A study at a college in the west coast reveals that, historically, 45% of the students are minority students. If random samples of size 75 are selected, what is the chance that more than half of the students in the sample will be minority students.

i. 0.5

ii. 0.45

iii. 0.8078

iv. 0.1922

The question is to solve the differential equation x'=2(100-x)

or, dx/dt=200- 2x

or, ∫dx/(200-2x) = ∫dt.  Now, put 200-2x=z. Or, -2dx=dz.

substituting the variables, we get

-(1/2)∫dz/z= dt

or, -(1/2) ㏑z= t + ㏑c

or, ln z= -(2t+ 2*㏑c)

or, z= (1/c²)*exp(-2t) substituting the value of x in z and 1/c²=c1

x= (200- c1* exp(-2t))/2  putting c1/2=c2

or, x= 100- (c2*exp(-2t)).

x(0) =80 or, 100-80= c2 or, c2=20

so, x= 100- (20*exp(-2t))

now x(t)=40, or, 40=100- (20*exp(-2t))

or, 60/20= exp(-2t)

or, ㏑3=-2t

or, t= -0.54

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Answer: B

(2.5, ∞)

Step-by-step explanation:

The solution set of the given logarithm inequality will be (2.5,∞).

The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.

In another word, a logarithm is a different way to denote any number.

As per the given logarithm function,

log₂(2x - 1) > 2

By log property

2x - 1 > 2 x 2

2x > 4 + 1

x > 5/2

x > 2.5 so the solution set will be 2.5 < x < ∞ or (2.5,∞).

Hence "The solution set of the given logarithm inequality will be (2.5,∞)".

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Answer:

2000

Step-by-step explanation:

Number of shares after split is 5/2 times the pre split value =800*5/2 = 2000

Therefore, there are 5670 possible serial numbers that can be generated.

In mathematics, combination refers to the selection of a group of objects from a larger set without considering the order of objects. It is a way of counting the number of ways of selecting objects from a set, where the order of selection does not matter. In other words, a combination is a way of choosing a subset of objects from a larger set, where the order of selection is not important. The number of combinations of n objects taken r at a time is denoted by "n choose r" and is calculated using the formula: nCr = n! / (r!(n-r)!) where n is the total number of objects and r is the number of objects being selected. The exclamation point denotes the factorial function, which is the product of all positive integers up to a given number.

Here,

First, we need to determine how many ways we can choose 4 letters from the first 9 letters of the alphabet with no repeats. This is a combination problem, and we can use the formula:

C(9,4) = 9! / (4! * 5!) = 126

Next, we need to determine how many ways we can choose 2 digits from the 10 digits with no repeats. This is another combination problem:

C(10,2) = 10! / (2! * 8!) = 45

Now, we can use the multiplication principle to find the total number of serial numbers:

126 * 45 = 5670

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The volume of a sphere with a radius of 3cm is 113.04 cm³, which is approximately equal to 36π cm³. So, the correct option is D).

The formula for calculating the volume of a sphere, V = 4/3πr³, is used to find the amount of space enclosed by a sphere with a given radius. In this case, the sphere has a radius of 3cm. By substituting this value into the formula, we can solve for the volume of the sphere.

V = 4/3πr³

V = 4/3 × 3.14 × 3³ = 113.04 cm³

= approximately 36π cm³

The result is 113.04 cm³, which is approximately equal to 36π cm³. This calculation is important in many applications, such as engineering, physics, and mathematics. The correct answer is D).

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_____The given question is incomplete, the complete question is given below:

What is the volume of sphere r = 3cm? responses A 8π cm³ 8 pi, cm³  B 16π cm³ 16 pi, cm³ C 27π cm³ 27 pi, cm³ D 36π cm³

Step-by-step explanation:

”. What this means is that there is less than a 5% probability that the results happened just by random chance, and therefore a 95% probability that a results reflects a meaningful pattern in human psychology. We call this statistical significance, and, statistically speaking, this is a pretty high standard

If this means that there is still a 5% chance those results are due to chance. This, combined with publication bias , are two main contributing factors to the reproducibility crisis.

When the results of research investigations affect whether or not they are published, it is known as publication bias.

It alludes to the propensity of academics, journals and other interested parties to publish studies with statistically significant or favourable outcomes while omitting or underreporting those with non-significant or unfavourable outcomes.distorted and incomplete.

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Answer:

Step-by-step explanation:

m∠e = m∠a ( Corresponding Angles)

\( {c}^{2} - {b}^{2} = {a}^{2} \)

\( {15}^{2} - {13}^{2} = {56}^{2} \)

\( \sqrt{56} = 7.5\: yd\)

//

\(sin = \frac{opp}{hyp} \)

\( {sin}^{ - 1} = \frac{13}{15} \)

\( = 60 \: degrees\)

//

\(180 - 90 - 60 = 30 \: degrees\)

ANSWER

k = 7

EXPLANATION

The unknown variable in this equation is k,

To find its value, first, we have to combine like terms. This means that on the left side of the equation, we have to combine the coefficients of k,

And then, divide both sides by 6,

Hence, the value of k is 7.

Answer:

7/10

Step-by-step explanation:

To find the area of a rectangle you need to mulitiply the length and the width.

Length= 7/8.

Width= 4/5

7/8 × 4/5= 7/10.

The DWL falls when the monopolist receives the subsidy because it leads to an increase in output and a decrease in price.

The cost function and demand function of a monopolist can be found in the question. These can be used to derive the marginal revenue and marginal cost.

The optimal level of output and profit can be derived using the marginal revenue and marginal cost equations. After that, you can confirm that the demand is elastic at the optimal output.

After that, you need to calculate the markup and the DWL associated with the monopoly output. Finally, you need to find the new optimal output and determine if the DWL increases or decreases.

Given:Cost Function C(Q) = ¼ Q2 Marginal cost MC(Q) = ½ Q Demand P = 100 – ¼ Q. a.

Sketch the market demand, marginal costs, and marginal revenues.

Market demand:Marginal cost:Marginal revenue: b. What is the monopolist’s optimal level of output and profits?In the monopolistic market, the optimal level of output and profits are given by the condition that Marginal Revenue = Marginal Cost.

Marginal Revenue is the derivative of Total Revenue with respect to Quantity, which can be found by using the demand equation and solving for Q:TR(Q) = P × Q = (100 – ¼ Q)Q = 100Q – ¼ Q2MR(Q) = dTR(Q)/dQ = 100 – ½ QMarginal Cost is given by the question as MC(Q) = ½ Q.

The monopolist's optimal level of output and profits can be found by equating MR and MC:100 – ½ Q = ½ Q => Q = 66.67 units of outputWhen Q = 66.67, the price is given by the demand equation:P = 100 – ¼ Q => P = 83.33.

Therefore, the monopolist's optimal output is 66.67 and optimal profits are (P – MC) × Q = (83.33 – 33.33) × 66.67 = $2,000.

Confirm that demand is elastic at the optimal output.The demand is elastic at the optimal output if the absolute value of the price elasticity of demand is greater than one.

The price elasticity of demand is given by:Ed = (% Change in Quantity Demanded)/(% Change in Price) = (dQ/Q)/(dP/P) × P/QSince MR = P(1 - 1/Ed), MR is greater than MC if Ed is less than 1 and less than MC if Ed is greater than 1. Therefore, the optimal output occurs where Ed is equal to
Substituting the values of P and Q, we get:Ed = (dQ/Q)/(dP/P) × P/Q = -1.47Therefore, demand is elastic at the optimal output.

Calculate the firm’s markup.The markup is given by the formula (P - MC)/P.Substituting the values of P and MC, we get:(83.33 - 33.33)/83.33 = 0.6 = 60% markup .

What is the DWL associated with the monopoly output?DWL (Deadweight Loss) is the difference between the total surplus in a competitive market and the total surplus in a monopoly market.

The formula for DWL is:DWL = (1/2)(Pmon - Pcomp)(Qcomp - Qmon)DWL can be calculated by using the demand equation and finding the quantity demanded at the monopoly price and the competitive price. At the monopoly price of $83.33, the quantity demanded is 66.67.

At the competitive price of $66.67, the quantity demanded is 100. Therefore, DWL can be calculated as follows:DWL = (1/2)(83.33 - 66.67)(100 - 66.67) = $1,111.1 f.

Suppose the government offered a $10 production subsidy to the monopolist. What is their new optimal output?The new optimal output will be where the new marginal cost equals the original marginal revenue.

The subsidy reduces the marginal cost to (1/2) Q - $10.

Therefore, the monopolist's new optimal output can be found by solving for Q:100 - 1/2 Q + 10 = 1/2 Q => Q = 74.07 units of outputWhen Q = 74.07, the price is given by the demand equation:P = 100 - 1/4 Q => P = $81.48 g. Does the DWL fall or rise?The DWL falls when the monopolist receives the subsidy because it leads to an increase in output and a decrease in price.

Therefore, the deadweight loss falls.

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The lowest integer value m can take in the inequality 7m + 5 > 49 - 3m is 5.

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

In other words, Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.

Therefore, let's solve the inequality for the lowest integer value of m

7m + 5 > 49 - 3m

add 3m to both sides of the inequality

7m + 5 > 49 - 3m

7m + 3m + 5 > 49 - 3m + 3m

10m + 5 > 49

subtract 5 from both sides of the inequality

10m + 5 > 49

10m + 5 - 5 > 49 - 5

10m > 44

m > 44 / 10

m > 4.4

Hence,

lowest integer = 5

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Answer:

98.4252

Step-by-step explanation:

This is because 1 millimeter is 0.0393701 inches;2,500 millimeters =0.0393701 multiply 2,500=98.4252.

Answer:

It’s would be 98

Step-by-step explanation:

Have a good rest of your day:)

Answer:

See below ~

Step-by-step explanation:

Sin A : opposing side of ∠A / hypotenuse

Sin C : opposing side of ∠C / hypotenuse

Cos A : adjacent side of ∠A / hypotenuse

Cos C : adjacent side of ∠C / hypotenuse

Answer:

The correct answer is no.

Step-by-step explanation:

If a number is a factor of another number, that means that it can be equally divided into it evenly.

I know that 3 x 20 = 60, and 73 - 60 = 13.

Since 3 is not a factor of 13, it is also not a factor of 73.

Hope this helps! :D

To find a value of c such that P(z ≥ c) = 0.55, we need to use a standard normal distribution table or calculator.From the standard normal distribution table, we find that the z-score corresponding to a right-tailed area of 0.55 is approximately 0.126.

Therefore, we have:

P(z ≥ c) = 0.55

P(z ≤ c) = 1 - P(z ≥ c) = 1 - 0.55 = 0.45

Using the standard normal distribution table, we find that the z-score corresponding to a left-tailed area of 0.45 is approximately -0.126.

So, c = -0.126.

Therefore, the value of c that satisfies P(z ≥ c) = 0.55 is approximately -0.126.

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The correct option is C. The company earned 74 billion dollars in 2008.

The constant term of the expression represent in terms of the context is that the company earned 74 billion dollars in 2008.

A constant term in mathematics is an algebraic expression that is constant since it does not involve variables. In a quadratic polynomial, for example. 3 is a fixed term. The equation has at most single constant term after grouping comparable terms.

In mathematics, a constant term is a factor in an algebraic equation whose meaning is constant or can't be changed due to the absence of variables that may be changed.

Consider the given polynomial;

t² + 12t + 74

As, 74 is the only term which does not contain any variable, thus it is the constant term.

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The complete question is-

A particular company's net sales, in billions, from 2008 to 2018 can be modeled by the expression t² + 12t + 74, where t is the number of years since the end of 2008. What does the constant term of the expression represent in terms of the context?

A. The company earned 74 billion dollars from 2008 to 2018.

B. The company earned 12 billion dollars from 2008 to 2018.

C. The company earned 74 billion dollars in 2008.

D. The company earned 12 billion dollars in 2008.

The statement If a simple random sample is chosen with replacement, each individual has the same chance of selection on every draw is True.

If a simple random sample is chosen with replacement, it means that after each selection, the chosen individual is placed back into the population before the next selection is made. In this case, each individual in the population has the same chance of being selected for every draw.

The process of replacing the selected individual ensures that the selection probabilities remain constant throughout the sampling process. As a result, each individual has an equal probability of being chosen on each draw, making the statement true.

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Answer:P= 16 + 2\|65 units; A= 56 units2

Step-by-step explanation:

Therefore the equation of the line is y=-x.

What is  equation of line?

 A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system. The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

Here the given equation is,

=>y+9=-(x-2)

=> y+9 = -x+2

=>y=-x+2-9

=> y=-x-7

Here the equation is y=mx+c where m = slope.

Then in given equation slope m= -1.

Here the given equation is parallel to the line passes through the origin.

Then they have equal slope, m=-1.

Now (\(x_1,y_1)\)=(0,0) and m=-1 then equation is

=> \(y-y_1=m(x-x_1)\)

=> y-0=-1(x-0)

=> y=-x.

Therefore equation of the line is y = -x.

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Calculate each of the probabilities using the formulas above, and subtract the cumulative probability of 5 or fewer adults saying yes from 1 to find the probability of more than 6 adults saying yes.

To solve this problem, we can use the binomial probability formula. Let's break down the information given:

Probability of an adult knowing what they will have for dinner: 28% or 0.28

Number of adults asked: 22

We want to find the probability that more than 6 adults will say yes.

First, let's find the probability of exactly 6 adults saying yes:

P(X = 6) = (22 C 6) * (0.28^6) * (0.72^16)

Here, (22 C 6) represents the number of combinations of choosing 6 adults out of 22. The term (0.28^6) represents the probability of 6 adults saying yes, and (0.72^16) represents the probability of the remaining 16 adults saying no.

Next, let's find the probability of 5 or fewer adults saying yes:

P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

To calculate P(X = 0), P(X = 1), ..., P(X = 5), P(X = 6), you can use the same formula as above, plugging in the respective values of X.

Finally, to find the probability of more than 6 adults saying yes, we can subtract the probability of 5 or fewer adults saying yes from 1:

P(X > 6) = 1 - P(X ≤ 6)

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Answer:

10,080 minutes

Step-by-step explanation:

7 x 24 x 60 = 10,080

This value represents the present worth below which the probability is 0.5, indicating a negative present worth.

To estimate the probability that the present worth is negative using the NORM.INV function in Excel,

we need to calculate the present worth of the project and then determine the corresponding probability using the normal distribution.

The present worth of the project can be calculated by finding the sum of the present values of the annual receipts over the 10-year period, minus the initial investment. The present value of each annual receipt can be calculated by discounting it back to the present using the minimum attractive rate of return (MARR).

Using the given information, the present value of the initial investment is $10,000. The present value of each annual receipt is calculated by dividing the expected return of $1,800 by \((1+MARR)^t\),

where t is the year. We then sum up these present values for each year.

We can use the NORM.INV function in Excel to estimate the probability of a negative present worth. The function requires the probability value, mean, and standard deviation as inputs.

Since we have a mean and standard deviation for the present worth,

we can calculate the corresponding probability of a negative present worth using NORM.INV.

This value represents the present worth below which the probability is 0.5. By using the NORM.INV function,

we can estimate the probability that the present worth is negative based on the given data and assumptions.

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Answer:

-24

Step-by-step explanation:

Answer:

-24

Step-by-step explanation:

There is ONLY ONE __ line parallel to the provided line that passes through a certain point that is not contained in the supplied line.

Parallel lines are any two or more lines that are in the same plane but never cross one another ( never intersect). Both have the same slope and are equally far from one another.

We have a line and a point outside the line;

from that point, we can generate many lines, but only one of those lines will be parallel to the line as it is. From a point, we can make many lines, but that point can only create one line that will be parallel to a given line.

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Answer:

38.75

Step-by-step explanation:

Not sure what you mean by ioth but when you add up all the numbers and divide by n, you get 38.75 (hopefully you can round it to whatever you want)

Answer:

scalene triangle for the first

equilateral triangle for the second

isosceles triangle for the 3rd

Answer:

The first is a scalene triangle. No two sides on a scalene trinagle will have the same length.

The second is an equilateral triangle. Equilateral literally means "equal sides".

The third is an isosceles triangle. These triangle will have perfect symmetry.

7.36 for each cap

$36.80 is the cost for 5 caps. if we divide the cost of the pack to the individual number of idems (caps), the equation (36.80÷5) will come out to $7.36, meaning $7.36 is the cost for each individual cap.

The particular antiderivative that satisfies the given condition is: C(x) = (4/9)x^4 - (9/8)x^3 + K1x + 2000

To find the particular antiderivative (or integral) of the given derivative \(C''(x) = 4x^2 - 3x\)  that satisfies the condition C(0) = 2000, we need to integrate the given function twice.

First, we integrate C''(x) to find C'(x):

\(C'(x) = ∫ (4x^2 - 3x) dx\)

To find the antiderivative of \(4x^2\), we use the power rule for integration: the power of x increases by 1 and is divided by the new power. Similarly, the antiderivative of -3x is \(-(3/2)x^2\).

\(C'(x) = ∫ (4x^2 - 3x) dx = (4/3)x^3 - (3/2)x^2 + K1\)

Here, K1 is the constant of integration. Next, we integrate C'(x) to find C(x):

\(C(x) = ∫ (C'(x)) dx = ∫ ((4/3)x^3 - (3/2)x^2 + K1) dx\)

To find the antiderivative of \((4/3)x^3\), we again use the power rule for integration. Similarly, the antiderivative of \(-(3/2)x^2\) is \(-(3/2)(1/3)x^3\).

The constant of integration K1 will also be integrated with respect to x, resulting in another constant of integration, K2.

\(C(x) = (1/3)(4/3)x^4 - (1/2)(3/2)x^3 + K1x + K2\)

Simplifying further, we have:

\(C(x) = (4/9)x^4 - (9/8)x^3 + K1x + K2\)

Now, we can apply the initial condition C(0) = 2000 to find the particular solution for K2:

\(C(0) = (4/9)(0)^4 - (9/8)(0)^3 + K1(0) + K2 = 2000\)

Since all the terms involving x become zero when x = 0, we have:

K2 = 2000

Therefore, the particular antiderivative that satisfies the given condition is: \(C(x) = (4/9)x^4 - (9/8)x^3 + K1x + 2000\)

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Answer:

Step-by-step explanation:

No. 6 is greater than the sum of 3 and 2.

No, These three numbers cannot be the measures of the sides of a triangle.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Three sides of triangle are,

⇒ 3, 6, 2

We know that;

The sum of two sides of a triangle are always greater than the third sides.

Here, Three sides of triangle are,

⇒ 3, 6, 2

So, We get;

⇒ 3 + 2 < 6

Thus, It is not possible to make a triangle.

Therefore, These three numbers cannot be the measures of the sides of a triangle.

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