The weights of steers in a herd are distributed normally. The standard deviation is 300lbs and the mean steer weight is 1100lbs. Find the probability that the weight of a randomly selected steer is greater than 920lbs. Round your answer to four decimal places.

Answer:

The smallest fraction is b 11/60

To find the smallest of the unknown fractions given that their average with 1/5 is 1/4, we denoted the smallest fraction as x, leading to a simple algebraic equation solution. After fixing an arithmetic error, we found that the smallest fraction is 1/6.

The question is asking for the smallest unknown fraction when the average of this smallest fraction, another fraction that is twice its size, and a known fraction 1/5 is 1/4. Let's denote the smallest fraction as x, which implies that the other fraction is 2x. Since the average of three numbers is the sum of those numbers divided by three, our equation is (1/5 + x + 2x) / 3 = 1/4. Simplifying the equation by combining like terms and solving for x will reveal the smallest fraction.

First, we sum the unknowns and the known fraction: 1/5 + x + 2x = 3x + 1/5. Now we multiply both sides of the equation by 3 (to eliminate the division by 3 on the left side), we get: 3x + 3/5 = 1/4. To solve for x, we must have like denominators, therefore we convert all fractions to have a common denominator of 20. The equation then becomes 60x + 12 = 5. Subtracting 12 from both sides gives us 60x = -7, thus x = -7/60.

However, since fractions cannot be negative in this context, we made an error in our calculations. We correctly need to equate 3x + 1/5 to 3/4 (because the average is 1/4 which is the same as 3/4 for three numbers), and now the solution proceeds without error. Solving from here, we find that x = 1/6, which is the smallest fraction and is the correct answer to the question.

Answer: Mean = 4.8

Standard deviation = 1.96

Step-by-step explanation:

The mean and standard deviation of the binomial distribution is given by :-

[tex]\mu=np\\\sigma=\sqrt{np(1-p)}[/tex], where n is the total number of trials , p is the the probability of success.

Given : The probability that the produced by a particular manufacturer are less than 1.680 inches in​ diameter = 20%=0.2

Sample size : n=24                                                 [since 1 dozen = 12]

Now, the  mean and standard deviation of the binomial distribution is given by :-

[tex]\mu=24\times0.2=4.8\\\\\sigma=\sqrt{24(0.2)(1-0.2)}\\\\=1.95959179423\approx1.96[/tex]

The mean of the binomial distribution for the balls less than 1.680 inches in diameter is 4.8, and the standard deviation is approximately 1.96.

To find the mean and standard deviation for a binomial probability distribution where 20% of all balls are less than 1.680 inches in diameter from a sample of two dozen (24) balls, we use the formulas for a binomial distribution. The mean (μ) of a binomial distribution is calculated as μ = n * p, where n is the number of trials and p is the probability of success on a single trial. In this case, n = 24 and p = 0.20.

The mean is μ = 24 * 0.20 = 4.8.

To calculate the standard deviation (σ), we use the formula σ = √(n * p * (1 - p)), where (1 - p) is the probability of failure. The standard deviation is σ = √(24 * 0.20 * 0.80) = √(3.84) ≈ 1.96.

Answer:

y=3/5x+13/5

Step-by-step explanation:

Finding the slope:

m=6/10

m=3/5

The y intercept is 13/5

Thus, the equation is y=3/5x+13/5

Answer:

Equation of the given line is, y = (3/5)x +13/5

Step-by-step explanation:

Points to remember

Equation of the line passing through the poits (x1, y1) and (x2, y2)  and slope m is given by

(y - y1)/(x - x1) = m    where slope m = (y2 - y1)/(x2 - x1)

To find the slope of line

Here (x1, y1) = (-6, -1) and (x2, y2) = (4, 5)

Slope = (y2 - y1)/(x2 - x1)

 = (5 - -1)/(4 - -6)

 = 6/10 = 3/5

To find the equation

(y - y1)/(x - x1) = m

(y - -1)/(x - -6) = 3/5

(y + 1)/(x + 6) = 3/5

5(y + 1) = 3(x + 6)

5y + 5 = 3x + 18

5y = 3x + 13

y = (3/5)x +13/5

Answer:

σ = 13 miles

Step-by-step explanation:

Let us consider X continuous random variable and λ be the parameter of exponential density function.

where E(x) = [tex]\frac{1}{\lambda}[/tex]

where  E(x) = is expected value=13

we have to find λ=[tex]\frac{1}{E(x)}[/tex]

                          λ=[tex]\frac{1}{13}[/tex]

                          λ=0.076

standard deviation = V(X) = σ =  [tex]\frac{1}{\lambda}[/tex]

now , σ =  [tex]\frac{1}{0.076}[/tex]

          σ = 13 miles is the distance between the two major crack.

Final answer:

The standard deviation of the distance between two major cracks in a highway, which follows an exponential distribution with a mean of 13 miles, is 13 miles.

Explanation:

The question asks for the standard deviation of the distance between two major cracks in a highway, given that this distance follows an exponential distribution with a mean of 13 miles.

In an exponential distribution, the mean (μ) and standard deviation (σ) are equal.

Therefore, the standard deviation of the distance between two major cracks is also 13 miles.

Answer: Our required probability is 0.947.

Step-by-step explanation:

Since we have given that

Number of light bulbs selected = 30

Probability that the light bulb produced in a facility are defective = 2.8% = 0.028

We need to find the probability that fewer than 3 defective bulbs are found.

We will use "Binomial distribution":

n = 30, p = 0.028

so, P(X>3)=P(X=0)+P(X=1)+P(X=2)

So, it becomes,

[tex]P(X=0)=(1-0.0.28)^{30}=0.426[/tex]

and

[tex]P(X=1)=^{30}C_1(0.028)(0.972)^{29}=0.368\\\\P(X=2)=^{30}C_2(0.028)^2(0.972)^28=0.153[/tex]

So, the probability that fewer than three defective bulbs are defective is given by

[tex]0.426+0.368+0.153\\\\=0.947[/tex]

Answer:

16.59 inches

Step-by-step explanation:

Mean value = u = 14.5 inches

Standard deviation = [tex]\sigma[/tex] = 0.9 in

We need to find the 99th percentile of the given distribution. This can be done by first finding the z value associated with 99th percentile and then using that value to calculate the exact value of hip breadth that lies at 99th percentile

From the z-table, the 99th percentile value is at a z-value of:

z = 2.326

This means 99% of the z-scores are below this value. Now we need to find the equivalent hip breadth for this z-score

The formula to calculate the z score is:

[tex]z=\frac{x-u}{\sigma}[/tex]

where, x is the hip breadth which is equivalent to this z-score.

Substituting the values we have:

[tex]2.326=\frac{x-14.5}{0.9}\\\\ 2.0934=x-14.5\\\\ x=16.5934[/tex]

Rounded to 2 decimal places, engineers should design the seats which can fit the hip breadth of upto 16.59 inches to accommodate the 99% of all males.

To find the hip breadth for men that separates the smallest 99% from the largest 1%, we can use the z-score formula and the standard normal distribution table. The hip breadth that separates the smallest 99% is approximately 16.197 inches.

To find the hip breadth for men that separates the smallest 99% from the largest 1%, we need to determine the z-score corresponding to a 99% percentile. Firstly, we will calculate the z-score using the formula: z = (x - μ) / σ, where x is the hip breadth, μ is the mean (14.5 in.), and σ is the standard deviation (0.9 in.). Secondly, we use the standard normal distribution table or a z-score calculator to find the z-score that corresponds to a 99% percentile. Finally, we can solve for x using the formula: x = z * σ + μ.

Substituting the values, we have z = (x - 14.5) / 0.9. From the standard normal distribution table, the z-score that corresponds to a 99% percentile is approximately 2.33.

Plugging the values into the equation, we get 2.33 = (x - 14.5) / 0.9. Solving for x gives us x = 2.33 * 0.9 + 14.5 = 16.197 in.

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Answer:

[tex]x=-2,0,3[/tex]

Step-by-step explanation:

We have been given a function [tex]f(x)=15x^3-15x^2-90x[/tex]. We are asked to find the zeros of our given function.

To find the zeros of our given function, we will equate our given function by 0 as shown below:

[tex]15x^3-15x^2-90x=0[/tex]

Now, we will factor our equation. We can see that all terms of our equation a common factor that is [tex]15x[/tex].

Upon factoring out [tex]15x[/tex], we will get:

[tex]15x(x^2-x-6)=0[/tex]

Now, we will split the middle term of our equation into parts, whose sum is [tex]-1[/tex] and whose product is [tex]-6[/tex]. We know such two numbers are [tex]-3\text{ and }2[/tex].

[tex]15x(x^2-3x+2x-6)=0[/tex]

[tex]15x((x^2-3x)+(2x-6))=0[/tex]

[tex]15x(x(x-3)+2(x-3))=0[/tex]

[tex]15x(x-3)(x+2)=0[/tex]

Now, we will use zero product property to find the zeros of our given function.

[tex]15x=0\text{ (or) }(x-3)=0\text{ (or) }(x+2)=0[/tex]

[tex]15x=0\text{ (or) }x-3=0\text{ (or) }x+2=0[/tex]

[tex]\frac{15x}{15}=\frac{0}{15}\text{ (or) }x-3=0\text{ (or) }x+2=0[/tex]

[tex]x=0\text{ (or) }x=3\text{ (or) }x=-2[/tex]

Therefore, the zeros of our given function are [tex]x=-2,0,3[/tex].

Answer:

Yes, because the experiment satisfies all the criteria for a binomial experiment.

Step-by-step explanation:

A binomial experiment has the following criterias,

1. There must be a fixed number of trials

2. Each trial is independent of the others

3. There must be only two outcomes  ( success and failure )

4. The probability of each outcome is same.

Given,

An experimental drug is administered to 80 randomly selected​ individuals, with the number of individuals responding favorably recorded,

The number of trials = 80 ( fixed )

Each individuals is independent,

Total outcomes = 2 ( yes or no ),

Also, the probability of each individual is same,

Hence, the given probability experiment represent a binomial​ experiment.

The answer is:

The only value of "x" that ARE NOT in the domain of the function g, are -2 and 3.

Restriction: {-2,3}

Since we are working with a quotient (or division), we must remember that the only restriction for this kind of functions are the values that make the denominator equal to 0, so, the domain of the function will include all the values of "x" that are different than the zeroes or roots of the denominator.

We have the function:

[tex]h(x)=\frac{x-3}{x^2-x-6}[/tex]

Where its denominator is :

[tex]x^2-x-6[/tex]

Now, finding the roots or zeroes of the expression, by factoring, we have:

We need to find two numbers which product is equal to -6 and its addition is equal to -1, these numbers are -3 and 2, we have:

[tex]-3*2=-6\\-3+2=-1[/tex]

So, the factorized form of the expression will be:

[tex](x-3)*(x+2)[/tex]

We have that the expression will be equal to 0 if "x" is equal to "-2" and "3", so, the values that are not in the domain of g are: -2,3.

Hence, we have:

Restriction: {-2,3}

Domain: (-∞,-2)U(-2,3)U(3,∞)

Have a nice day!

To find the values of x that are not in the domain of the function g(x), we need to identify any values for x that would make the function undefined. The function g(x) = (x - 3) / (x^2 - x - 6) becomes undefined when the denominator is equal to zero, since division by zero is not allowed.
Thus, we need to find the values of x that make the denominator x^2 - x - 6 equal to zero. To do this, we'll solve the quadratic equation:
x^2 - x - 6 = 0
To solve this quadratic equation, we can factor the quadratic expression, or use the quadratic formula. We'll try factoring first:
x^2 - x - 6 = (x - 3)(x + 2)
Set each factor equal to zero and solve for x:
x - 3 = 0  -->  x = 3
x + 2 = 0  -->  x = -2
So, the values of x that are not in the domain of g(x) are -2 and 3, because these are the values that make the denominator equal to zero. Hence, g(x) is undefined at x = -2 and x = 3.
Therefore, the values that are NOT in the domain of g are:
-2, 3

Taking the transform of both sides gives

[tex]\mathcal L_s\{x''+8x'+15x\}=0[/tex]

[tex](s^2X(s)-sx(0)-x'(0))+8(sX(s)-x(0))+15X(s)=0[/tex]

where [tex]X(s)[/tex] denotes the Laplace transform of [tex]x(t)[/tex], [tex]\mathcal L_s\{x(t)\}[/tex]. Solve for [tex]X(s)[/tex] to get

[tex](s^2+8s+15)X(s)=2s+13[/tex]

[tex]X(s)=\dfrac{2s+13}{s^2+8s+15}=\dfrac{2s+13}{(s+3)(s+5)}[/tex]

Split the right side into partial fractions:

[tex]\dfrac{2s+13}{(s+3)(s+5)}=\dfrac a{s+3}+\dfrac b{s+5}[/tex]

[tex]2s+13=a(s+5)+b(s+3)[/tex]

If [tex]s=-3[/tex], then [tex]7=2a\implies a=\dfrac72[/tex]; if [tex]s=-5[/tex], then [tex]3=-2b\implies b=-\dfrac32[/tex]. So

[tex]X(s)=\dfrac72\dfrac1{s+3}-\dfrac32\dfrac1{s+5}[/tex]

Finally, take the inverse transform of both sides to solve for [tex]x(t)[/tex]:

[tex]x(t)=\dfrac72e^{-5t}-\dfrac32e^{-3t}[/tex]

The initial value problem is a second-order homogeneous differential equation that can be solved using the Laplace Transform. After substituting the initial conditions and simplifying the equation, one can decompose the equation using partial fraction decomposition and finally find the solution in the time domain.

Your given initial value problem is a second-order homogeneous differential equation. You should use the Laplace Transform to solve it. The Laplace transform of this equation is: L{x''(t) + 8x'(t) + 15x(t)} = 0 which simplifies to s²X(s) - sx(0) - x'(0) + 8[sX(s) - x(0)] + 15X(s) = 0. Substituting the initial conditions x(0) = 2 and x'(0) = -3, we get s²X(s) - 2s - (-3) + 8[sX(s) - 2] + 15X(s) = 0, then simplify to (s² + 8s + 15)X(s) = 2s + 3.

The roots of the quadratic equation s² + 8s + 15 = 0 are -5 and -3. So, the solution of the equation X(s) = (2s + 3) / (s² + 8s + 15) can be solved by using partial fraction decomposition. Therefore, the solution in the time domain would be x(t) = 2e⁻³ᵗ - e⁻⁵ᵗ.

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The rate at which the area of the square is increasing when the area of the square is [tex]\( 81 \, \text{cm}^2 \) is \( 90 \, \text{cm}^2/\text{s} \)[/tex].

Let x represent the length of a side of the square, and A represent the area of the square.

We know that the area A of a square is given by [tex]\( A = x^2 \).[/tex]

Differentiating both sides with respect to time t, we get:

[tex]\[ \frac{dA}{dt} = 2x \frac{dx}{dt} \][/tex]

Given that each side of the square is increasing at a rate of [tex]\( 5 \, \text{cm/s} \), we have \( \frac{dx}{dt} = 5 \, \text{cm/s} \).[/tex]

We are asked to find the rate at which the area of the square is increasing when the area of the square is [tex]\( 81 \, \text{cm}^2 \)[/tex], so we need to find [tex]\( \frac{dA}{dt} \) when \( A = 81 \)[/tex].

We can find x when A=81:

[tex]\[ A = x^2 \]\[ 81 = x^2 \]\[ x = 9 \][/tex]

Now, plug in x=9 and [tex]\( \frac{dx}{dt} = 5 \)[/tex] into the equation for  [tex]\[ \frac{dA}{dt} = 2x \frac{dx}{dt} \][/tex]

[tex]\[ \frac{dA}{dt} = 2(9)(5) \][/tex]

[tex]\[ \frac{dA}{dt} = 90 \, \text{cm}^2/\text{s} \][/tex]

So, the rate at which the area of the square is increasing when the area of the square is [tex]\( 81 \, \text{cm}^2 \) is \( 90 \, \text{cm}^2/\text{s} \)[/tex].

Final answer:

The probability that the sample mean carapace length is more than 4.25 inches is 0.0764.

Explanation:

To find the probability that the sample mean carapace length is more than 4.25 inches, we need to use the properties of the normal distribution. First, we need to calculate the z-score for the sample mean using the formula:
z = (x - μ) / (σ / sqrt(n))
Where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values:
z = (4.25 - 4.125) / (1.05 / sqrt(175))

Simplifying:
z = 1.428571

Next, we need to find the cumulative probability from the z-table. The table will give us the probability of getting a z-score less than or equal to a given value. Since we want the probability that the sample mean is more than 4.25 inches, we need to subtract the cumulative probability from 1:
Probability = 1 - cumulative probability

Looking up the cumulative probability in the z-table, we find that it is approximately 0.9236. Therefore, the probability that the sample mean carapace length is more than 4.25 inches is:
Probability = 1 - 0.9236 = 0.0764

Answer:

Option D "If n is odd or n is 2 then n is prime"

Step-by-step explanation:

we know that

To form the converse of the conditional statement, interchange the hypothesis and the conclusion.

In this problem

the conditional statement is "If n is prime then n is odd or n is 2."

The hypothesis is "If n is prime"

The conclusion is "n is odd or n is 2."

therefore

interchange the hypothesis and the conclusion

The converse is "If n is odd or n is 2 then n is prime"

Final answer:

The converse of 'If n is prime then n is odd or n is 2' is 'If n is odd or n is 2 then n is prime', therefore, the correct answer from the given options is D.

Explanation:

The converse of the statement 'If n is prime then n is odd or n is 2' is constructed by reversing the hypothesis and the conclusion. The converse would state 'If n is odd or n is 2 then n is prime'. Hence, the correct answer is D. We establish the converse by suggesting that the given properties (being odd or being the number 2) necessarily imply that a number is prime; however, it's important to note that while all prime numbers other than 2 are indeed odd, not all odd numbers are prime. Therefore, the converse is not logically equivalent to the original statement.

Answer:

100⁄25  60⁄15  4⁄1

Step-by-step explanation:

20/5 = 4

We need to see what equals 4

100⁄25 = 4

10⁄2=5

60⁄15=4

40⁄2=20

4⁄1=4

Answer:

  525%

Step-by-step explanation:

The relationship between the variables is ...

  cost + markup = selling price

  cost + 84%(selling price) = selling price

  cost = selling price(100% -84%) = 16%(selling price)

Then the markup based on cost is ...

  markup/cost = (84%(selling price))/(16%(selling price)) = 84/16

  markup/cost = 5.25 = 525%

Answer:

Given:  [tex]\begin{bmatrix}2&5&-2&1&2\\1&1&-2&1&4\end{bmatrix}[/tex]

[tex]2x_{1}+5 x_{2}  - 2_{3} + x_{4} + 2x_{5}\\[tex]

[tex]x_{1}+ x_{2}  - 2_{3} + x_{4} + 4x_{5}\\[/tex]

The system of linear equations in matrix form may be written as:

AX=B,

where,

A is coefficient matrix of order [tex]2\times 4[/tex] and is given by:

A = [tex]\begin{bmatrix}2&5&-2&1&2\\1&1&-2&1&4\end{bmatrix}[/tex]

X is variable matrix of order  [tex]5\times 1[/tex] and is given by:

X=  [tex]\begin{bmatrix}x_{_{1}}\\x_{_{2}}\\x_{3}\\x_{4}\\x_{5}\end{bmatrix}[/tex]

and B is the contant matrix of order [tex]2\times 1[/tex] and is given by:

B = [tex]\begin{bmatrix}1\\5\end{bmatrix}[/tex]

Now, AX=B

[tex]\begin{bmatrix}2&5&-2&1&2\\1&1&-2&1&4\end{bmatrix}[/tex]. [tex]\begin{bmatrix}x_{_{1}}\\x_{_{2}}\\x_{3}\\x_{4}\\x_{5}\end{bmatrix}[/tex] = [tex]\begin{bmatrix}1\\5\end{bmatrix}[/tex]

Answer:

84.38, 73.74

Step-by-step explanation:

score given 81.6, 72.0, 81.1, 86.4, 70.2, 83.1

sample size (n) = 6

[tex]mean = \dfrac{81.6+ 72.0+ 81.1+ 86.4+ 70.2+ 83.1}{6}[/tex]

mean = 79.06

standard deviation

[tex]\sigma =\sqrt{\frac{\sum (x-\bar{x})^2}{n-1}}[/tex]

[tex]\sigma =\sqrt{\frac{ (81.6-79.06)^2+(72-79.06)^2+(86.4-79.06)^2+(70.2-79.06)^2+(81.1-79.06)^2+(83.1-79.06)^2}{6-1}}[/tex]

σ = 6.47

level of significance (α) = 1 - 90% = 10%

confidence interval

[tex]\bar{x} \pm t_{\alpha}(\frac{S}{\sqrt{n}})\\79.06 \pm 2.015(\frac{6.47}{\sqrt{6} })[/tex]

=79.06 ± 5.32

= 84.38, 73.74

The 90% confidence interval for the mean score is calculated using the sample mean, standard deviation, and the Z-value from a Z-distribution table. The resulting range gives us a 90% confidence that the real population mean lies within this interval.

To compute a 90% confidence interval for the mean score, we use the sample data we have, our sample mean, and our standard deviation. The confidence interval gives us a range of values that likely includes the true population mean. We use the standard statistical formula for the 90% confidence interval: X ± (Z(α/2) * (σ/√n))

First, calculate the sample mean (X) and the standard deviation (σ). The scores are: 81.6, 72.0, 81.1, 86.4, 70.2, 83.1. The X will be the total of all the scores divided by 6, and σ will be a measure of how much they deviate from the mean.

Next, insert these values into the determining a confidence interval formula. You will need the Z(α/2) value for a 90% confidence interval, which is 1.645 in a Z-distribution table. Finally, take your X ± the calculated result to achieve the 90% confidence interval.

Remember: a 90% confidence interval means that you can be 90% confident that the true mean for all students lies within this interval.

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Answer:

$1343.25

Step-by-step explanation:

995*1.35=1343.25

Answer:

Step-by-step explanation:

Consider the 3x3 matrices in row echelon form:

[tex]\left[\begin{array}{ccc}1&2&0\\0&1&2\\0&0&0\end{array}\right][/tex]

and

[tex]\left[\begin{array}{ccc}1&2&0\\0&1&2\\0&0&1\end{array}\right][/tex]

a) The augmented matrix

[tex]\left[\begin{array}{ccc|c}1&2&0&1\\0&1&2&1\\0&0&0&2\end{array}\right][/tex]

corresponds to an inconsistent system.

b) The augmented matrix

[tex]\left[\begin{array}{ccc|c}1&2&0&1\\0&1&2&1\\0&0&0&0\end{array}\right][/tex]

corresponds to a consistent system with infinite solutions.

(c) The augmented matrix

[tex]\left[\begin{array}{ccc|c}1&2&0&1\\0&1&2&1\\0&0&1&1\end{array}\right][/tex]

corresponds to a consistent system with infinite solutions.

Answer:

Oil supply will run out in 44.283 years.

Step-by-step explanation:

There are 1.338 trillion barrels of oil in proven reserves.

If oil consumption is 82.78 million barrels per day then we have to calculate the number of years in which supply of oil runs out.

In this sum we will convert 1.338 million barrels of oil into million barrels first then apply unitary method to calculate the time in which oil supply runs out.

Since 1 trillion = [tex]10^{6}[/tex] million

Therefore, 1.338 trillion = 1.338×[tex]10^{6}[/tex] million

∵ 82.78 million barrels oil is the consumption of = 1 day

∴ 1 million barrels oil is the consumption of = [tex]\frac{1}{82.78}[/tex] day

∴ 1.338×[tex]10^{6}[/tex] barrels will be consumed in = [tex]\frac{1.338(10^{6})}{82.78}[/tex] days

= 16163.3245 days

≈ [tex]\frac{16163.3245}{365}[/tex] years

≈ 44.283 years

Therefore, oil supply will run out in 44.283 years

Answer:

Step-by-step explanation:

For these we have to assume the price and cost functions are linear.

Let p, c, r, P, q represent price, cost, revenue, Profit, and quantity (of items), respectively. The 2-point form of the equation for a line is ...

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

Price Function

Using the two-point form for price, we get ...

  p = (60 -65)/(20 -10)(q -10) +65 = -5/10(q -10) +65

  p = (-1/2)q +70 . . . . price per item

Cost Function

Using the two-point form for cost, we get ...

  c = (1050 -650)/(20 -10)(q -10) +650 = 40(q -10) +650

  c = 40q +250 . . . . cost for q items

Revenue Function

Revenue is the product of price and quantity:

  r(q) = qp

  r(q) = (1/2)q(140 -q) . . . . revenue from sale of q items

Profit Function

Profit is the difference between revenue and cost.

  P(q) = r(q) -c = 1/2q(140 -q) -(40q +250)

  P(q) = -1/2q^2 +30q -250

  P(q) = (-1/2)(q -10)(q -50) . . . . factored form

Break-Even Points

The profit function will be zero when its factors are zero, at q=10 and q=50. The price function tells us the corresponding prices are $65 and $45 per item, respectively.

Maximum Profit

The profit function is a maximum at the quantity halfway between the break-even points. There, q = (10+50)/2 = 30, and P(30) is ...

  P(30) = -1/2(30-10)(30-50) = 1/2(20^2) = 200 . . . . dollars

Quantity for Maximum Profit

This was found to be 30 in the previous section.

Answer: Matrix B is non- invertible.

Step-by-step explanation:

A matrix is said to be be singular is its determinant is zero,

We know that if a matrix is singular then it is not invertible.    (1)

Or if a matrix is invertible then it should be non-singular matrix.      (2)

Given :  A and B are n x n matrices from which A is invertible.

Then A must be non-singular matrix.                            ( from 2 )

If AB is singular.

Then either A is singular or B is singular but A is a non-singular matrix.

Then , matrix B should be a singular matrix.                   ( from 2 )

So Matrix B is non- invertible.                                     ( from 1 )

Answer: Option(c) is correct.

Step-by-step explanation:

Data engineering is a set of guidelines and approaches that characterize the kind of information gathered and how it is put away and utilized.  

The Data engineering includes the means, for example, gathering of data, storage of information in the databases and access the information at whatever point required.  

So,data engineering refers to information storage, database plan and information structures.  

Consequently Data quality isn't clarified in Data engineering.

Answer:

The answer is zero or option D.

Step-by-step explanation:

Proponents of rational expectations theory argued that, in the most extreme case, if policymakers are credibly committed to reducing inflation and rational people understand that commitment, and quickly lower their inflation expectations, the sacrifice ratio could be as small as 0.

Answer:

Mortality rate is 0.5 per 1000 habitant

the number of deaths have increased (from 210 to 250)

Step-by-step explanation:

Hello

Mortality rate is the number of deaths in a specific population,usually expressed in units of deaths per 1,000 individuals per year

[tex]Mortality\ rate\ (S)= \frac{(D)}{(P)} *10^{n} \\\\\\\\[/tex]

where

S=Mortality rate

D=deaths

P= population

n= is a conversion form ,such as multiplying by  10^{3}=1000, to  get mortality rate per 1,000 individuals( we will use n=3)

step 1

asign

S=unknown

D=250

P=500000

n=3, (for each  1000 people)

step 2

Replace

[tex]S=\frac{250}{500000}*1000\\S=\ 0.5\ per\ 1000[/tex]

Mortality rate is 0.5 per 1000 habitant

step 3

what if S=0.42

S=0.42(assuming it is 0.42 per 1000,n=3)

D=unknown

P=500000

[tex](S)= \frac{(D)}{(P)} *10^{n}\\\\isolatin D\\\\S*P=D*10^{n}\\ D=\frac{S*P}{10^{n} } \\\\and\ replacing\\\\D=\frac{(0.42)*(500000)}{10^{3} }\\\\ Deaths=210\\[/tex]

the number of deaths have increased (from 210 to 250)

Have a great day

Answer:

1234.08 weeks.

Step-by-step explanation:

Since, the amount formula in compound interest is,

[tex]A=P(1+r)^t[/tex]

Where, P is the principal amount,

r is the rate per period,

t is the number of periods,

Given,

P = $ 150,000,

Annual rate = 8 % = 0.08,

So, the weekly rate, r = [tex]\frac{0.08}{52}[/tex]  ( 1 year = 52 weeks )

A = 1,000,000

By substituting the values,

[tex]1000000=150000(1+\frac{0.08}{52})^t[/tex]

[tex]\frac{1000000}{150000}=(\frac{52+0.08}{52})^t[/tex]

[tex]\frac{20}{3}=(\frac{52.08}{52})^t[/tex]

Taking log both sides,

[tex]log(\frac{20}{3})=t log(\frac{52.08}{52})[/tex]

[tex]\implies t = \frac{log(\frac{20}{3})}{ log(\frac{52.08}{52})}=1234.07630713\approx 1234.08[/tex]

Hence, for become a millionaire we should wait 1234.08 weeks.

Final answer:

To investigate if African Americans are underrepresented among teachers in a St. Louis suburb, a hypothesis test can be set up comparing the proportion of African American teachers to the African American population in the city. The null hypothesis is that the proportions are equal, while the alternative hypothesis is that the teacher proportion is less. A statistical test, such as a chi-square test, can then be used to assess representation.

Explanation:

To determine whether African Americans are underrepresented in the schoolteacher hiring in a St. Louis suburb, we can set up a hypothesis test. According to the data provided, African Americans make up 5.7% of the city's population. Out of 405 teachers in the school system, only 15 are African American. To establish the hypotheses, we consider the null hypothesis (H0) that African Americans are represented in teaching positions at the same rate as they are in the general population, and the alternative hypothesis (H1) that African Americans are underrepresented in teaching positions compared to their proportion in the general population.

For the null hypothesis (H0): The proportion of African American teachers is equal to the proportion of the African American population in the city (5.7%). For the alternative hypothesis (H1): The proportion of African American teachers is less than the proportion of the African American population in the city (5.7%). The next step is to perform a statistical test, such as a chi-square test of independence, to determine if the observed data (15 out of 405 teachers) significantly deviates from what would be expected under the null hypothesis, based on the proportion of the African American population in the city.

If the p-value obtained from the statistical test is below a predetermined significance level, usually 0.05, we would reject the null hypothesis in favor of the alternative hypothesis, suggesting that African Americans are indeed underrepresented. This statistical approach does not consider other factors that may influence hiring, but it does provide a starting point to understand representation.

Answer:

The acceleration is 1.0416 m/[tex]s^{2}[/tex]

Step-by-step explanation:

In order to solve this problem we first need to know the formula for acceleration which is the following.

[tex]acceleration = \frac{final.velocity - initial.velocity}{final.time - initial.time}[/tex]

Since the time acceleration is calculated as [tex]m/s^{2}[/tex] we need to convert the km/h into m/s. Since 1km = 1000m and 1 hour = 3600 seconds, then

[tex]\frac{20*1000 }{3600s} = \frac{20,000m}{3600s} = \frac{20m}{3.6s}[/tex]

**Dividing numerator and denominator by 1000 to simplify**

[tex]\frac{65*1000 }{3600s} = \frac{65,000m}{3600s} = \frac{65m}{3.6s}[/tex]

**Dividing numerator and denominator by 1000 to simplify**

Now we can plug in the values into the acceleration formula to calculate the acceleration.

[tex]acceleration = \frac{\frac{65m}{3.6s}-\frac{20m}{3.6s} }{12s-0s}[/tex]

[tex]acceleration = \frac{\frac{45m}{3.6s}}{12s}[/tex]

[tex]acceleration = \frac{\frac{12.5m}{s}}{12s}[/tex]

[tex]acceleration = \frac{\frac{1.0416m}{s}}{s}[/tex]

Finally we can see that the acceleration is 1.0416 m/[tex]s^{2}[/tex]

In order to find the acceleration, we first need to convert the speed from km/h to m/s. Then we use the formula for acceleration which is the change in velocity divided by the change in time. The final acceleration is approximately 1.042 m/s².

The subject of the question pertains to the concept of acceleration in Physics. Acceleration, measured in meters per second per second (m/s²), is the rate at which an object changes its velocity. To determine this, we first have to convert the velocities from kilometers per hour (km/h) to meters per second (m/s). We know that 1 km = 1,000 m and 1 hour = 3,600 s. Therefore:

Next we use the formula for acceleration: a = Δv / Δt. The change in velocity (Δv) is the final velocity minus the initial velocity. Thus, Δv = 18.06 m/s - 5.56 m/s = 12.5 m/s. The change in time (Δt) is given as 12 seconds.

Substituting these values into the formula, we get: a = Δv / Δt = 12.5 m/s ÷ 12 s = 1.042 m/s². Therefore, the car's acceleration, assuming it's constant, is approximately 1.042 m/s².

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Answer with explanation:

The given differential equation

  y'y''=2--------(1)

We have to apply the following substitution

  u=y'

 u'=y"

Applying these substitution in equation (1)

u u'=2

[tex]u \frac{du}{dx}=2\\\\ u du=2 dx\\\\ \int u du=\int 2 dx\\\\\frac{u^2}{2}=2 x+K\\\\\frac{y'^2}{2}=2 x+K\\\\y'^2=4 x+2 K\\\\y'=(4 x+2 K)^{\frac{1}{2}}\\\\ dy=(4 x+2 K)^{\frac{1}{2}} d x\\\\\int dy=\int(4 x+2 K)^{\frac{1}{2}} d x\\\\y=\frac{(4 x+2 K)^{\frac{3}{2}}}{4 \times \frac{3}{2}}+J\\\\y=\frac{(4 x+2 K)^{\frac{3}{2}}}{6}+J[/tex]

Where , J and K are constant of Integration.

Answer:

Step-by-step explanation:

The factor-of-ten relationship between the different units means we can combine the numbers in decimal fashion. If 1 unit is 1 zhang, then 1 chi is 0.1 zhang and 1 cun is 0.01 zhang. Hence 6 chi 8 cun is 0.68 zhang.

Let x and y represent the width and height, respectively. In terms of zhang, we have ...

  y - x = 0.68

  x^2 +y^2 = 1^2

Substituting y = 0.68 +x into the second equation gives ...

  x^2 + (x +0.68)^2 = 1

  2x^2 +1.36x - 0.5376 = 0 . . . . . eliminate parentheses, subtract 1

Using the quadratic formula, we have ...

  x = (-1.36 ±√(1.36^2 -4(2)(-0.5376)))/(2·2) = (-1.36 ±√6.1504)/4

  x = 0.28 . . . . . the negative root is of no interest

  y = 0.28 +0.68 = 0.96

In units of chi and cun, the dimensions are ...

  height: 9 chi 6 cun

  width: 2 chi 8 cun

Answer:

Height: 9 chi 6 cun

Width: 2 chi 8 cun

Step-by-step explanation:

Now there is a door whose height is more than its width by 6 chi 8 cun. The distance between the [opposite] corners is 1 zhang. The height of the door is  9 chi 6 cun  and the width of the door is 2 chi 8 cun.

1 zhang = 10 chi = 100 cun