tenth )

using the cosine ratio in right triangle ABC

cos72° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{BC}{17.3}[/tex] ( multiply both sides by 17.3 )

17.3 × cos72° = BC , then

BC ≈ 5.3 ( to the nearest tenth )

The reason the "+ C" is not needed in the antiderivative when evaluating a definite integral is; The C's cancel each other out as desired.

Let us say we want to estimate the definite integral;

I = [tex]\int\limits^a_b {f'(x)} \, dx[/tex]

Now, for any C, f(x) + C is an antiderivative of f′(x).

From fundamental theorem of Calculus, we can say that;

[tex]I = \int\limits^a_b {f'(x)} \, dx = \phi(a) - \phi(b)[/tex]

where Ф(x) is any antiderivative of f'(x). Thus, Ф(x) = f(x) + C would not work because the C's will cancel each other.

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Answer:

[tex]\text{The quotient is}~ x^2 +2x +5 \\\\\text{The remainder is}~ -3[/tex]

Step-by-step explanation:

Using it's concept, it is found that the domain of the graphed function is given as follows:

D. [tex]-4 \leq x \leq 2[/tex]

It is the set that contains all possible input values for the function. In a graph, it is given by the values of x.

In this graph, x assumes values between -4 and 2, inclusive due to the closed circle, hence the domain is given by:

D. [tex]-4 \leq x \leq 2[/tex]

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Answer: It will arrive at 5:55 P.M

Step-by-step explanation: