Consider a binomial experiment. if the number of trials is increased, what happens to the expected value? To the standard deviation? Explain

Answer:

Domain is 1 and 7 and range is -5and -4

Step-by-step explanation:

because domain is a first group element and range is a second element of a set

Answer:

$75

My answer might be a bit off since I'm not really sure what you mean by "Rs 80", which I interpreted as $80, but if my interpretation is wrong, you can still use all the same steps and you should get the correct answer

Step-by-step explanation:

So we can represent the price of each tumbler as the variable "P", since it's some unknown value we're solving for. Let's also just say that "T" is the total price that she paid for all of the tumblers.

Using this equation we can derive the following equation.

1000P = T

Since multiplying the price of each glass tumbler times the price of one glass tumbler should equal the entire price.

Now she only sold 900 of them, since 100 were broken, and she sold them each for 80. So knowing this we can find how much she made in total from selling the remaining 900 glass tumblers

900 * 80 = 72,000

Now if she made a loss of 4%, that means the total money she made back, is only 96% the amount of money she paid for the product. The reason for this is (100-4)% represents a 4% loss.

Remember, how T represents the entire price, well we know that 72,000 represents 96% of it's value. To find what x% is of some number, you generally convert the percentage into a decimal by dividing by 100, so to find x% of some variable "a" you generally use the following equation: [tex]a*\frac{x}{100}[/tex] where the value of this expression will be equal to x% of a.

So let's convert 96% to decimal form: [tex]\frac{96}{100} = 0.96[/tex]. Now if we multiply this decimal 0.96 by T, we should get 72,000 since the 72,000 represents 96% of the original value

[tex]0.96T = 72,000[/tex]

To find the original value of T, we simply divide both sides by 0.96

[tex]T = 75,000[/tex]

So now that we know the original total price, we can use the original equation we derived to solve for P, which represents the price of each individual tumbler.

Original Equation

[tex]1000P = T[/tex]

Substitute 75,000 as T

[tex]1000P = 75,000[/tex]

Divide both sides by 1,000

[tex]75=P[/tex]

This means she sold each for 75

Using a linear function, the total charge from parking in the lot for 72 hours is of:

b. $146.

A linear function is modeled by:

y = mx + b

In which:

Both the basic fee, which is the y-intercept, and the hourly fee, which is the slope, are of $2, hence the cost of parking x hours is given by:

C(x) = 2x + 2

Hence the cost for parking 72 hours is:

C(72) = 2 x 72 + 2 = 2 x 73 = $146.

Which means that option b is correct.

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Answer:

J

Step-by-step explanation:

Stephen read about 9 pages more each week.

What is a linear equation in math?

If stephen reeds 278 pages in 7 week ,

To find number of pages read in 1 week, divide 278 by 7

                    = [tex]\frac{278}{7}[/tex]  ⇒ 39.71

Another person reads 31 pages each week.

So stephen reads allmost 40  per week and alice 31.

Then, we need to find the difference between them

Difference = 40 - 31 = 9

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The 90% confidence interval for the true difference between the population proportions is [ - 0.0908, - 0.0092]

Given,

[tex]N_{1}[/tex] = 731

[tex]N_{2}[/tex] = 644

[tex]P_{1}[/tex] = 0.33

[tex]P_{2}[/tex] = 0.28

z score for 90% confidence interval = 1.645

Here, the confidence interval formula :

( [tex]P_{1} -P_{2}[/tex]) ± z [tex]\sqrt{\frac{P_{1}(1-P_{1}) }{N_{1} }+ \frac{P_{2}(1-P_{2}) }{N_{2} } }[/tex]

Substituting the values, we get

    (0.33 - 0.28) ± 1.645 [tex]\sqrt{\frac{0.33(1-0.33)}{731}+\frac{0.28(1-0.28)}{644} }[/tex]

=   0.05 ± 1.645 [tex]\sqrt{0.0003024624+0.0003130435}[/tex]

=   0.05 ± 1.645 [tex]\sqrt{0.0006155059}[/tex]

=    0.05 ± 1.645 × 0.0248093914

=    0. 05 ± 0.0408114489

Confidence interval:

- 0.05 - 0.0408114489 = - 0.0908114489 ≈ - 0.0908

- 0.05 + 0.0408114489 = - 0.0091885511 ≈ - 0.0092

The confidence interval for the true difference between the population proportions is [ - 0.0908, - 0.0092]

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Answer:

Maximum/Minimum Value:  (0,−2)   is a local minima (1/8,8)  is a local maxima

Explanation: Use the derivative to find the maximum and minimum

Answer:

Period = ¹/₄

Step-by-step explanation:

The cosine function is periodic, meaning it repeats forever.

Standard form of a cosine function:

f(x) = A cos(B(x + C)) + D

where:

Given function:

[tex]y=-5 \cos (8 \pi x)+3[/tex]

Comparing the given function with the standard form:

[tex]\implies \sf Period=\dfrac{2 \pi}{B}=\dfrac{2 \pi}{8 \pi}=\dfrac{1}{4}[/tex]

Therefore, the period of the given function is ¹/₄.

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The order of magnitude for total attended for a high school football team is 3

The given parameters are:

Average number of fan = 1000

Number of home games = 5

The total number of fans in the 5 games is:

Total number of fans = Average number of fan * Number of home games

Substitute known values in the above equation

Total number of fans = 1000 * 5

Express 1000 as 10^3

Total number of fans = 10^3 * 5

Rewrite the equation as:

Total number of fans = 5 * 10^3

The power of 10 represents the order of magnitude

Since the power of 10 is 3, the order of magnitude is 3

Hence, the order of magnitude for total attended for a high school football team that averages 1,000 fans for each of its 5 home games is 3

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The minimum number of books required to be equally distributed among the students are 1,440 books.

To find the minimum required books so that they can be equally distributed:

The number of students in three sections of class 6th are 32, 36, and 40.

Now, find the LCM od 32, 36, and 40.

The LCM od 32, 36, and 40 will be 1,440.

Therefore, the minimum number of books required to be equally distributed among the students are 1,440 books.

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Answer:

  67.5 cm²

Step-by-step explanation:

The figure can be decomposed into figures whose area formulas you know.

As the attached figure shows, one way to decompose the figure is by extending the horizontal line. This divides the figure into an upper trapezoid and a lower rectangle.

The area of a trapezoid is given by the formula ...

  A = 1/2(b1 +b2)h

where b1 and b2 are the parallel bases, and h is the height.

The bases of the trapezoid in this figure are 6 and 3 cm, and the height is 5 cm. Its area is ...

  A = 1/2(6 cm +3 cm)(5 cm) = 22.5 cm²

The area of a rectangle is given by the formula ...

  A = LW

where L and W represent the length and width, respectively.

The dimensions of the rectangle in this figure are 15 cm long by 3 cm wide. Its area is ...

  A = (15 cm)(3 cm) = 45 cm²

The total area of the figure is the sum of the areas of the trapezoid and rectangle:

  A = (22.5 cm²) + (45 cm²) = 67.5 cm²

The are of the figure is 67.5 cm².

The zeroes of the function g(x) = x² +3x -4 as given in the task content is; x = -4 and x = 1.

It follows from the task content that the function g(x) given in the task content is; g(x) = x² +3x -4.

On this note, it follows that the zeroes of the function can be determined by solving the quadratic function as follows;

x² +4x -x -4 = 0

(x+4) (x-1) = 0

Ultimately, it can be concluded that the values of x which represents the zeroes of the function are; x = -4 and x = 1.

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The numerical expression, 2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3 = 67/24 on simplification using the BODMAS rule.

In the question, we are asked to simplify the numerical expression:

2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3.

To simplify the expression, we will follow the BODMAS rule, where B means Brackets, O means Of, D means Divide, M means Multiplication, A means Addition, and S means Subtraction.

2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3

= 2/3 ÷ 16 + (3/4 + 1/6) ÷ 1/3 {Solving 2⁴ = 16, before proceeding BODMAS}.

= 2/3 ÷ 16 + ((9+2)/12) ÷ 1/3 {Solving Brackets by taking LCM}

= 2/3 ÷ 16 + 11/12 ÷ 1/3 {Simplifying}

= 2/3 * 1/16 + 11/12 * 3/1 {Solving divisions by taking reciprocals}

= 1/24 + 11/4 {Multiplying}

= (1 + 66)/24 {Adding using LCM}

= 67/24 {Simplifying}.

Thus, the numerical expression, 2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3 = 67/24 on simplification using the BODMAS rule.

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The provided question is incomplete. The complete question is:

"Type the correct answer in the box. Use numerals instead of words. For this item, a non-integer answer should be entered as a fraction using / as the fraction bar.

Simplify the numerical expression.

2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3

The expression has a value equal to."

The area of the barn quilt is 3 sq.ft.

The amount of sugar needed to make 1/2 of a batch of cookies is 1/5 of a cup.

Number of boys are practicing hitting the ball = 4

Number of bags of lemons used by Rachel on Tuesday = 1[tex]\frac{3}{4}[/tex]

1. A painted barn blanket needed to be 1 1/3 feet by 2 1/4 feet in size.

Area of the barn quilt = 1 1/3*2 1/4

                                  = 4/3*9/4

                                  = 3 sq. ft.

2. The recipe for Mrs. Smith's oatmeal cookies asks for 2/5 cups of sugar.

Sugar needed for making 1/2 of a batch of cookies = 1/2*2/5

                                                                                 = 1/5 of a cup

3. Six boys are practicing baseball throwing, catching, and hitting in the park. Two thirds of those six youngsters are practicing hitting.

Number of boys practicing hitting the ball = 6*2/3 = 4

4. At the park's lemonade kiosk, Rachel works. She used 1 and 2/5 bags of lemons on Monday. She used 1 and 1/4 times as many lemons on Tuesday as she did on Monday.

Number of bags of lemon used on Tuesday = 7/5*5/4

                                                                     = 7/4

                                                                     = 1 and 3/4 bags

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Answer:

Using the usual notations and formulas,

Using the usual notations and formulas,mean, mu = 3550

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculate

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:Probability that a car randomly selected is less than 3000

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:Probability that a car randomly selected is less than 3000=P(X < 3000) = 0.2636 (to 4 decimals)

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:Probability that a car randomly selected is less than 3000=P(X < 3000) = 0.2636 (to 4 decimals)Probability that a car randomly selected is greater than 3000

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:Probability that a car randomly selected is less than 3000=P(X < 3000) = 0.2636 (to 4 decimals)Probability that a car randomly selected is greater than 3000=1 - P(X < 3000) = 1 - 0.2636 (to 4 decimals) =0.7364 (to 4 decimals)

Answer:

18.0  cm to 1 decimal point.

Step-by-step explanation:

First  work out the unknown side (s) of the right triangle using the Pythagoras theorem:

s^2  = 13^2 - 5^2

       = 169 - 25 = 144

s = sqrt 144 = 12 cm.

Now consider the other triangle:

s = 12

The missing angle = 180 - 65 - 40 = 75 degrees.

By the Sine Rule:

x / sin 75 = 12 / sin40

x = 12 sin 75 / sin 40

  = 18.03

    -

Y receives $30000 less than if the profit were divided in proportion to how much they invested.  

In a proportional tax system, everyone is compelled to pay the same amount of taxes as a percentage of their income.

Profit will Divide into 4 equal parts.

The total Profit for the month is  = $120,000

The party will receive a sum of = $30,000

This shows that Y also receive the same amount

Y = $30,000 (Profit received)

Now

If the Profits were divided in proportion to the investments made .

The proportion on investment made by Y.

The total investment made = $12000+$6000+$25000+$7000

                                            = $50000

Out of this the Amount invested by Y = $25000

The Proportional Profit of Y.

=  (25000/ 50000) x 120000                      

= $60,000

So Y receives 60000 - 30000

                       = 30000

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Based on the scale, the actual length of the Golden Gate Bridge is  68,600 inches.

A scale drawing is a reduced form in terms of dimensions of an original image / building / object. The scale drawing is usually reduced at a constant dimension. An example of a scale drawing is a map.

The scale of a drawing is usually written in this format -  length in the drawing, a colon (:), then the matching length on the original image. An example of a scale is 1 : 19,600. This scale means that 1 inch of the postcard represents 19.600 of the original Golden Gate Bridge.

Actual length of the Bridge = scale x length of the bridge in the postcard

19,600 x 3.5 = 68,600 inches

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Step-by-step explanation:

it is a line, so that is 1 point, where it cuts the x-axis.

in general that means y = 0.

so,

0 = 4x - 3

4x = 3

x = 3/4

the point, where the line cuts the x-axis is

(3/4, 0)

The end behavior of the given polynomial is that as x → -∞ or  x → ∞, then, f(x) → 5

We are given the polynomial;

f(x) = 5x/(x - 25)

Now, we want to find the limits as x → ±∞. Let us rearrange the given polynomial to get; f(x) = 5/(1 - (25/x))

Thus, applying limits we have;'

lim x → ±∞ [5/(1 - (25/x))]

From algebraic limit laws we know that;

If f(x) = k, then;

lim x → +∞ [f(x)] = k

Also, lim x → -∞ [f(x)] = k

Thus, applying limits at infinity to our polynomial gives;

lim x → ±∞ [5/(1 - (25/x))] = 5/(1 - 0) = 5

This is because lim x → ∞ for 1/x is 0.

Thus, f(x) has horizontal asymptotes at y = 5

Thus, we conclude that the end behavior is that as x → -∞ or  x → ∞, then, f(x) → 5

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Samantha and Mia are 13 km apart from each other.

A right triangle's squared sides add up to the hypotenuse's squared length, according to the Pythagorean Theorem.

Mia is 7 kilometers north of Julia's home as she walked at a speed of 7 kilometers per hour.

Samantha walked at an average speed of 11 km/h, and she is now 11 kilometers west of Julia's home.

A right-angled triangle is formed by Julia's house, Mia and Samantha's locations after one hour, and the figure's points.

Hypotenuse of the triangle, which measures distance between the females

the Pythagorean theorem,

H² = P² + B²

H² = 7² + 11²

H² = 49 + 121

H = √170

H = 13.038

H = 13km

Between them, there is a 13 kilometer distance.

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Answer: Option 2

Step-by-step explanation:

Let f(y)=x.

[tex]x=2y+3\\\\x-3=2y\\\\y=\frac{1}{2}x-\frac{3}{2}\\\\f^{-1}(x)=\frac{1}{2}x-\frac{3}{2}[/tex]

The inverse of the function is,

⇒ f ⁻¹(x) = 1/2 (x - 3)

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The function is,

⇒ f (x) = 2x + 3

Now,

We can find the inverse of function as;

⇒ f (x) = 2x + 3

Put y = f (x);

⇒ y = 2x + 3

Solve for x;

⇒ y - 3 = 2x

⇒ x = 1/2 (y - 3)

⇒ f ⁻¹(x) = 1/2 (x - 3)

Thus, The inverse of the function is,

⇒ f ⁻¹(x) = 1/2 (x - 3)

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The sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex] diverges.

For given question,

We have been given a sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex]

We need to determine whether the sequence converges or diverges.

From given sequence we have, [tex]a_{n+1}=\frac{(n+1)^2}{(n+1)^3+5(n+1)}[/tex]

We use Ratio Test.

According to Ratio Test, [tex]r=\frac{a_{n+1}}{a_n}[/tex], where sequence converges if and only if |r| < 1.

Consider,

[tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_n} |\\\\= \lim_{n \to \infty} |\frac{\frac{(n+1)^2}{(n+1)^3+5(n+1)}}{\frac{n^2}{n^3+5n}} |\\\\\\= \lim_{n \to \infty} |\frac{(n+1)^2(n^3+5n)}{n^2[(n+1)^3+5(n+1)]} |\\\\=\infty[/tex]

Since [tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_n} |[/tex] is not defined, the sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex] diverges.

Therefore, the sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex] diverges.

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Based on the amount of money that Jerl had and then the amount that she put away, the possible values of the number of dollars in the original pile of money was ( 200, 440).

The amount that was above $200 that she found can be x which means that the greater side of the inequality is:

= 200 + x

She then gave away $80:

= 120 + x

She gave away 1/3 of the money so the amount left is:

= 2/3 x (120 + x)

The lesser side of the inequality:

(x + 2) - 200 = x

So then:

((120 + x) x 2) / 3 > x

240 + 2x > 3x

240 > x

x < 240

The interval that shows the possible values of the original pile of money is therefore:

( 200, 440)

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The group that would best represent a sample of the study population is: C: one thousand of their customers with a current smart phone data plan.

A sample that best represents a population under study is a sample that is a subset of the entire population, that is, research subjects that are drawn as samples should reflect the general characteristics of the entire population without leaving out any part of the population. Also, a good sample should enable a researcher make generalization.

A sample that is a subset of a population and reflects the characteristics of the general population would not be biased.

Given the situation above, the population of the study are smart phone customers that use dat in the cell phone company. So, a sample that would better represent this general population would be customers that currently have a smart phone plan, since the average amount of data they use is what the cell pone company wants to ascertain.

Therefore, the group that would best represent a sample of the study population is: C: one thousand of their customers with a current smart phone data plan.

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