You may need to use the appropriate appendix table or technology to answer this question. A binomial probability distribution has p-0.20 and n 100. (a) What are the mean and standard deviation? mean 20 standard deviation 4 (b) Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain, O Yes, because np z 5 and n(1 -p) 2 5. O No, because np 5 and n(1 -P) 5 O Yes, because np 5 and n(1 -P)5. O No, because np < 5 and n(1 - p)5 O Yes, because n 2 30. (e) What is the probability of exactly 23 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.) 0.0755 (a) what is the probability of 16 to 24 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.) 0.6822 (e) What is the probability of 13 or fewer successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.) 0.0308

Answer:

1.93233498E244

Step-by-step explanation:

Answer:

3.14159265

Step-by-step explanation:

Let's prove

Sum of all interior angles of a quadrilateral is 360°

\(\\ \rm\rightarrowtail 6x+9x+9x+6x=360\)

\(\\ \rm\rightarrowtail 12x+18x=360\)

\(\\ \rm\rightarrowtail 30x=360\)

\(\\ \rm\rightarrowtail x=12\)

The value of x is,

⇒ x = 12

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

Quadrilateral ABCD is shown in figure, with m ∠A=(9x)°, m ∠B=(6x)°,

m ∠C=(9x)°, and m ∠D=(6x)°

Now, We know that;

The sum of all angles in the Quadrilateral are 360°.

Hence , We get;

⇒ ∠A + ∠B + ∠C + ∠D = 360°

⇒ 9x + 6x + 9x + 6x = 360

⇒ 30x = 360

⇒ x = 360/30

⇒ x = 12

Thus, The value of x is,

⇒ x = 12

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The probability that the obstetrician has delivered no child with polydactyly is 0.8187.

To find the probability that the obstetrician has delivered no child with polydactyly, we can use the formula:

P(no polydactyly) = \((1 - P(polydactyly))^{number of births}\)

First, we need to find the probability of a child having polydactyly. This is given as 1 in every 500, which can be expressed as a decimal: 1/500 = 0.002.

Next, we find the probability of a child not having polydactyly: 1 - 0.002 = 0.998.

Now, we can find the probability of the obstetrician delivering no child with polydactyly in 100 unrelated and independent births by raising the probability of no polydactyly to the power of the number of births (100):

P(no polydactyly in 100 births) = (0.998)¹⁰⁰ ≈ 0.8187

So, the probability that the obstetrician has delivered no child with polydactyly is approximately 0.8187.

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A rhombus with MK = 24 m, JL = 20, ∠MJL = 50°. So, NK = 24 m, NL = 24.8 m, ML = 24.8 m, and JM = 20 m.

We need the information about the measurements or a description of the missing measures in the rhombus. We can make it MK = 24 m, JL = 20, ∠MJL = 50° for example. Since it's a rhombus, all sides are equal in length. Therefore, NK = MK = 24 m, JM = JL = 20 m, and ML = NL.

To find ML (or NL), we can use the Law of Cosines on the triangle MJL. In this case,

ML² = JM² + JL² - 2(JM)(JL)cos(∠MJL):

ML² = 20² + 20² - 2(20)(20)cos(50°)

ML² = 400 + 400 - 800cos(50°)

ML² ≈ 617.4

Taking the square root of both sides, we get ML ≈ √617.4 ≈ 24.8 m.

So, NK = 24 m, NL = 24.8 m, ML = 24.8 m, and JM = 20 m.

The complete question is The quadrilateral below is a rhombus. Given MK = 24 m, JL = 20, ∠MJL = 50°. Find NK, NL, ML, and JM. Any decimal answers should be rounded to the nearest tenth.

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The solution to the initial value problem using the method of separation of variables is y = (x³/3) - (1/2)x + 4/3.

To solve the initial value problem y' = x² - 1/2 with the initial condition y(2) = 3, we can use the method of separation of variables. Here are the steps:

Step 1: Separate the variables

Write the given differential equation in the form:

dy/dx = x² - 1/2

Step 2: Integrate both sides

Integrate both sides of the equation with respect to x:

∫dy = ∫(x² - 1/2) dx

Integration yields:

y = (x³/3) - (1/2)x + C

Step 3: Apply the initial condition

To find the constant C, substitute the initial condition y(2) = 3 into the equation obtained in Step 2:

3 = (2³/3) - (1/2)(2) + C

Simplifying the equation:

3 = 8/3 - 1 + C

3 = 8/3 - 3/3 + C

3 = 5/3 + C

Therefore, C = 3 - 5/3 = 9/3 - 5/3 = 4/3.

Step 4: Write the final solution

Substitute the value of C back into the equation obtained in Step 2:

y = (x³/3) - (1/2)x + 4/3

So, the solution to the initial value problem y' = x² - 1/2, y(2) = 3 is y = (x³/3) - (1/2)x + 4/3.

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Answer:

answer is 4

Step-by-step explanation:

12 / 3

The number of bottles that can be bought with $3 is 4 bottles.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

12 bottles = $9

Divide 3 into both sides.

4 bottles = $3

Thus,

4 bottles can be bought for $3.

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Based on the length of a certain bacterium and the measurement of the colony, the total length of the colony is 1.431 x 10².

The length of the colony can be calculated as:

= Length of bacterium x length of colony

Solving gives:

= 2.7 x 10⁻² x 5.3 x 10³

= 0.027 x 5,300

= 143.1

= 1.431 x 10²

In conclusion, the total length of the colony if put in a straight line is 1.431 x 10².

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Answer:

n = 3

Step-by-step explanation:

The entire equation needs to cancel out and for q to cancel out, n needs to be 3.

To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -5 and b = 286.

x = -b/2a

x = -286/(2(-5))

x = 28.6

So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).

Therefore, the widgets should be sold for $28.60 to maximize the company's profit.

Hope I helped ya...

Answer:

29 cents

Step-by-step explanation:

The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:

\(y=-5x^2+286x-2275\)

The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.

The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:

\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)

For the given equation, a = -5 and b = 286.

Substitute these into the formula:

\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)

\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)

\(\implies x_{\sf vertex}=\dfrac{286}{10}\)

\(\implies x_{\sf vertex}=28.6\)

Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.

Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.

Answer:

50.24

Step-by-step explanation:

d equals 2r r=4 four squared equals 16 16 * π = 50.24

Answer:

If r=0, there is absolutely no relationship between the two variables.

Step-by-step explanation:

a) It is like winning a free entry ticket raffle.

b) The probability that you will win something (either a free raffle entry or a cash prize -  \(\frac{1}{3}\) .

c) The probability that you win nothing at all is - \(\frac{2}{3}\)

a)  One of every five people plays and gets a free entry in a raffle.

  P(Free entry)= \(\frac{1}{5}\)

Two of every fifteen people play and win a small cash prize.

   P( Small prize)= \(\frac{2}{15}\)

  P(Free entry) = \(\frac{1}{5}\)

                        = \(\frac{1 . 3}{5 . 3}\) = \(\frac{3}{15}\)

​                 \(\frac{3}{15}\) > \(\frac{2}{15}\)

​    P(Free entry) > P( Small prize)

b)  P(Win something)   =P(Free entry)  +  P(Small prize)

                                     = \(\frac{1}{5} + \frac{2}{15}\)

                                     = \(\frac{3}{15} + \frac{2}{15}\)      ( use addition)

                                     = \(\frac{3 + 2}{15}\)

                                     = \(\frac{5}{15}\) = \(\frac{1}{3}\)

c) P(Win nothing)  +  P(Win something) = 1

  P(Win nothing) = 1 - P(Win something)

   P(Win nothing)  = 1 - \(\frac{1}{3}\)         (use subtraction)

   P(Win nothing) = \(\frac{3}{3} - \frac{1}{3}\)

   P(Win nothing) = \(\frac{2}{3}\)

So,

a) It is like winning a free entry ticket raffle.

b) The probability that you will win something (either a free raffle entry or a cash prize -  \(\frac{1}{3}\) .

c) The probability that wins nothing at all is - \(\frac{2}{3}\)

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The complete question is :

The city has created a new contest to raise funds for a big Fourth of July fireworks celebration. People buy tickets and scratch off a special section on the ticket to reveal whether they have won a prize. One out of every five people who play gets a free entry in a raffle. Two out of every fifteen people who play win a small cash prize. a. If you buy a scratch-off ticket, is it more likely that you will win a free raffle ticket or a cash prize? Explain your answer. b. What is the probability that you will win something (either a free raffle entry or a cash prize)? c. What is the probability that you will win nothing at all? To justify your thinking, write an expression to find the complement of winning something.

​

​

Answer:

0

Step-by-step explanation:

Since you didn't attach an image of the graph I'll have to do this the hard way.

x + 2y = 2  (1)

2x + 4y = -8 (2)

x + 2y = -4 (Divide equation (2) by 2)

0 = 6 (Subtract the third equation from the first)

Since 0 is not equal to 6 the answer is No Solutions.

Answer:

no solutions

Step-by-step explanation:

x+2y=2

2x+4y=−8​

Multiply the first equation by -2

-2x -4y = -4

Add this to the second equation

-2x-4y = -4

2x +4y = -8

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

0x+0y = -12

0 = -12

This is never true so there are no solutions

Answer:

12x + 3y

Step-by-step explanation:

Not sure what the blanks are, but here is what I did

8x + y + 4x + 2y

(combine like terms)

8x + 4x + 3y

(combine like terms)

12x + 3y

Answer:

20X=Y

so 15 lawns mowed

20×15=300

Answer:

A polynomial is a combination of terms separated by

+

or

−

signs. A polynomial does not contain variables raised to negative or fractional exponents, variables in the denominator or under a radical, or any special features such as trigonometric functions, or logarithms.

Polynomial

Step-by-step explanation:

The generalized 9th degree polynomial is given below \(a_1x^9+a_2x^8+a_3x^7+a_4x^6+a_5x^5+a_6x^4+a_7x^3+a_8x^2+a_9x+a_{10}=0\) where \(a_1,a_2,....a_9\) are the coefficients and \(a_{10}\) is constant. The polynomial \(x^9\) is known as the nonic equation.

Given :

Polynomial  -- \(x^9\)

The following steps can be used in order to classify the given polynomial:

Step 1 - The generalized polynomial equation is given below:

\(a_1x+a_2x^2 + a_3x^3+a_4x^4+a_5x^5+.............+a_nx^n=0\)

where \(a_1,a_2,....,a_n\) are the coefficients.

Step 2 - The generalized quadratic equation is given below:

\(ax^2+bx+c=0\)

where a, b are the coefficients and c is the constant.

Step 3 - So the generalized 9th degree polynomial is given by:

\(a_1x^9+a_2x^8+a_3x^7+a_4x^6+a_5x^5+a_6x^4+a_7x^3+a_8x^2+a_9x+a_{10}=0\)

where \(a_1,a_2,....a_9\) are the coefficients and \(a_{10}\) is constant.

The polynomial \(x^9\) is known as the nonic equation.

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Irrational numbers are numbers that could be written in fractions. Like 1/2 or 5/10. Both are fractions and can be written like them.

Answer:

there is no question but i think out of a,b,c and e i think b or c

Step-by-step explanation:

sorry

The smallest number of coins you could have had before finding the bag of 53 coins is 371. which is more than 200.

There are seven bags, so there are 7x coins in total:

7x = T.

Since the number of coins in each bag must be an integer, (T + 53) must be a multiple of 8. We know that T = 7x, so we can write this as follows:

(7x + 53) ≡ 0

(mod 8)This means that 7x ≡ 3 (mod 8).

The solutions to this congruence are

x ≡ 3, 11 (mod 8).

Since x is a positive integer, we take

x = 11

(the other possibility, x = 3,

leads to a smaller value for T).

Therefore, T = 7x = 77, and the total number of coins after the bag of 53 coins is found is

T + 53 = 130.

After redistributing the coins into eight equal bags, each bag contains 16 coins.

Therefore, the number of coins you had initially was

7x = 77,

so the smallest number of coins you could have had before finding the bag of 53 coins is

77 - 53 = 24.

After redistributing the coins, you had

8 × 16 = 128 coins left,

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Answer:

5:1

Step-by-step explanation:

I think

Answer:

960 I believe.

Step-by-step explanation:

Answer:

yes get those raisins taylor

Step-by-step explanation:

woo! go taylor

Answer:

(a) 8000 times 5 times 2 = 800

Answer:

$7.22 per foot squared

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

We need the unit rate here. The best way to do this is to write a proportion.

Let x = the $ for 1 ft.

130/18 = x/1

130 = 18x

Divide by 18

x = $7.22

Now, we check to make sure we are correct.

130/18 = 7.22/1

130 = 130 ✅

Answer:

550

Step-by-step explanation:

To get to sea level from the submarine we need to raise 200 feat, and then 350 more to reach the helicopter. 200+350=500 overall

The slope of the line tangent to the polar curve

r=4θ^2 at the point where

θ=π/4 is -8 Given that the polar curve is

r = 4θ². We have to find the slope of the tangent line at

θ = π/4. Now, we know that

r = f(θ) which is defined as below

f(θ) = 4θ²Let's find the first derivative of r with respect to θ. We get

dr/dθ = d/dθ (4θ²)

=> 8θAt θ

= π/4,

dr/dθ

= 8(π/4)

= 2π We can find the slope of the tangent line as below

y/x = tan(θ)

=> y' / x' = slope of the tangent line

=> slope of the tangent line

= y' / x'At θ

= π/4, the point on the curve is (4(π/4)²,

π/4) = (π, π/4) Now, we know that

x = r cosθ and

y = r sinθ Differentiating both the above equations with respect to θ, we get

dx/dθ = cosθ(-4θsinθ) + r cosθ

= -4θsinθcosθ + 4θ²cosθ

dy/dθ = sinθ(4θcosθ) + r sinθ

= 4θsin²θ + 4θ²sinθAt

θ = π/4, we have

dx/dθ = -2√2 and

dy/dθ = 2√2 Hence, slope of the

tangent line = dy/dθ / dx/dθ

= (2√2) / (-2√2)

= -1. So, slope of the tangent line at

θ = π/4 is -8. Therefore, the correct answer is -8.

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For the lines to be parallel the two angles need to be equal to each other:

128-x = x

Add 1x to both sides

128 = 2x

Divide both sides by 2:

X = 128/2

X = 64

Answer: x = 64

When the weight moves from x = -8 cm to x = 8 cm, the spring moves from its maximum stretched position to its maximum compressed position.Hence, the spring oscillates between its maximum stretched and compressed positions when the weight is set in motion. Therefore, the spring is a simple harmonic oscillator.

Given: Displacement x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0. To find: What is the spring?Explanation:We know that displacement is given by x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0.Comparing this with the standard equation, x

= Acos(ωt+ φ)A

= amplitude

= 8 cmω

= angular frequencyφ

= phase angleWhen the spring is at equilibrium position, the weight attached to the spring does not move. Hence, no force is acting on the weight at the equilibrium position. Therefore, the spring is neither stretched nor compressed at the equilibrium position.Now, the spring is set in motion resulting in a displacement of x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0. The maximum displacement of the spring is 8 cm in the positive x direction. When the weight is at x

= 8 cm, the restoring force of the spring is maximum in the negative x direction and it pulls the weight towards the equilibrium position. At the equilibrium position, the weight momentarily stops. When the weight moves from x

= 8 cm to x

= -8 cm, the spring moves from its natural length to its maximum stretched position. At x

= -8 cm, the weight momentarily stops. When the weight moves from x

= -8 cm to x

= 8 cm, the spring moves from its maximum stretched position to its maximum compressed position.Hence, the spring oscillates between its maximum stretched and compressed positions when the weight is set in motion. Therefore, the spring is a simple harmonic oscillator.

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The displacement of the weight attached to the spring is given by the equation x = 8 cos t. The amplitude of the motion is 8 centimeters and the period is 2π seconds.

The equation x = 8 cos t represents the displacement of a weight attached to a spring in simple harmonic motion. In this equation, x is measured in centimeters and t is measured in seconds.

The amplitude of the motion is 8 centimeters, which means that the weight oscillates between x = 8 and x = -8.

The period of the motion can be determined from the equation T = 2π/ω, where ω is the angular frequency. In this case, ω = 1, so the period T is 2π seconds.

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Answer:

x = 20

Step-by-step explanation:

\(\frac{10}{x}\) = \(\frac{x}{40}\)

We cross-multiply and get

400 = \(x^{2}\)

\(\sqrt{400}\) = \(\sqrt{x^{2} }\)

x = 20

So, the answer is x = 20