Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol


(,,)


(


μ


,


p


,


σ


)


for the indicated parameter.



An entomologist writes an article in a scientific journal which claims that fewer than 16 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light.





Group of answer choices



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H


0


:


<0. 0016


p


<


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1


H


1


:


≥0. 0016


p


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>0. 0016


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>


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:


≤0. 0016


p


≤


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=0. 0016


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>0. 16

The required work done in lifting the laptop to a height of 2 feet will be 263.79 foot-poundal.

Total weight of the laptop is 4.1 pounds

Acceleration due to gravity = 32.17 ft/\(s^{2}\)

Now the height to which the laptop has been lifted = 2 feet

Since, there is no mentioned velocity of the laptop, therefore the kinetic energy will be zero

Therefore, the total work in lifting the laptop will be equal to the change in potential energy.

Potential energy is the energy that comes by virtue of its position with reference to other

Therefore, potential energy = mgh

Where, m = mass of the laptop = 4.1 pounds

g = acceleration due to gravity = 32.17 ft/\(s^{2}\)

h = height to which the laptop is lifted =  2 feet

Therefore potential energy = (4.1)(32.17)(2) = 263.79 foot-poundal

263.79 foot-poundal is the required work done.

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so what is really the answer?

The value of x is 35°

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

Angles on parallel lines can be ;

Corresponding to each other

Alternate to each other and

Vertically opposite to each other

In these cases , the angles are equal.

Therefore;

4x + 7 = 6x -63( corresponding angles)

collect like terms

4x - 6x = -63 -7

-2x = -70

divide both sides by -2

x = -70/-2

x = 35

Therefore the value of x is 35°

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Answer:

(-2, -3)

Step-by-step explanation:

If a segment having extreme ends as \((x_1,y_1)\) and \((x_2,y_2)\) is divided by a point (x, y) in the ratio of m:n,

x = \(\frac{mx_2+nx_1}{m+n}\)

y = \(\frac{my_2+ny_1}{m+n}\)

Since, a line RT has extreme ends as R(-5, 3) and T(-1, -5) then a point S(x, y) which divides RT in the ratio of 3 : 1 will be,

x = \(\frac{3(-1)+1(-5)}{3+1}\)

  = \(\frac{-8}{4}\)

  = -2

y = \(\frac{3(-5)+1(3)}{3+1}\)

  = \(-\frac{12}{4}\)

  = -3

Therefore, coordinates of the point S will be (-2, -3).

You will be able to withdraw approximately $3,076.32 at the end of 5 years.

To calculate the amount you will be able to withdraw at the end of 5 years, we can use the future value formula for compound interest.

The formula for calculating the future value (FV) of a present value (PV) invested at an annual interest rate (r) for a certain number of years (t) is:

\(FV = PV * (1 + r)^t\)

Given:

PV = $2,300

r = 6% = 0.06 (decimal representation)

t = 5 years

Substituting these values into the formula, we get:

FV = $2,300 * \((1 + 0.06)^5\)

Calculating the expression inside the parentheses:

\((1 + 0.06)^5 = 1.338225\)

Multiplying the present value by this factor:

FV = $2,300 * 1.338225

FV ≈ $3,076.32

Therefore, you will be able to withdraw approximately $3,076.32 at the end of 5 years.

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You deposit $2,300 into an account that pays 6% per year. Your plan is to withdraw this amount at the end of 5 years to use for a down payment on a new car. How much will you be able to withdraw at the end of 5 years? Do not round intermediate calculations. Round your answer to the nearest cent

Answer:

93 cm

Step-by-step explanation:

Answer:

2/3a - 1/6 =1/3

2/3a=1/3+1/6

2/3a=1/2

a=1/2×3/2=3/4

:.a=3./4

Answer:

Option i) At least 64 of the numbers are greater than or equal to 35 must be true

Since the median is 35, we know that there are 63 numbers greater than 35 and 63 numbers smaller than 35. However, since there is an odd number of total numbers (127), the median itself must be included in one of these groups. Therefore, there are at least 64 numbers that are greater than or equal to 35.

The rate it is snowing is 1 1/2 inches per hour.

The equation for the amount of snowing is s = 1 1/2t

The time when there would be 12 inches of snow on the ground is 8 hours

The time is started snowing is 12pm.

The rate at which it is snowing is the amount of snow per hour. The rate at which it is snowing can be determined using this equation:

Rate = (total amount of snow at 6pm - snow at 2pm) / difference in time

Snow at 6pm = snow at 2pm + increase in the inches of snow

3 + 5 = 8 inches

Rate = (8 - 3) / (6 - 2)

5 / 4 = 1 1/2 inches per hour

The equation that would be used to model the amount it is snowing would be a linear equation because the amount of snow increases at a constant rate.

Amount of snow = rate x number of hours

s = 1 1/2t

The time the snow would reach 12 inches:

12 = 1 1/2t

t = 12 ÷ 1 1/2

12 ÷ 3/2

12 x 2/3 = 8 hours

Time it started snowing :

3 = 1 1/2t

t = 3 ÷ 3/2

3 x 2/3 = 2 hours

2pm - 2hours = 12pm

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100 square centimeters are in the area of the largest possible inscribed triangle having one side as a diameter of circle.

What is the area?

A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface. In general, square units such as square inches, square feet, etc. are used as the standard unit of area.

Base = 2r = 2*10 = 20 cm

Height = r=  10 cm

Area =  1/2 * base * height

        =   1/2 * 20 * 10

        =   100 square centimeters

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Step-by-step explanation:

1.5x + 6-3= 4.5x- 2

1.5x+3=4.5x-2

we transposed

4.5x-1.5x= 3+2

3x= 5

we divide both sides by 3

3x/3= 5/3

x= 5/3

y = 1.5x + 0.5 is the equation of the line passing through the coordinate points

The formula for finding the equation of a line in slope-intercept form is expressed as:

y =mx + b

where:

m is the slope

b is the intercept

Determine the slope

slope = 5-2/3-1

slope = 3/2

slope = 1.5

Determine the y-intercept

y = mx + b

5 = 1.5(3) + b

5 = 4.5 + b

b = 0.5

Hence the required equation of the line passing through ( 1,2) and (3,5) is

y = 1.5x + 0.5

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Complete question

What's the equation of a line that passes through (1,2) (3,5)?

The critical value of f(x) = 5x⁶ - 3x⁵ is x = 0.5 which is also its maxima point

f(x) = 5x⁶ - 3x⁵

differentiation w.r.t x

=> f'(x) = 30x⁵ - 15x⁴

Putting f'(x) = 0

30x⁵ - 15x⁴ = 0

=> x⁴(30x - 15) =0

=> 30x - 15 = 0

=> x = 15/30

=> x = 0.5 , 0

Critical number is 0.5 , 0

(B) To find where f(x) is increasing

for x > 0.5 ,

(30x-15) > 0 => x⁴(30x - 15) > 0

Therefore , f(x) is increasing at ( 0.5 , ∞ )

(C)To find where f(x) is decreasing

for x < 0.5 ,

(30x-15) < 0 => x⁴(30x - 15) < 0

Therefore , f(x) is decreasing at ( -∞ , 0.5)

(D) Differentiation f'(x) again w.r.t to x

f'(x) = 30x⁵ - 15x⁴

f"(X) = 150x⁴ - 60x³

Substituting critical values of x

=> 150(0.5)⁴ - 60(0.5)³

=>9.375 - 7.5

=> -1.875 < 0 , Hence , x = 0.5 is point of maxima

(E) no point of minima

Similarly , we can solve other parts

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Q1: The regression intercept for stock A can be determined by considering the given regression results and assuming a constant risk-free rate (rf) of 8% with total returns instead of excess returns. The intercept represents the expected return of stock A when the market return (RM) is zero. To calculate the intercept, we need to subtract the product of the market return coefficient and the constant risk-free rate from the intercept of the excess return regression. In this case, the intercept for stock A would be -1.1% - (0.95 * 8%) = -1.87%.

Q2: To calculate the standard deviation of the portfolio, we use the given investment proportions and the standard deviations of stocks A and B. The standard deviation of a portfolio can be calculated by considering the investment proportions and the individual stock standard deviations. Using the given information, we can calculate the standard deviation of the portfolio to be 33.82 (rounded to two decimal places). The beta of the portfolio can be calculated by weighting the betas of stocks A and B according to their investment proportions. Based on the given information, the beta of the portfolio is calculated to be 1.09 (rounded to two decimal places).

Q3: The firm-specific variance of the portfolio represents the part of the portfolio's total variance that is not explained by the market index. To calculate the firm-specific variance, we need the portfolio's total variance and the square of the portfolio beta multiplied by the market variance. However, the necessary values are not provided in the given information, so the firm-specific variance cannot be determined without additional information.

Q4: The covariance between the portfolio and the market index represents the measure of their co-movement. It can be calculated by multiplying the portfolio beta, the standard deviation of the portfolio, and the standard deviation of the market index. However, the necessary values for the calculation are not provided in the given information, so the covariance between the portfolio and the market index cannot be determined without additional information.

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The sentence "If it is a dog (d), it has fleas (f)" can be represented in symbolic form as d → f.

In symbolic logic, we represent the components of a sentence using letters or symbols. In this case, the given sentence has two components: "it is a dog" and "it has fleas." To represent these components, we assign the letter 'd' to "it is a dog" and the letter 'f' to "it has fleas."

The sentence "If it is a dog, it has fleas" implies a conditional relationship between the two components. It states that if something is a dog (d), then it has fleas (f). This can be symbolically represented as d → f, where the arrow (→) denotes the conditional relationship.

The given sentence, "If it is a dog (d), it has fleas (f)," can be represented in symbolic form as d → f. The arrow (→) in symbolic logic represents the conditional relationship. It indicates that if something is a dog (d), then it has fleas (f). In this symbolic representation, 'd' stands for "it is a dog," and 'f' represents "it has fleas."

The sentence is a conditional statement because it presents a hypothetical relationship between the two components. The truth value of the sentence depends on whether the antecedent (d) is true or false. If something is indeed a dog, then it implies that it has fleas. However, if it is not a dog, the statement does not make any specific claim about fleas.

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9.4248 cu in/min volume of the balloon changing at the time when its radius is 5 inches

To solve this, you need to know how to find a derivative and use two equations.

The formula for a sphere's volume in terms of radius and chain rule is represented by the two equations. It will be useful to use the formula dV/dt = dV/dR x dR/dt.

V = (4/3)(Pi)r^3 ; dV/dr = 4(Pi)r^2 ;

dV/dt = ( dV/dr)(dr/dt)

DV/dr = 4(3.1416)(5)(5) = 314.16 ;

dr/dt = 0.03 in/min

DV/dt = ( 314.16 in sq)( 0.03 in/min) = 9.4248 cu in/min

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The simplified form of the expression -6w + (–8.3) + 1.5+ (–7w) is -13w - 6.8.

Given the expression in the question;

-6w + (–8.3) + 1.5+ (–7w)

To simplify, first remove the parenthesis

Note that;

-6w + × - 8.3 + 1.5 + × - 7w

-6w - 8.3 + 1.5 - 7w

Next collect and add like terms

-6w - 7w - 8.3 + 1.5

Add -6w and -7w

-13w - 8.3 + 1.5

Add -8.3 and 1.5

-13w - 6.8

Therefore, -13w - 6.8 is the simplified form.

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Answer:

Below, you can see the graph of the function:

f(x) = x + cos(k*x)

for different values of k, as follows:

red: k = 1

green: k = 2

orange: k = 0.

Now let's find the values of k such that our function does not have local maxima nor local minima.

First, remember that for a given function f(x), the local maxima or minima points are related to the zeros of the first derivate of f(x).

This means that if:

f'(x0) = 0.

Then x0 is a maxima, minima or an inflection point.

Then if a function is such that the f'(x) ≠ 0 , ∀x, then this function will not have local maxima nor minima.

Now we have:

f(x) = x + cos(k*x)

then:

f'(x) = 1  - k*sin(k*x)

This function will be zero when:

1 = k*sin(k*x)

1/k = sin(k*x)

now, remember that -1 ≤ sin(θ) ≤ 1

then if 1/k is smaller than -1, or larger than 1, we will not have zeros.

And this will happen if -1 < k < 1.

The partial fraction decomposition of the function is given by x^4 / ((x^3-x)(x^2-x-4)) is A/x + B/(x-1) + C/(x+1) + D/(x^2+2x+2) + E/(x^2-x-4) and 2x^6 - 64x^3 is F/x + G/x^2 + H/x^3 + I(x-4) + J(x^2+4x+16) + K(x+4), respectively.

Partial fraction decomposition is a method used to simplify complex rational expressions by expressing them as a sum of simpler fractions. In first part, the given function is factored as x^4/(x^3-x)(x^2-x-4).

To perform the partial fraction decomposition, we need to find the coefficients A, B, C, D, and E, such that

x^4 / ((x^3-x)(x^2-x-4)) = A/x + B/(x-1) + C/(x+1) + D/(x^2+2x+2) + E/(x^2-x-4)

Similarly, in next part, the given function is factored as 2x^3(x^3-32), and the partial fraction decomposition would involve finding coefficients F, G, H, I, J, and K, such that

2x^6 / (x^3-32) = F/x + G/x^2 + H/x^3 + I(x-4) + J(x^2+4x+16) + K(x+4)

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The predicted probability of scoring 80 or better on the final exam for a student attending all 10 lectures is 97.13%.

The predicted probability of scoring 80 or better on the final exam for a student attending all 10 lectures is 97.13%. This probability is derived from statistical analysis considering the correlation between lecture attendance and exam scores. By attending all lectures, the student receives comprehensive instruction, indicating a high likelihood of success.

The calculated probability implies a 97.13% chance of achieving the desired score. However, it's important to note that this prediction assumes lecture attendance as the sole influencing factor and doesn't account for individual study habits or other variables.

While attending lectures is beneficial, it's also crucial for students to engage in additional studying and practice to optimize their chances of achieving the desired grade.

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Answer:

He can wash 14 cars in one day. 14:1

Step-by-step explanation:

You divide 58 by 4

Answer:

14.5 cars

Step-by-step explanation:

58 Cars

÷ 4

4 Days

÷ 4

=

14.5 Cars

1 Day

=

14.5 Cars

Day

= 14.5 Cars per Day

Deck of Cards: 52 total, 4 suits of 13 each. Clubs and Spades are black, Hearts and Diamonds are red. Jack (J), Queen (Q), and King (K) are face cards.

Clubs: 2 3 4 5 6 7 8 9 10 J Q K A

Spades: 2 3 4 5 6 7 8 9 10 J Q K A

Hearts: 2 3 4 5 6 7 8 9 10 J Q K A

Diamond: 2 3 4 5 6 7 8 9 10 J Q K A

Here, we use the probability formula to calculate the answer.

Possible outcome = 52

We are to find the probability that it is a two or a club.

From 52 deck of cards, we have 4 twos and 13 clubs

Therefore,

The probability that it is a two or a club

Final answer = 0.3077 to 4 decimal places

Correlated variables are two explanatory factors that are connected to both the response variable and each other. The statistical relationship between two variables, which shows how they change together, is referred to as correlation.

Explanatory variables are used in regression analysis to forecast or explain the response variable. A correlation between two explanatory variables indicates that changes in one are influenced by changes in the other. Understanding the relationship between the explanatory variables and the response variable can be significantly impacted by this correlation. When analysing data, it's crucial to take into account the presence of correlated variables in order to avoid problems like multicollinearity and properly interpret the analysis's findings.

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The length of the equilateral triangle = 4.8m

Given that,

The area of the equilateral triangle = 10.2 m²

The formula for the area of an equilateral triangle = \(\sqrt{3} /4 a^{2}\)

Therefore,  

\(\sqrt{3} /4 a^{2}\) = 10.2

\(a^{2}\) = 10.2 × \(4/\sqrt{3}\)

\(a^{2}\) = 10.2 × 4/ 1.732

\(a\) = 4.85

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Answer:

$19.99 for each cartridge.

Step-by-step explanation:

For this problem, we are finding the cost of the three printer cartridges. Since the problem says that the tax was 5.95, we can subtract that from 90.91.

90.91-5.95=

84.96

Next, since we know that the software package was 24.99, we can subtract that from 84.96.

84.96-24.99=

59.97

Finally, since there are three printer cartridges, we can divide 59.97 by 3, and get our answer.

59.97/3=

19.99

Each printer cartridge would cost $19.99.

Hope this helps and have a good day! :D

Answer:

The IQR (interquartile range) of the data set represented by this box plot is 22 units.

Step-by-step explanation:

Each number of the data set represented as a box plot is something the numbers have individually. The lowest number there (the first number), 38, is called the minimum. The highest number there (the last number), 75, is called the maximum. The second number there, 45, is called the lower quartile. The third number there, 50, is called the median or middle quartile. The fourth number there, 67, is called the higher quartile. In order to find the interquartile range, you need to find the difference between the lower quartile and higher quartile, which means to subtract.

67 (highest quartile) - 45 (lower quartile) = 22 (interquartile range)

Therefore, the IQR (interquartile range) of the data set represented by this box plot is 22 units.

Answer:

It’s 22

Step-by-step explanation:

Answer:

4957.56

Step-by-step explanation:

Call the 3 sides of the triangle as a,b,c.

We have : a + b + c = 321
Since it's an equilateral triangle, a=b=c
=> a = b = c = 321/3 = 107ft.

To calculate an area of an equilateral triangle, we can use the formula :

\(\sqrt{3}\\\)/4 x \(a^{2}\)

=> A = \(\sqrt{3}\\\)/4 x \(107^{2}\) = approx. 4957.56



Marginal revenue and marginal profit when 2500 widgets are sold is $175 and $-17.5 respectively and when 7500 widgets are sold is $125 and $-207.5 respectively.

The cost function is given by:

C(x)\ =\ 15000\ +\ 100x\ -\ 0.03x^2\ +\ 0.000004x^3

The demand function is given by:

p\left(x\right)=200-0.005x

The marginal revenue and marginal profit are determined by differentiating revenue function R(x) and profit function P(x) respectively. The relationship between cost function C(x), revenue function R(x) and profit function P(x) is:

P(x)\ =\ R(x)\ -\ C(x)

The revenue function is determined by multiplying demand function p(x) and number of widgets x, hence

R(x)\ =xp(x)\ =\ x(200\ -\ 0.005x)\ =\ 200x\ -\ 0.005x^2

The profit function is given by:

P(x)\ =\ (200\ -\ 0.005x^2)\ -\ (15000\ +\ 100x\ -\ 0.03x^2\ +\ 0.000004x^3)

P(x)\ =\ -0.000004x^3\ -\ 0.025x^2\ +\ 100x\ -\ 15000

Differentiating profit function to determine marginal profit:

P\left(x\right)=-0.000004x^3-0.025x^2+100x-15000

P'(x)\ =\ -0.0000012x^2\ -\ 0.05x\ +\ 100

Differentiating revenue function to determine marginal revenue:

R(x)\ =\ 200x\ -\ 0.005^2

R'(x)\ = 200 – 0.01x

Evaluating these differentials when x = 2500 and x = 7500

P'(x)\ =\ -0.0000012x^2\ -\ 0.05x\ +\ 100

P'(2500)\ =\ -0.0000012(2500)^2\ -\ 0.05(2500)\ +\ 100\ =\ -17.5

P'(7500)\ =\ -0.0000012(7500)^2\ -\ 0.05(7500)\ +\ 100\ =\ -207.5

R'(x)\ = 200 – 0.01x

R'(2500)\ = 200 – 0.01(2500) = 175

R^\prime\left(7500\right)=200-0.01\left(7500\right)=125

Hence, marginal revenue and marginal profit when 2500 widgets are sold is $175 and $-17.5 respectively and when 7500 widgets are sold is $125 and $-207.5.

Note: The question is incomplete. The complete question probably is: Question: The weekly cost to produce x widgets is given by: C(x)\ =\ 15000\ +\ 100x\ -\ 0.03x^2\ +\ 0.000004x^3 and the demand function for the widgets is given by: p(x) = 200 - 0.005x. Determine the marginal revenue and marginal profit when 2500 widgets are sold and when 7500 widgets are sold assume that the company sells exactly what they produce.

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Answer:

0.001 and 1/1000

Step-by-step explanation:

Find the direct proportion:

28/7 = 4

When F is known divide it by the proportion to get a:

A = 40/4

A = 10