According to the data reported by the New York State Department of Health regarding West Nile Virus for the years 2000-2004, the least squares line equation for the number of reported dead birds (x) versus the number of human West Nile virus cases (y) is ŷ = −10.2638 + 0.0491x. If the number of dead birds reported in a year is 844, how many human cases of West Nile virus can be expected? (Round your answer to the nearest whole number.)

Answer:

  C.  Hyperbola opening up and down

Step-by-step explanation:

A graph tells the tale.

___

The term with the positive coefficient identifies the axis along which the hyperbola opens. Here, that is the y-axis, so the figure opens up and down.

The minus sign between the squared terms indicates it is a hyperbola, rather than a closed curve (ellipse or circle). The fact that both terms are squared indicates it is not a parabola.

Answer:

The correct option is 2.

Step-by-step explanation:

According to the the center-of-gravity technique, the coordinates of the center-of-gravity location are

[tex](\frac{\sum x_iL_i}{\sum L_i},\frac{\sum y_iL_i}{\sum L_i})[/tex]

Where ([tex](x_i,y_i)[/tex] represent the coordinates and [tex]L_i[/tex] is demand.

We have to find the Y-coordinate of the center-of-gravity location.

The sum of product of demand and corresponding y coordinates is

[tex]\sum y_iL_i=65\times 2200+55\times 900+95\times 1300+200\times 1750+175\times 3100=1208500[/tex]

The sum of demanded units is

[tex]\sum L_i=2200+900+1300+1750+3100=9250[/tex]

The Y-coordinate of the center-of-gravity location is

[tex]y_0=\frac{\sum y_iL_i}{\sum L_i}[/tex]

[tex]y_0=\frac{1208500}{9250}[/tex]

[tex]y_0=130.6486[/tex]

[tex]y_0\approx 131[/tex]

The Y-coordinate of the center-of-gravity location is 131. Therefore the correct option is 2.

The center-of-gravity Y-coordinate is calculated by summing the product of the Y-coordinates and their respective demands, then dividing by the sum of all demands. The Y-coordinate of the center-of-gravity location is approximately 131 miles.

The center-of-gravity location is calculated by using a specific formula: (Sum of (Demand * Y-coordinate) /Sum of Demand). Let's use the Y-coordinates given and their corresponding demands.

It would look like this:
((2200*65) + (900*55) + (1300*95) + (1750*200) + (3100*175)) / (2200+900+1300+1750+3100)

Do the math to find out the Y-coordinate:
143,000 + 49,500 + 123,500 + 350,000 + 542,500 = 1,208,500
2200+900+1300+1750+3100 = 9250
1,208,500/9250 = 130.59
So the Y-coordinate of the center-of-gravity location is approximately 131 miles.

https://brainly.com/question/33524483

#SPJ3

Answer:

  no

Step-by-step explanation:

The total number of coins in all sets is 21, an odd number. In order for there to be equal numbers in all sets, the total number of coins must be even. Each step adds an even number of coins, so there is no number of steps that will add an odd number of coins to make the total be even.

Answer:

(-2,2)

Step-by-step explanation:

Let's find the answer.

Because a tangent line for a parabola function is equal to 0 only at its vertex then:

[tex]f(x)=(x+2)^{2}+2[/tex]

[tex]f'(x)=2*(x+2)[/tex]

[tex]f'(x)=2x+4[/tex] so then:

[tex]f'(x)=0[/tex] when

[tex]0=2x+4[/tex]

[tex]-2=x[/tex]

For x=-2 f(x) is:

[tex]f(x)=(x+2)^{2}+2[/tex]

[tex]f(1)=(-2+2)^{2}+2[/tex]

[tex]f(x)=2[/tex]

In conclusion, the vertex of the given parabola is (-2,2), so the answer is C. Although in your answer is reported as (-2.2) but I think was a typing mistake.

Answer with explanation:

The Fibonacci series is as follows:and it's first ten entries are

0,1,1,2,3,5,8,13,21,34,.....

You can see that after first two terms, each term that is from third term,sum of previous two consecutive terms.

1→1

2→0

3→1=1+0

4→2=1+1

5→3=2+1

6→5=3+2

7→8=5+3

8→13=5+8

9→21=13+8

10→34=21+13

[tex]\rightarrow f_{11}=f_{10}+f_{9}\\\\=34+21\\\\f_{11}=55\\\\\rightarrow f_{12}=f_{11}+f_{10}\\\\=55+34\\\\f_{12}=89\\\\\rightarrow f_{13}=f_{12}+f_{11}\\\\=89+55\\\\f_{13}=144\\\\\rightarrow f_{ia}=f_{i(a-1)}+f_{i(a-2)}[/tex]

[tex]1\cdot2^4+1\cdot2^3+1\cdot 2^0=16+8+1=25[/tex]

[tex]11001_2=25_{10}[/tex]

Final answer:

To convert (11001)_2 to decimal, multiply each binary digit by the corresponding power of 2 based on its position, starting from the right. Add the products to get the decimal value, which in this case is 25.

Explanation:

To convert the binary number (11001)_2 to its decimal equivalent, you must understand that each digit represents a power of 2, starting from the rightmost digit which is the least significant bit (LSB). The leftmost digit is the most significant bit (MSB). Now, let's convert (11001)_2 to decimal:

The rightmost digit (1) is in the 20 place, so it is worth 1*20 = 1.

The next digit to the left (0) is in the 21 place, so it is worth 0*21 = 0.

Continuing to the left, the next digit (0) is in the 22 place, so it's worth 0*22 = 0.

The next digit (1) is in the 23 place, so it's worth 1*23 = 8.

Finally, the leftmost digit (1) is in the 24 place, so it's worth 1*24 = 16.

Add up all the values: 16+0+0+8+1 = 25. So, the decimal expansion of (11001)_2 is 25.

Answer:

y=-8

Step-by-step explanation:

So if you draw a circle with center at the origin (0,0) with radius 8.  

So we have:

That means the radius stretches to (0,-8); down 8 units from (0,0).

The radius stretches to (0,8); up 8 units from (0,0).

The radius stretches to (8,0); right 8 units from (0,0).

The radius stretches to (-8,0); left 8 units from (0,0).

We are looking for a line tangent to our circle at (0,-8). Since this was down 8 units.  Then our equation is horizontal and y=a number. They-coordinate in (0,-8) is -8, so the we have y=-8.

If someone said tangent at (0,8), we would have said y=8 .

If someone said tangent at (8,0), we would have said x=8.

If someone said tangent at (-8,0), we have have said x=-8.

The equation of the line that is tangent to the circle with radius 8 at (0,-8) and center at the origin is y=-8. This is because the tangent line is horizontal at that point as it is perpendicular to the radius line lying along the y-axis.

In the context of Mathematics, particularly geometry, the line that is tangent to a circle at a given point is perpendicular to the radius drawn to that point. Since the circle's center is at the origin (0,0) and the radius is extended to the point (0,-8), this radius lies along the y-axis. Therefore, the equation of the tangent line which is perpendicular to this radius would be a horizontal line through the point (0,-8), given by the equation y=-8.

Remember that tangent line by definition touches the circle at only one point without intersecting it and the line is perpendicular to the radius at that point of tangency. In this particular scenario, the radius and tangent are perpendicular lines in the coordinate system: the radius aligns with the y-axis, hence the tangent aligns with the x-axis.

https://brainly.com/question/32207644

#SPJ3

Answer:

probability  is 0.778

Step-by-step explanation:

Given data in question

success of probability (p) = 41% = 0.41

no of sample (n)  = 400

individual = 150

to find out

probability that the sample proportion will be at least 135/400

solution

first we calculate the mean i.e

mean = p × n

mean = 400 × 0.41

mean = 164

now we calculate standard deviation = [tex]\sqrt{400(0.41) 0.59}[/tex]

standard deviation =  9.83666

we know P(X ≥ 135) = P(Z ≥ (150 - 164)/9.83666)

P(X ≥ 135) = P(Z ≥ (-1.42324)

from table 1 find corresponding probability

P(X ≥ 135) = 1 - P(Z ≥ (-1.42324)

= 1 - 0.9222 = 0.778

probability  is 0.778

Answer:

postpositivist

Step-by-step explanation:

Of the all four options "post positivist" philosophical assumption are reflected in quantitative research designs

"post positivist" believes that, theory, hypothesis, background knowledge,believes and values of researchers can alter the actual observations. Post positivist consider both quantitative and qualitative methods to be a valid form of approaches unlike "positivist" which emphasize only on quantitative methods.

The philosophical assumption reflected in quantitative research designs is postpositivist. Postpositivism believes in the existence of an objective reality that can be studied through empirical observation and measurement.

The philosophical assumption reflected in quantitative research designs is postpositivist. Postpositivism is a philosophical stance that believes in the existence of an objective reality that can be studied through empirical observation and measurement. Quantitative research designs aim to gather numerical data that can be analyzed statistically to uncover patterns and relationships in the data. A postpositivist approach to research values objectivity, generalizability, and the use of rigorous methodologies.

https://brainly.com/question/13012373

#SPJ12

The confidence interval is [tex]\fbox{(5.8, 8.1)}[/tex] and [tex]\fbox{\text{Option A}}[/tex] is correct.

Further Explanation:

Given:

The least value is [tex]1[/tex] that is the least attractive.

The highest value is [tex]10[/tex] that is the most attractive.

The observations are,

7, 7, 3, 8, 5, 6, 6, 9, 9, 8, 6, 9.

Calculation:

The sum of all observations is [tex]83[/tex].

The population mean is [tex]\mu[/tex].

The standard deviation [tex]s[/tex] is [tex]1.832[/tex].

The sample mean [tex]\bar^{X}[/tex] is [tex]6.92[/tex].

Level of significance [tex]\alpha[/tex] =  [tex]5\%[/tex].

Formula for confidence interval = [tex]\left( \bar{X} \pm t_{n-1, \frac{\alpha}{2}\%} \frac{s}{\sqrt{n}} \right)[/tex]

Confidence interval =[tex]\left( 6.92 \pm t_{12-1, \frac{5}{2}\%} \frac{1.832}{\sqrt{12}} \right)[/tex]

The value of [tex]t_{11, \frac{5}{2}\%[/tex]=[tex]2.201[/tex]

Confidence interval = [tex]( 6.92 \pm 2.201}\times \frac{1.832}{\sqrt{12}}) \right)[/tex]

Confidence interval = [tex]( 6.92 - 2.201}\times 0.5288 ,6.92 + 2.201}\times \0.5288) \right)[/tex]

Confidence interval = [tex](6.92-1.1639,6.92+1.1639)[/tex]

Confidence interval = [tex]\fbox{(5.8, 8.1)}[/tex]

The [tex]95\%[/tex] confidence interval gives us an idea that [tex]95\%[/tex] chances of the true mean or population mean lies in the interval.

A. We are [tex]95\%[/tex] confident that the interval from [tex]5.8[/tex] to [tex]8.1[/tex] actually contains the true mean of attractiveness rating of all adult females.

B. The results tell nothing about the population of all adult females, because participants in speed dating are not a representative sample of the population of all adult females.

C. We are confident that [tex]95\%[/tex] of all adult females have attractiveness ratings between [tex]5.8[/tex] and [tex]8.1[/tex].

[tex]\fbox{\text{Option A}}[/tex] is Correct as we are [tex]95\%[/tex] confident that the interval from [tex]5.8[/tex] to [tex]8.1[/tex] actually contains the true mean of attractiveness rating of all adult females.

Option B is not correct as the confidence interval tells us about the population mean.

Option C is not correct as the individual rating can be more than [tex]5.8[/tex] or less than the [tex]8.1[/tex].

Learn More:

1. Learn more about collinear https://brainly.com/question/5795008

2. Learn more about binomial term https://brainly.com/question/1394854

Answer Details:

Grade: College Statistics

Subject: Mathematics

Chapter: Confidence Interval

Keywords:

Probability, Statistics, Speed dating, Females rating, Confidence interval, t-test, Level of significance , Normal distribution, Central Limit Theorem, t-table, Population mean, Sample mean, Standard deviation, Symmetric, Variance.

The confidence interval for the population mean attractiveness rating of all adult females is 5.8 to 8.1, and we are 95% confident that this interval contains the true mean attractiveness rating.

In this study of speed dating, male subjects were asked to rate the attractiveness of their female dates on a scale from 1 (not attractive) to 10 (extremely attractive). A sample of attractiveness ratings was provided: 7, 7, 3, 8, 5, 6, 6, 9, 9, 8, 6, 9. The objective is to construct a confidence interval with a 95% confidence level to estimate the true mean attractiveness rating of all adult females.

The calculated confidence interval is 5.8 to 8.1. This means that we are 95% confident that the interval from 5.8 to 8.1 contains the true mean attractiveness rating of all adult females. The margin of error, represented by the range of the interval, provides a level of precision in our estimation.

The confidence interval suggests that the true mean attractiveness rating for all adult females falls within the specified range. It does not provide an exact value for the mean, but it indicates a plausible interval within which the true mean is likely to be found. Additionally, the confidence interval does not imply a causal relationship, but rather a statistical estimate based on the observed sample.

1. A coin is tossed four times. What is the probability of getting four heads?

Each toss has a 1/2 chance of getting a head.

So the chance of getting all four heads can be calculated as :

[tex]1/2\times1/2\times1/2\times1/2=1/16[/tex]

2. A coin is tossed four times. What is the probability of getting two heads?

Each toss can have 2 results, so 4 flips will have [tex]2^{4}[/tex] or 16 results.

Getting two heads means getting two tails also. So, we can get the number of times two heads come = [tex]\frac{4!}{2!2!}[/tex] = 6

We can write the groups like - {HHTT,HTHT,HTTH,THHT,THTH,TTHH}

So, the required probability is : 6/16 or 3/8.

3. Not getting two heads means getting 3 tails and 1 head or all tails.

Probability of having all tails = [tex]1/2\times1/2\times1/2\times1/2=1/16[/tex]

Probability of one head(1st trial) and three tails = 1/16

Probability of one head (2nd trial) and three tails (the 1st, 3rd and 4th trials) = 1/16

Probability of one head (3rd trial) and three tails (the 1st, 2nd and 4th trials) = 1/16

Probability of one head (4th trial) and three tails (the 1st, 2nd and 3rd trials) = 1/16

So, the total probability showing only one or none head and at least three tails = [tex]1/16+1/16+1/16+1/16+1/16=5/16[/tex]

Answer: Population mean = [tex]\mu=5.5[/tex]

Sample mean = [tex]\overline{x}=6.25[/tex]

Step-by-step explanation:

We know that the population mean [tex]\mu[/tex] is the average of the entire population.

The sample mean [tex]\overline{x}[/tex] is the mean of the sample which is derived from the whole population randomly.

Given : A recent article in a college newspaper stated that college students get an average of 5.5 hrs of sleep each night.

Thus , the population mean = 5.5 hrs

Also, On average, the sampled students slept 6.25 hours per night.

It implies , the sample mean =  6.25 hours

Final answer:

The sample mean is 6.25 hours of sleep per night from the student's survey of 25 students, while the claimed population mean is 5.5 hours as stated in the college newspaper article.

Explanation:

In this scenario, the sample mean is the average amount of sleep that the 25 randomly sampled students reported, which is 6.25 hours per night.

The claimed population mean is the value mentioned in the college newspaper article, stating that college students get an average of 5.5 hours of sleep each night.

The sample mean represents the average found from the sample taken by the student, while the claimed population mean represents the average that is supposedly true for the entire population of college students.

Answer:

The arrow diagram and the matrix representation for the relation is shown below.

Step-by-step explanation:

The given relation is

R={(1, 2), (3, 4), (2, 3), (3, 2), (2, 1), (3, 1), (4, 3)}

If a relation is defined as

[tex]R=\{(x,y)|x\in R,y\in R\}[/tex]

Then the set of x values is domain and set of y values is range.

The domain of the function is

Domain={1, 2, 3, 4)

The range of the function is

Range={1, 2, 3, 4)

In arrow diagram, we have two sets first set represents the domain and second set represents the range. The arrow connecting the element represent the relation.

In matrix representation,

[tex]M_{ij}=\begin{cases}1 & \text{ if } (x_i,y_j)\in R \\ 0 & \text{ if } (x_i,y_j)\notin R\end{cases}[/tex]

The arrow diagram and the matrix representation for the relation is shown below.

The arrow diagram and matrix representation offer effective visualizations to understand and communicate the relationships within the given relation R={(1, 2), (3, 4), (2, 3), (3, 2), (2, 1), (3, 1), (4, 3)}.

The given relation R={(1, 2), (3, 4), (2, 3), (3, 2), (2, 1), (3, 1), (4, 3)} can be analyzed step by step. The domain, representing the set of x values, is Domain={1, 2, 3, 4}, and the range, representing the set of y values, is Range={1, 2, 3, 4}.

The arrow diagram visually represents this relation, with the first set depicting the domain and the second set depicting the range. Arrows connect elements to illustrate the relationships within the given set.

The matrix representation further encapsulates this relation, with rows corresponding to the elements of the domain and columns to the elements of the range. The presence of an entry in the matrix indicates a relation between the respective elements.

This method provides a concise and organized representation of the given relation. Overall, the arrow diagram and matrix representation serve as effective tools to comprehend and communicate the relationships within the specified set.

To learn more about arrow diagram

https://brainly.com/question/35400301

#SPJ6

Answer:

72

Step-by-step explanation:

In order to find the acceleration we need first to defined it, so:

acceleration=((final velocity)-(initial velocity))/time interval

[tex]a=(vf-vi)/dt[/tex]

But (vf-vi) actually represents the velocity change, so (vf-vi)/dt represents the velocity change rate. This means that in our case:

[tex]a=(36miles/hour)/(0.5hours)[/tex]

[tex]a=72miles/hour^2[/tex]

In conclusion the acceleration is [tex]a=72miles/hour^2[/tex], without units just 72.

Answer: 0.375

Step-by-step explanation:

The given interval : (0,6)  [in minutes]

Let X represents the waiting time of a passenger.

We know that the cumulative uniform distribution function for interval (a,b) is given by :_

[tex]F(x)=\begin{cases}0,&\text{ for } x<a\\\frac{x-a}{b-a},& \text{for } a\leq x\leq 1\\1,& \text{for }x>b\end{cases}[/tex]

Then , the  probability that a randomly selected passenger has a waiting time greater than 2.25 minutes. is given by :_

[tex]P(2.25<x)=\dfrac{2.25-0}{6-0}=0.375[/tex]

Hence, the required probability : 0.375

Answer:

Step-by-step explanation:

the answer is 0.625 reason is the probability is 62.5% and when you take

(6-2.25)/(6-0)

= (3.75)/(6)

=0.625

Answer: 0.4052

Step-by-step explanation:

Given : Mean : [tex]\mu=\text{307 ​grams}[/tex]

Standard deviation : [tex]\sigma = \text{4.1 grams}[/tex]

The formula for z -score :

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x=308 ,

[tex]z=\dfrac{308-307}{4.1}=0.24390\approx0.24[/tex]

The p-value = [tex]P(z>0.24)=1-P(z<0.24)[/tex]

[tex]=1-0.5948348= 0.4051652\approx0.4052[/tex]

Hence, the probability that a can will be sold that holds more than 308 ​grams =0.4052.

Answer:

The correct option is A.

Step-by-step explanation:

It is given that the probability of exactly 44 green marbles.

We need to use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability.

A continuity correction is an adjustment that is made when a discrete distribution is approximated by a continuous distribution.

For example: In discrete x=7, then in continuous 6.5<x<7.5. It means we need to subtract 0.5 in the number to find the lower limit and we need to add 0.5 in the given number to find the upper limit.

Similarly,

In discrete x=44, then in continuous

44-0.5<x<44+0.5

43.5<x<44.5

The area between 43.5 and 44.5. Therefore the correct option is A.

Answer:

(c) 5x - 3y = 11

Step-by-step explanation:

using slope intercept form

we know equation of line is

y= mx+c........(1)

where m is slope which  can be written as [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-7-3}{-2-4} =\frac{-10}{-6} =\frac{5}{3}[/tex]

substituting value in equation (1)

[tex]y=\frac{5}{3} x+c[/tex]

now inserting value of point (4,3)

[tex]3=\frac{5}{3}\times 4+c[/tex]

[tex]c=\frac{-11}{3}[/tex]

[tex]y=\frac{5}{3} \times x-\frac{11}{3}\\[/tex]

on solving we get

[tex]5x - 3y = 11[/tex]

Answer with explanation:

⇒689!=689×688×687×686×........×7×6×5×4×3×2×1

So, 689! is divisible by 7.

We have to find the remainder when,

 [tex]\frac{a}{m}=\frac{207^{321}+689!}{7}\\\\=\frac{207^{321}}{7}+\frac{689!}{7}\\\\=\frac{(210-3)^{321}}{7}+0\\\\=\frac{_{0}^{321}\textrm{C}\times (210)^{321}\times (3)^{0} -_{1}^{321}\textrm{C}\times (210)^{320}\times (3)^{1}+_{2}^{321}\textrm{C}\times (210)^{319}\times (3)^{2}-----(-1)\times _{321}^{321}\textrm{C}\times (321)^{0}\times (3)^{321}}{7}\\\\ \text{As ,210 is divisible by 7}\\\\=\frac{ (3)^{321}}{7}[/tex]

⇒[tex]3^7[/tex] ,when divided by 7, gives remainder 3.

[tex]\frac{ (3)^{321}}{7}=\frac{ (3)^{45\times 7+6}}{7}\\\\=3+\frac{3^6}{7}\\\\=3+1\\\\=4[/tex]

So,Remainder when

                    [tex]\frac{207^{321}+689!}{7}[/tex] is 4.

Answer:  After 3.75 seconds

Step-by-step explanation:

 For a Quadratic function in the form [tex]f(x)=ax^2+bx+c[/tex], if [tex]a<0[/tex] then the parabola opens downward.

Rewriting the given function as:

[tex]h(t) = - 16t^2+120t[/tex]

You can identify that [tex]a=-16[/tex]

Since [tex]a<0[/tex] the the parabola opens downward.

Therefore, we can conclude that the x-coordinate of the vertex is the time in seconds in which the ball will reach the maximum height. You can  find it with this formula:

[tex]t=\frac{-b}{2a}[/tex]

Substitute values, we get

[tex]t=\frac{-120}{2(-16)}=3.75\ seconds[/tex]

Final answer:

The time at which the ball reaches its maximum height is calculated using the vertex formula for a quadratic equation. In this case, the ball achieves maximum height after 3.75 seconds.

Explanation:

The function given is a quadratic equation in the form h(t) = 120t - 16t2, representing the height of a ball thrown vertically upward after t seconds. To find the time when the ball reaches its maximum height, we need to determine the vertex of the parabola represented by this equation.

The standard form of a quadratic equation is ax2 + bx + c. In this form, the time to reach the maximum height occurs at t = -b/(2a). Applying this to our equation, where a = -16 and b = 120, we calculate t = -120/(2*(-16)) = 120/32 = 3.75 seconds. Therefore, the ball reaches its maximum height after 3.75 seconds.

The probability that the time between two unplanned shutdowns of a power plant is between 18 and 24 days, following an exponential distribution with a mean of 30 days, is approximately 0.0033.

For an exponential distribution, the probability density function (PDF) is given by:

[tex]\[ f(x) = \lambda e^{-\lambda x} \][/tex]

where [tex]\( \lambda \)[/tex] is the rate parameter, and for an exponential distribution, [tex]\( \lambda = \frac{1}{\text{mean}} \)[/tex].

Given a mean of 30 days, [tex]\( \lambda = \frac{1}{30} \)[/tex].

Now, to find the probability that the time between two unplanned shutdowns is between 18 and 24 days, integrate the PDF over this interval:

[tex]\[ P(18 < X < 24) = \int_{18}^{24} \lambda e^{-\lambda x} \, dx \]\[ P(18 < X < 24) = \int_{18}^{24} \frac{1}{30} e^{-\frac{x}{30}} \, dx \][/tex]

Let's complete the calculations step by step.

[tex]\[ P(18 < X < 24) = \int_{18}^{24} \frac{1}{30} e^{-\frac{x}{30}} \, dx \]\[ P(18 < X < 24) = -\frac{1}{30}e^{-\frac{x}{30}} \Big|_{18}^{24} \][/tex]

Now, evaluate the integral at the upper and lower limits:

[tex]\[ P(18 < X < 24) = -\frac{1}{30} \left(e^{-\frac{24}{30}} - e^{-\frac{18}{30}}\right) \]\[ P(18 < X < 24) = -\frac{1}{30} \left(e^{-0.8} - e^{-0.6}\right) \][/tex]

Using a calculator:

[tex]\[ P(18 < X < 24) \approx -\frac{1}{30} \left(0.44933 - 0.54881\right) \]\[ P(18 < X < 24) \approx -\frac{1}{30} \times (-0.09948) \]\[ P(18 < X < 24) \approx 0.003316 \][/tex]

Therefore, the probability that the time between two unplanned shutdowns is between 18 and 24 days is approximately 0.0033 (rounded to four decimal places).

Answer:

The company needs to sell 9000 units in order to turn a profit of $40,000

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.

From the question we can get some important hints before creating our formula. First the Selling Price will be profit so it will be a positive number, but both unit cost and fixed costs are losses so they will be negative values in our formula. Also our formula will depend on the amount sold which we can represent as the variable x. With these hints we can create our formula as the following

[tex](60x-20x)-400,000 = y[/tex]

Where:

Now that we have our formula the question asks how many units need to be sold in order to earn a profit of $40,000. We can calculate this by replacing the $40,000 with y and solving for x like so,

[tex](60x-20x)-400,000 = 40,000[/tex] .... add 400,000 on both sides

[tex]40x= 360,000[/tex] ... divide both sides by 40

[tex]x= 9000[/tex]

The company needs to sell 9000 units in order to turn a profit of $40,000

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

a) After 30 years, the amount in the account will be approximately $499,355.18.

b) The total money deposited over 30 years will be $144,000.

c) The total interest earned over 30 years will be approximately $355355.18.

We have,

Given:

Monthly deposit: $400

Interest rate: 5% (expressed as a decimal, 0.05)

Time: 30 years (in months, 30 * 12 = 360 months)

a.

To calculate the amount in the account after 30 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Amount in the account

P = Initial deposit (first deposit)

r = Annual interest rate

n = Number of times interest is compounded per year

t = Time in years

In this case:

P = $400 x 360 = $144000

r = 0.05

n = 12 (compounded monthly)

t = 30

Substituting the values into the formula:

A = 144000(1 + 0.05/12)^(12 * 30)

A ≈ $499,355.18

b.

The total money deposited can be calculated by multiplying the monthly deposit by the number of months:

Total Money Deposited = Monthly deposit * Number of months

Total Money Deposited = $400 * 360

Total Money Deposited = $144,000

c.

The total interest earned can be calculated by subtracting the total money deposited from the amount in the account:

Total Interest Earned = Amount in the account - Total Money Deposited

Total Interest Earned = $499,355.18 - $144,000

Total Interest Earned ≈ $355355.18

Therefore,

After 30 years, the amount in the account will be approximately $499,355.18.

The total money deposited over 30 years will be $144,000.

The total interest earned over 30 years will be approximately $355355.18.

Learn more about compound interest here:

https://brainly.com/question/13155407

#SPJ4

To find the future value of the account after 30 years, use the compound interest formula. Multiply the monthly deposit by the number of months to find the total money put into the account. The total interest earned is found by subtracting the total money put into the account from the future value.

To calculate the future value of the account, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value, P is the principal (initial deposit), r is the interest rate in decimal form, n is the number of times interest is compounded per year, and t is the number of years.

a. Plugging in the values, we have [tex]A = 400(1 + 0.05/12)^(12*30)[/tex]. Using a calculator, the future value after 30 years will be approximately $1000.40.

b. To find the total money put into the account, we multiply the monthly deposit by the number of months. In this case, it will be $[tex]400 * 12 * 30 = $144,000.[/tex]

c. The total interest earned can be found by subtracting the total money put into the account from the future value. In this case, it will be $[tex]1000.40 - $144,000 = -$143,999.60.[/tex]

https://brainly.com/question/14295570

#SPJ3

Answer:

The proposition is false if p is true.

Step-by-step explanation:

I made the truth table in the picture, to fill it you need to know:

v : only is false when both propositions are false.

^ : only is true when both propositions are true.

⇒: only is false when the left proposition is true and the right proposition is false.

So, the answer is the third option.

The truth table analysis shows that the proposition (p & (q \/ p)) → ~p is a tautology, meaning it is always true regardless of the truth values of p and q.

To determine the truth value of the proposition (p & (q \/ p)) \/ ~p, we need to construct a truth table and evaluate the proposition for all possible truth values of p and q.

Truth Table Construction

Let's go step by step:

Construct two initial columns for the variables p and q with their possible truth values.

Create a column for the sub-proposition (q \/ p), which is true if either q or p (or both) is true.

Construct the column for the main proposition (p & (q \/ p)) which is true if both p is true and the previous sub-proposition is true.

Determine the negation of p (~p), which is true when p is false.

Finally, combine the results to evaluate the column for the entire proposition (p & (q \/ p)) \/ ~p, using the implication operator (→), whose result is only false when the antecedent is true and the consequent is false.

After evaluating, we find that the proposition is always true, making it a tautology. Therefore, the original proposition (p & (q \/ p)) → ~p is always true irrespective of the truth values of p and q.

Answer:

y=5x-6

Step-by-step explanation:

Hello

let´s see  , we have   P1(3,9) and P2(4.14)

first let's find its slope

[tex]m=\frac{y2-y1}{x2-x1}   = \frac{14-9}{4-3}[/tex]

[tex]m=\frac{5}{1} \\m=5[/tex]

the slope is 5.

[tex]y-y_{0} = m(x-x_{0} )\\\\using P1\\\\ y-9 = 5(x-3)\\\\y=5x-15+9\\\\y=5x-6[/tex]

where x is the independent variable and y is the dependent variable

Have a great day.

To find the equation of the line that passes through (3, 9) and (4, 14), calculate the slope and use the point-slope form, resulting in the equation y = 5x - 6 in slope-intercept form.

To find an equation of the line that passes through the points (3, 9) and (4, 14), we will first calculate the slope (m) of the line using the formula: m = (y2 - y1) / (x2 - x1). Substituting the given points into the formula, we have m = (14 - 9) / (4 - 3) = 5. With the slope known, we can use one of the points and the slope to write the equation in point-slope form, which is y - y1 = m(x - x1). Using the point (3, 9), the equation becomes y - 9 = 5(x - 3). To put this into slope-intercept form, we simplify to get y = 5x - 6.

Answer:

0.75

Step-by-step explanation:

We have been given that 400  people were asked whether gun laws should be more stringent. 300 hundred said "yes," and 100 said "no".

To find the point estimate of the proportion in the population who will respond "yes", we need to divide number of people who said yes by total number of people that is 300 by 400.

[tex]\text{People who will respond yes}=\frac{300}{400}[/tex]

[tex]\text{People who will respond yes}=\frac{3}{4}[/tex]

[tex]\text{People who will respond yes}=0.75[/tex]

Therefore, the  point estimate of the proportion in the population who will respond "yes" is 0.75.

Answer:

D. x=7√3 , y=4√2

Step-by-step explanation:

Step 1: Lets assume an imaginary line from A to B to make the triangle ABC( (refer to the attached image).

AB = 4

BD = 3

Step 2: Find the value of y by the sin formula.

opposite = 4

adjacent = BC

hypotenuse = AC

sin (angle) = opposite/hypotenuse

sin (45) = 4/AC

√2/2 = 4/AC

AC = y = 4√2

Step 3: Find the value of x

Tan (45) = opposite/adjacent

1 = 4/CB

CB = 4

x = CB + BD

x = 4 + 3

x = 7

Therefore, the answer is D where x = 7 and y = 4√2

!!

Answer:

[tex]2\sqrt{x}=\frac{5t^2}{2}+2[/tex]

Step-by-step explanation:

Given: [tex]\frac{\mathrm{d} x}{\mathrm{d} t}=5t\sqrt{x}\,,\, x(0)=1[/tex]

Solution:

A differential equation is said to be separable if it can be written separately as  functions of two variables.

Given equation is separable.

We can write this equation as follows:

[tex]\frac{dx}{\sqrt{x}}=5t\,dt[/tex]

On integrating both sides, we get

[tex]\int \frac{dx}{\sqrt{x}}=\int 5t\,dt[/tex]

Formulae Used:

[tex]\int \frac{1}{\sqrt{x}}=2\sqrt{x}\,\,,\,\,\int t\,dt=\frac{t^2}{2}[/tex]

So, we get solution as [tex]2\sqrt{x}=\frac{5t^2}{2}+C[/tex]

Applying condition: x(0) = 1, we get [tex]C=2[/tex]

Therefore, [tex]2\sqrt{x}=\frac{5t^2}{2}+2[/tex]

Answer:

The annual rate of return is 13.14%.

Step-by-step explanation:

As it is not mentioned whether the amount was compounded, so we will assume this to be simple interest.

Given is - A $3500 loan was settled ten years later with a payment of $8100.

Means total amount paid back was = $8100

And original principle was = $3500

So, interest paid = [tex]8100-3500=4600[/tex] dollars

Now simple interest formula is :

[tex]I=p\times r\times t[/tex]

Where p = 3500

I = 4600

r = ?

t = 10

Now putting these values in formula we get;

[tex]4600=3500\times r\times10[/tex]

[tex]r=4600/35000[/tex]

r=  0.1314

So, rate of interest = 13.14%