Suppose that the number of worker-hours required to distribute new telephone books to x% of the households in a certain rural community is given by the function W(x)=250x/(400−x). (a) What is the domain of the function W? (Give the domain in interval notation. If the answer includes more than one interval write the intervals separated by the "union" symbol, U.) (b) For what values of x does W(x) have a practical interpretation in this context? (c) How many worker-hours were required to distribute new telephone books to the first 70% of the households? (d) How many worker-hours were required to distribute new telephone books to the entire community? (e) What percentage of the households in the community had received new telephone books by the time 3 worker-hours had been expended?

Answer:

The answer to your question is (-1, -1)

Step-by-step explanation:

Data

A (1, -6)

B (-3, 4)

Formula

Xm = [tex]\frac{x1 + x2}{2}[/tex]

Ym = [tex]\frac{y1 + y2}{2}[/tex]

Process

1.- Substitute the values in the formula

x1 = 1   x2 = -3

Xm = [tex]\frac{1 - 3}{2} = \frac{-2}{2} = -1[/tex]

y1 = -6   y2 = 4

Ym = [tex]\frac{-6 + 4}{2} = \frac{-2}{2} = -1[/tex]

2.- The midpoint is  (-1, -1)

For this case we have the following functions:

[tex]f (x) = x-7\\g (x) = x ^ 2 + 1[/tex]

We must find [tex](f * g) (x)[/tex]. By definition we have to:

[tex](f * g) (x) = f (x) * g (x)[/tex]

So:

[tex](f*g)(x)=(x-7)(x^2+1)[/tex]

We apply distributive property:

[tex](f * g) (x) = x ^ 3 + x-7x ^ 2-7\\(f * g) (x) = x ^ 3-7x ^ 2 + x-7[/tex]

We evaluate at [tex]x = -1:[/tex]

[tex](f * g) (- 1) = (- 1) ^ 3-7 (-1) ^ 2 + (- 1) -7\\(f * g) (- 1) = - 1-7 (1) -1-7\\(f * g) (- 1) = - 1-7-1-7[/tex]

Equal signs are added and the same sign is placed:

[tex](f * g) (- 1) = - 16[/tex]

Answer:

[tex](f * g) (- 1) = - 16[/tex]

Answer:

(a) The gallons of water in a tub and the number of minutes since the tap was opened.

(c) The length of a side of a square and the perimeter of the square.

(d) The length of a side of a square and the area of the square.

Step-by-step explanation:

Direct variation:

[tex]\text{If y varies directly with x}\\y = kx\\\text{where k is a proportionality constant.}[/tex]

(a) The gallons of water in a tub and the number of minutes since the tap was opened.

As the minutes for which the tap is opened increases, there is an increase in the amount of water in tub.

Thus, there is a direct variation  between the gallons of water in a tub and the number of minutes since the tap was opened.

(b) The height of a ball and the number of seconds since it was thrown.

As the time increases after the ball was thrown, its height increases. But after some time the height decreases and becomes zero.

Thus, this not an example of direct variation.

(c) The length of a side of a square and the perimeter of the square.

As the side of square increases the perimeter increases.

Thus, there is a direct variation between length of a side of a square and the perimeter of the square.

(d) The length of a side of a square and the area of the square.

As the side of square increases the area increases.

Thus, there is a direct variation between length of a side of a square and the area of the square.

Answer:

The answer is B.

Step-by-step explanation:

The variable A in the I=PAT equation stands for affluence. It represents the average consumption of each person in the population. As the consumption of each person increases, the total environmental impact increases as well. The choice B is the best choice that represents average consumption of each person in the population.

Answer:

10 stereos must the salesperson sell to make the same amount of money with both plans.

Step-by-step explanation:

Let the Number of stereo sold = x

According to Plan A

250 + 25X

According to Plan B

50X

According to given condition

250 + 25X = 50X

250 = 50X - 25X

250 = 25X

X = 250/25

X= 10

Answer:

32-35 Week case

[tex]z = \frac{2025-2500}{800}=-0.594[/tex]

40 week case

[tex]z = \frac{2225-2700}{375}=-1.27[/tex]

For this case since the z score is lower (-1.27<-0.574) for the baby of 40 week this one would be the baby that weighs less relative to the gestation period

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

32-35 Week case

Let X the random variable that represent the weight, and for this case we know the distribution for X is given by:

[tex]X \sim N(2500,800)[/tex]  

Where [tex]\mu=2500[/tex] and [tex]\sigma=800[/tex]

The z score given by:

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

And if w replace for the value of x=2025 we got:

[tex]z = \frac{2025-2500}{800}=-0.594[/tex]

40 week case

Let X the random variable that represent the weight, and for this case we know the distribution for X is given by:

[tex]X \sim N(2700,375)[/tex]  

Where [tex]\mu=2700[/tex] and [tex]\sigma=375[/tex]

The z score given by:

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

And if w replace for the value of x=2225 we got:

[tex]z = \frac{2225-2700}{375}=-1.27[/tex]

For this case since the z score is lower (-1.27<-0.574) for the baby of 40 week this one would be the baby that weighs less relative to the gestation period

Option D is the correct answer.

Step-by-step explanation:

The given system of equations are [tex]y=2x[/tex] and [tex]y=x^{2} +1[/tex]

To plot the equations in the graph, if we know the values of x and y coordinates.

To plot the equation [tex]y=2x[/tex] in the graph, let us substitute the value for x to find the value of y-coordinate.

For, [tex]x=0[/tex] ⇒ [tex]y=0[/tex]

For, [tex]x=1[/tex] ⇒ [tex]y=2[/tex]

For, [tex]x=2[/tex] ⇒ [tex]y=4[/tex]

Similarly, to plot the equation [tex]y=x^{2} +1[/tex], let us substitute the value for x,

For, [tex]x=0[/tex] ⇒ [tex]y=1[/tex]

For, [tex]x=1[/tex] ⇒ [tex]y=2[/tex]

For, [tex]x=2[/tex] ⇒ [tex]y=5[/tex]

These values are plotted in the graph. The graph that represents the system of equations is attached below.

Thus, the correct answer is option D.

Answer:

d

Step-by-step explanation:

Answer:

a) [tex]P(X>0.5)=P(\frac{X-\mu}{\sigma}>\frac{0.5-\mu}{\sigma})=P(Z>\frac{0.5-0.4}{0.05})=P(z>2)[/tex]

[tex]P(z>2)=1-P(z<2)[/tex]

[tex]P(Z>2) = 1-P(Z<2)= 1- 0.97725=0.02275[/tex]

b)[tex]P(0.4<X<0.5)=P(\frac{0.4-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{0.5-\mu}{\sigma})=P(\frac{0.4-0.4}{0.05}<Z<\frac{0.5-0.4}{0.05})=P(0<z<2)[/tex]

[tex]P(0<z<2)=P(z<2)-P(z<0)[/tex]

[tex]P(0<z<2)=P(z<2)-P(z<0)=0.97725-0.5=0.47725[/tex]

c) [tex]a=0.4 +1.28*0.05=0.464[/tex]

So the value of height that separates the bottom 90% of data from the top 10% is 0.464.  

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the reaction time of a driver to visual stimulus of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(0.4,0.05)[/tex]  

Where [tex]\mu=0.4[/tex] and [tex]\sigma=0.05[/tex]

We are interested on this probability

[tex]P(X>0.5)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

[tex]P(X>0.5)=P(\frac{X-\mu}{\sigma}>\frac{0.5-\mu}{\sigma})=P(Z>\frac{0.5-0.4}{0.05})=P(z>2)[/tex]

And we can find this probability using the complement rule:

[tex]P(z>2)=1-P(z<2)[/tex]

And using the normal standard table or excel we have this:

[tex]P(Z>2) = 1-P(Z<2)= 1- 0.97725=0.02275[/tex]

Part b

[tex]P(0.4<X<0.5)=P(\frac{0.4-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{0.5-\mu}{\sigma})=P(\frac{0.4-0.4}{0.05}<Z<\frac{0.5-0.4}{0.05})=P(0<z<2)[/tex]

And we can find this probability on this way:

[tex]P(0<z<2)=P(z<2)-P(z<0)[/tex]

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

[tex]P(0<z<2)=P(z<2)-P(z<0)=0.97725-0.5=0.47725[/tex]

Part c

For this part we want to find a value a, such that we satisfy this condition:

[tex]P(X>a)=0.10[/tex]   (a)

[tex]P(X<a)=0.90[/tex]   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.90 of the area on the left and 0.10 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.90 and P(z>1.28)=0.1

If we use condition (b) from previous we have this:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.9[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.9[/tex]

But we know which value of z satisfy the previous equation so then we can do this:

[tex]z=1.28=\frac{a-0.4}{0.05}[/tex]

And if we solve for a we got

[tex]a=0.4 +1.28*0.05=0.464[/tex]

So the value of height that separates the bottom 90% of data from the top 10% is 0.464.  

Answer:

a) 0.0228

b) 0.4772

c) 0.336

Step-by-step explanation:

Mean(μ) = 0.4 seconds

Standard deviation (σ) = 0.05 seconds

From normal distribution,

Z= (x - μ) / σ

a) P(x > 0.5)

Let x be the random variable for the required seconds

When x= 0.5

Z = (0.5 - 0.4)/0.05

Z = 2

From the normal distribution table, 2= 0.4772

φ(Z) = 0.4772

Recall that when Z is positive,

P(x >a) = 0.5 - φ(Z)

P(x > 0.5) = 0.5 - 0.4772

= 0.0228

b) For x = 0.4

Z= (x - μ) / σ

= (0.4 - 0.4) / 0.05

= 0

For x= 0.5

Z= (x - μ) / σ

= (0.5 - 0.4) / 0.05

= 2

From the table, P(0.4 < x < 0.5) = P(0 < Z < 2)

So we have

P(Z < 2) - P(Z<0)

From the table, 2 = 0.4772 and 0 = 0

We then have

0.4772 - 0

= 0.4772

c) we are looking for x such that 90% of the values lie above it or 10% of the value lie below it.

From the table , 10% probability gives a z value of -1.28

x = μ + Zσ

x = 0.4 + (-1.28*0.05)

x = 0.4 - (1.28*0.05)

= 0.336

Answer:

160m/s

Step-by-step explanation:

The object can hit the ground when t = a; meaning that s(a) = s(t) = 0

So, 0 = -16a² + 400

16a² = 400

a² = 25

a = √25

a = 5 (positive 5 only because that's the only physical solution)

The instantaneous velocity is

v(a) = lim(t->a) [s(t) - s(a)]/[t-a)

Where s(t) = -16t² + 400

and s(a) = -16a² + 400

v(a) = Lim(t->a) [-16t² + 400 + 16a² - 400]/(t-a)

v(a) = Lim(t->a) (-16t² + 16a²)/(t-a)

v(a) = lim (t->a) -16(t² - a²)(t-a)

v(a) = -16lim t->a (t²-a²)(t-a)

v(a) = -16lim t->a (t-a)(t+a)/(t-a)

v(a) = -16lim t->a (t+a)

But a = t

So, we have

v(a) = -16lim t->a 2a

v(a) = -32lim t->a (a)

v(a) = -32 * 5

v(a) = -160

Velocity = 160m/s

Using movement concepts, it is found that:

----------------------------------

The height of the object after t seconds, dropped from a height of 500 feet, is given by:

[tex]h(t) = -16t^2 + 500[/tex]

----------------------------------

It hits the ground when [tex]h(t) = 0[/tex], thus:

[tex]h(t) = 0[/tex]

[tex]-16t^2 + 500 = 0[/tex]

[tex]16t^2 = 500[/tex]

[tex]t^2 = \frac{500}{16}[/tex]

[tex]t = \sqrt{\frac{500}{16}}[/tex]

[tex]t = 5.59[/tex]

The object hits the ground after 5.59 seconds.

----------------------------------

The velocity is the derivative of the position, thus:

[tex]v(t) = h^{\prime}(t) = -32t[/tex]

The velocity when it impacts the ground is v(5.59), thus:

[tex]v(5.59) = -32(5.59) = -178.88[/tex]

The object hits the ground at a velocity of -178.88 feet per second.

A similar problem is given at https://brainly.com/question/14516604

Answer:

B) tenants in common.

Explanation:

There were two men, first was James Smith, and second was Bill Ross who bought a property mutually for their business venture by declared proportionate interest of 1/3 as well as 2/3 sequentially without the right regarding survivorship. Both of them want their shares to be acquired by their spouses'. Both hold a partnership but not a company. James, as well as Bill, most likely took the title as tenants in common. Because tenants in common possess versatility in whence they divide control as well as assign the rights concerning survivorship. Joint tenants, on the different hand, keep the property in similar shares while a common partnership is a business unit serving separate sharers. Severalty, as asserted beforehand, is individual ownership.

Answer:

[tex]y=\frac{5}{3} x-\frac{38}{3}[/tex]

the value of b is -38/3

Step-by-step explanation:

[tex]y=\frac{5}{3} x+b[/tex] goes through the point (7,-1)

we need to find out b for the given equation using (7,-1)

Plug in 7 for x  and -1 for y

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

[tex]-1=\frac{5}{3} (7)+b[/tex]

[tex]-1=\frac{35}{3}+b[/tex]

subtract 35/3 from both sides

[tex]-1 -\frac{35}{3} =b[/tex]

[tex]\frac{-38}{3} =b[/tex]

Replace it in the original equation

[tex]y=\frac{5}{3} x-\frac{38}{3}[/tex]

Answer:

  x = 0

Step-by-step explanation:

The argument x+3π/2 shifts the sine function 3π/2 to the left, making it equivalent to -cos(x). Then the equation becomes ...

  -2cos(x) = -2

  cos(x) = 1

On the interval [0, 2π), cos(x) is only 1 at x=0.

Answer:

Step-by-step explanation:

Distance covered= 195miles

Time = 180min = 3hours

Speed = distance/time

Speed = 195/3

Speed = 65miles/hour

Travis is driving at an average rate of speed of 65 miles per hour.

Speed in mathematics is one of the measurable quantity which is defined as the ratio of the distance covered by an object to the time taken to cover that distance.

Or in other words, speed of an object can be defined as the rate of change of the position of that object in any direction.

Speed is a scalar quantity, as it only has magnitude and no direction.

Speed can be calculated by the formula,

Speed = Distance / Time

Distance Travis travelled = 195 miles

Time taken to travel that distance = 180 minutes

                                                        = 180 / 60 hours

                                                        = 3 hours.

Speed = 195 / 3

           = 65 miles per hour

Hence the average rate of speed of Travis in the drive is 65 miles per hour.

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Answer: 100

Step-by-step explanation:

The sum of frequencies for all classes will always equal to the number of element in a data set.

Between 0-100 there will be 100 numbers.

So that it's 100

In the field of statistics, when you group data into classes, the sum of the frequencies always equates to the sample size. The reason is that every element or member of your sample belongs to only one class.

In statistics, the term frequency is related to the times a data value occurs. When dealing with numerical datasets grouped into classes for data analysis, the sum of frequencies for all classes always equals the total sample size. This is because every member of the sample belongs to one and only one class. For example, if you conducted a survey on the favorite fruits of 100 people (your sample size), and you grouped the responses into classes - apples, bananas, oranges, etc., the sum of the frequencies (i.e., the total number of people that prefer each fruit) should add up to 100 (the sample size).

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Answer:

Option a) c + s = 5.                                  

Step-by-step explanation:

Let variable c represent acre of corn crop and variable s represent acre of  strawberries crop.

5 acres can support corn and strawberries.

Thus, this can be expressed with the help of equation.

[tex]c + s = 5[/tex]

Farmer wants to make $5,500 from his crops.

He can make $1,000 per acre of corn and $1,500 per acre of strawberries.

This can be written as:

[tex]1000c + 1500s = 5500[/tex]

We have to find the constraint for the given system.

A constraint is something that limits or controls what we want to do. Here, the amount of land is limited and act as a constraint for the given situation.

Thus, the constraint for the given system is

Option a) c + s = 5.

Answer:

The answer to your question is    5x + 6y - 42 = 0  

Step-by-step explanation:

Data

y-intercept = 7

parallel to -5x - 6y = 1

Process

1.- Find the slope

                             - 6y = 5x + 1

                                 y = -5/6 x - 1/6

As the lines are parallels, the slope is the same in both lines

                                 m = -5/6

2.- Find the equation of the new line

If the line has a y-intercept of 7, it means that the point is (0, 7)

                       y - y1 = m(x - x1)

Substitution

                      y - 7 = -5/6 (x - 0)

Simplification

                      y - 7 = -5/6x

Equal to zero

                     5/6x + y - 7 = 0

Multiply by 6

                     5x + 6y - 42 = 0           This is the equation of the line

Answer:

6y = -5x + 42

Step-by-step explanation:

-5x - 6y = 1

-6y = 5x + 1---------------------(i)

y = -5x/6 - 1/6

comparing the equation above with y = mx + c, we have;

m = -5/6

for condition of parallelism

the gradient of the new line = -5/6

Using the formula

y = mx + c

y = -5x/6 + 7

6y = -5x + 42

Answer:

the answer is a

Step-by-step explanation:

Answer:

only red = 1/12, only water proof = 1/12 , only cool = nil we assume nil for toys with three collections( cool, red, waterproof) as it was not stated.

11/6 are neither red, water proof and cool.  

Step-by-step explanation:

outside the circles contain probability of neither red, cool and water proof. where the circles intersect shows probability of both either red and cool, water proof and cool and water proof and red etc. where all the circles intersect if for the three combinations which is nill. Attached is the diagram

Answer:

The answer representation is attached below

Step-by-step explanation:

This is a representation on a diagram.

n(R) = Number of red toys

n(WP) Number of water proof toys

n(C) = Number of cool toys

n(R∩WP) = Number of red and waterproof

n(R∩C) = Number of red and cool

n(WP∩C) = Number of waterproof and cool

n(R'∩WP∩C) = Neither red, waterproof nor cool

From the image as depicted on a venn diagram, each part is represented and filled ont the diagram, the small circle space filled represent the information given in the question.

Answer:

1. The correct answer is 46%

2. The correct answer is .07

3. The correct answer is (34%,58%)

4. The correct answer is (32%,60%)

Step-by-step explanation:

1. Let's calculate the percentage or proportion of patients that were dogs:

p = (7 + 4 + 5 + 5 + 2)/50 = 23/50 = 0.46

The correct answer is 46%

2. Let's estimate the standard error, using the given formula, this way:

S.e = √ (0.46 * 0.54)/50 = √0.049 = 0.07

The correct answer is .07

3. Let's calculate the confidence limits of the 90% confidence interval, this way:

Confidence limits = proportion +/- 1.645 * standard error

Confidence limits = 0.46 +/- 1.645 * 0.07

Confidence limits = 0.46 +/- 0.12

Confidence limits = 0.34, 0.58

The correct answer is (34%,58%)

4. Let's calculate the confidence limits of the 95% confidence interval, this way:

Confidence limits = proportion +/- 1.96 * standard error

Confidence limits = 0.46 +/- 1.96 * 0.07

Confidence limits = 0.46 +/- 0.14

Confidence limits = 0.32, 0.60

The correct answer is (32%,60%)

Answer:

46%

0.07

(34%,58%)

(32%,60%)

Step-by-step explanation:

i got it right

Only option 1: 3y+3z is equivalent to given expression

Step-by-step explanation:

In order to find the equivalent expression to given expression, we have to simplify each of the options to compare with the given expression

Given expression is:

[tex]3y+3z[/tex]

Option 1:

[tex]3(y+z)\\= 3y+3z[/tex]

Option 2:

[tex]3y+z[/tex]

Option 3:

[tex]10y+2z+y+z\\= 10y+y+2z+z\\= 11y+3z[/tex]

Option 4:

[tex]6+y+3z[/tex]

Hence,

Only option 1: 3(y+z) is equivalent to given expression

Keywords: Polynomials, expressions

Learn more about polynomials at:

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Answer:

the transmitter signal is picked up for 42.63m of the drive.

Ans = 42.63m

Step-by-step explanation:

Solution

Let triangle ABC formed by line from 56 miles south of transmitter, to the transmitter itself then to 53 miles west of the transmitter with sides

AB BC AC

Where AB = 56 miles

and BC = 53 miles

Therefore AC = Sqr((56m)^2 +(53m)^2) = 77.10m

The point of intersection of the radius of the radio transmitter signal and the triangle formed by the path of travel of the traveller and the lines AB and AC 

To find the perpendicular line that can be drawn from C to AB we have from trigonometric relations

56 × sin(t) = 53 × sin (90 - t) because the traveller moves from directly south of the transmitter to directly west of the transmitter

Hence we have

56×sin(t) = 53×cos(t) because sin(90-t) = cos(t)

Rearranging 56×sin(t) = 53×cos(t) we have

1=(56×sin(t))/ (53×cos(t))

or (sin(t)/ cos(t))=1/(56/53)=53/56

That is tan(t)=53/56 and ACTAN(t) = 43.42°

Angle (t)

Drawing a perpendicular line from the point of the radio transmitter C to the travel path of the traveller AB   and calling the point of Intersection E we have EC = 53×sin(43.42)=38.49m

It is seen that the distance from the point of intersection of the radius of the radio transmitter and intersection of the line CE and AB  is EI1 where I1 is the first point of intersection of the radius of the radio transmitter and the line AB

EI1=Sqr((44m)^2-(38.49m)^2)

= 21.31m

Also since the triangles CEI1 and CEI2 are identical, it follows that EI1 = EI2 = 21.32m

The distance over which the traveller will be able to receive the signal from the radio transmitter while travelling from point A to point B is the distance I1 to I2 which is equal to 2*I

=2×21.31=42.63m

Ans = 42.63m

The signal will be picked up for approximately 3.015 miles of the drive.

To solve this, first, find the equations of the circle and the line representing the transmitter's broadcast range and the path of the drive, respectively.

Then, find the intersection points. Calculate the distances from these points to the transmitter.

Determine the portion of the drive where the distance is within the broadcast range (44 miles).

It turns out the signal is picked up only for a short portion of the drive near one of the intersection points.

The equation of a circle with center (h, k) and radius r is:

(x - h) ²+ (y - k)² = r²

Given that the transmitter broadcasts in a 44-mile radius and assuming the center of the circle is at the origin (0,0) the equation of the circle is:

x² + y² = 44²

The equation of a straight line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Given that the drive is along a straight line from a city 56 miles south of the transmitter to a second city 53 miles west of the transmitter, the line can be represented as:

y = - 56/53 * x + 56

Next, we'll find the points of intersection between the circle and the line, which is step 3.

Substitute y = - 56/53 * x + 56 into x² + y² = 44² to solve for the x-coordinates of the intersection points. Then, use these x-coordinates to find the corresponding y-coordinates.

x² + (- 56/53 * x + 56)² = 44²

Expanding and simplifying this equation will give us a quadratic equation in x, which we can solve to find the x-coordinates of the intersection points.

x² + (3136/2809 * x² - 5376/53 * x + 3136) = 44²

x² + 3136/2809 * x² - 5876/53 * x + 3136 - 44² = 0

59345/2809 * x² - 5376/53 * x + 3136 - 44² = 0

345x² - 150992x + 17424 - 44² * 2809 = 0

59345x² - 150992x + 0 = 0

x = (-b±√b-4ac)/2a

Where a = 59345, b = -150992, and c = 0

x= [150992±√(-150992)2-4(59345)(0)] / 2(59345)

x= (150992±√22793455664) / 118690

x₁= (150992±151034) / 118690

x₁ = 302026 / 118690 = 2.545

x₂ = (150992-151034) / 118690

x₂ = -42 / 118690

≈ -0.00035

Now, we'll find the corresponding y-coordinates by substituting these x-values into

the equation of the line y = - 56/53 * x + 56

For x =2.545:

y₁ = - 56/53 * 2.545 + 56

y₁ ≈ 1.615

For x ≈ -0.00035:

y₂ = - 56/53 * (- 0.00035) + 56

y₂ ≈ 56

So, the two points of intersection are approximately (2.545, 1.615) and (-0.00035, 56).

The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by:

d = √(x₂-x₁)² + (y₂ - y₁)²

Let's calculate the distances from these intersection points to the origin (transmitter),

which is (0,0).

For point (2.545, 1.615) :

[tex]d_1 = \sqrt{(2.545 - 0)^2 + (1.615 - 0)^2}[/tex]

d[tex]d_1 = \sqrt{2.545^2 + 1.615^2}[/tex]

[tex]d_1 \approx \sqrt{6.475 + 2.61}[/tex]

[tex]d_1 \approx \sqrt{9.085}[/tex]

[tex]d_1 \approx 3.015[/tex]

For point (-0.00035, 56):

[tex]d_2 = \sqrt{(-0.00035 - 0)^2 + (56 - 0)^2}[/tex]

[tex]d_2 = \sqrt{(-0.00035)^2 + 56^2}[/tex]

[tex]d_2 \approx \sqrt{0 + 3136}[/tex]

[tex]d_2 \approx \sqrt{3136}[/tex]

[tex]d_2 = 56[/tex]

Since the signal from the transmitter can be picked up within a 44-mile radius, we need to determine at what points along the path the distances to the transmitter are less than or equal to 44 miles.

From our calculations, we see that d₁ ≈ 3.015 miles and d₂ = 56 miles.

Thus, the signal will be picked up during the portion of the drive where

d₁ ≤ 44 miles.

Therefore, the signal will be picked up for approximately 3.015 miles of the drive.

Answer:

a) f(x) = (x + 6)(x + 2)(x – 3)

b) [tex]f(x) = x^3 + 5x^2 - 12x - 36[/tex]

Step-by-step explanation:

We have to find the polynomial with zeroes as -6, -2, and 3.

Roots are those values of x for which the polynomial is zero.

a) f(x) = (x + 6)(x + 2)(x – 3)

[tex]f(x) = (x + 6)(x + 2)(x -3)=0\\\Rightarrow x+6 = 0, x+2 = 0, x-3 = 0\\\Rightarrow x = -6,x = -2, x = 3[/tex]

b)

[tex]f(x) = x^3 + 5x^2 - 12x - 36 \\\text{It can be factored as}\\f(x) = (x+6)(x-3)(x+2) = 0\\\Rightarrow (x+6)=0,(x-3)=0,(x+2)=0\\\Rightarrow x = -6, x = 3, x = -2[/tex]

c) f(x) = (x – 6)(x – 2)(x + 3)

[tex]f(x) = (x - 6)(x - 2)(x + 3) =0\\\Rightarrow (x -6)(x -2)(x + 3) = 0\\\Rightarrow (x -6)=0,(x -2)=0,(x + 3)=0\\\Rightarrow x = 6, x = 2, x = -3[/tex]

d)

[tex]f(x) = x^3 - 5x^2 - 12x + 36\\f(x) = (x-2)(x+3)(x-6)=0\\\Rightarrow (x-2) = 0, (x+3)=0,(x-6)=0\\\Rightarrow x =2, x = -3, x = 6[/tex]

Hi there! Since the ratios of students at Hanover High School are in different scales, we need to scale them up! First, let's take the ratio 1:2. This can be scaled up to 5:10. Now, combine the two ratios to find the ratio of freshmen to sophomores. 3:10 + 5:10 = 8:10. The remaining number is 2, since 8 + 2 = 10, so the ratio of freshmen to sophomores is 2:10!

Hope this was helpful!

Answer:

[tex]h'=\frac{dh}{dr}=-\frac{2}{r^3\pi}[/tex]

Step-by-step explanation:

Assuming the dough is of cylindrical shape and that the volume must stay the same the equation for the volume of the cylinder is the following:

[tex]V=r^2\pi h[/tex]

where V is the volume, r the radius and h the height of the cylinder. If you get h to the left hand side you get the following equation:

[tex]h=\frac{V}{r^2\pi}[/tex]

To find the rate of change of the height you need to derive the above equation with respect to r:

[tex]h'=-\frac{2}{r^3\pi}[/tex]

Rate of change is simply how much a quantity changes, over another.

The expression for the rate of change of the dough in terms of height h and radius r is [tex]\mathbf{h' = \frac{-2}{\pi r^3}}[/tex]

From the complete question, we have:

[tex]\mathbf{V = \pi r^2h}[/tex]

Next, we make h the subject

[tex]\mathbf{h = \frac{V}{\pi r^2}}[/tex]

Rewrite as:

[tex]\mathbf{h = \frac{V}{\pi}r^{-2}}[/tex]

Differentiate with respect to r

[tex]\mathbf{h' = -2\times \frac{V}{\pi}r^{-2-1}}[/tex]

[tex]\mathbf{h' = -2\times \frac{V}{\pi}r^{-3}}[/tex]

Rewrite as:

[tex]\mathbf{h' = \frac{-2V}{\pi r^3}}[/tex]

Remove V, to leave the answer in terms of r and h

[tex]\mathbf{h' = \frac{-2}{\pi r^3}}[/tex]

Hence, the expression for the rate of change of the dough in terms of height h and radius r is [tex]\mathbf{h' = \frac{-2}{\pi r^3}}[/tex]

Read more about rates of change at:

https://brainly.com/question/12786410

Answer:

a) [tex] P(Y\geq 10) = PX \leq 2) = 0.558[/tex]

b) [tex] E(X) = \mu_X = np = 12*0.2 = 2.4[/tex]

[tex] \sigma_X = \sqrt{np(1-p)}=\sqrt{12*0.2*(1-0.2)}=1.386[/tex]

[tex] E(Y) = \mu_Y = np = 12*0.8 = 9.6[/tex]

[tex] \sigma_Y = \sqrt{np(1-p)}=\sqrt{12*0.8*(1-0.8)}=1.386[/tex]

For this case the expected value of people lying is 2.4 and the complement is 9.6 and that makes sense since we have a total of 12 poeple.

And the deviation for both variables are the same.

Step-by-step explanation:

Assuming this previous info : "A federal report finds that lie detector tests given to truthful persons have probability about 0.2 of  suggesting that the person is deceptive. A company asks 12 job applicants about thefts from previous employers, using  a lie detector to assess their truthfulness. Suppose that all 12 answer truthfully. Let X = the number of people who the lie  detector says are being deceptive"

For this case the distribution of X is binomial [tex] X \sim N(n=12, p=0.2)

And we define the new random variable Y="the number of people who the lie detector says are telling the truth" so as we can see y is the oppose of the random variable X, and the distribution for Y would be given by:

[tex] Y \sim Bin (n=12,p=1-0.2=0.8)[/tex]

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

Part a

For this case we want to find this probability:

[tex] P(Y \geq 10) = P(Y=10)+P(Y=11) +P(Y=12)[/tex]

And if we find the individual probabilites we got:

[tex]P(Y=10)=(12C10)(0.8)^{10} (1-0.8)^{12-10}=0.283[/tex]

[tex]P(Y=11)=(12C11)(0.8)^{11} (1-0.8)^{12-11}=0.206[/tex]

[tex]P(Y=12)=(12C12)(0.8)^{12} (1-0.8)^{12-12}=0.069[/tex]

And if we replace we got:

[tex] P(Y \geq 10) =0.283+0.206+0.069=0.558[/tex]

And for this case if we find [tex] P(X\leq 2)=P(X=0) +P(X=1)+P(X=2)[/tex]  for the individual probabilites we got:

[tex]P(X=0)=(12C0)(0.2)^0 (1-0.2)^{12-0}=0.069[/tex]

[tex]P(X=1)=(12C1)(0.2)^1 (1-0.2)^{12-1}=0.206[/tex]

[tex]P(X=2)=(12C2)(0.2)^2 (1-0.2)^{12-2}=0.283[/tex]

[tex] P(X\leq 2)=0.283+0.206+0.069=0.558[/tex]

So as we can see we have [tex] P(Y\geq 10) = P(X \leq 2) = 0.558[/tex]

Part b

Random variable X

For this case the expected value is given by:

[tex] E(X) = \mu_X = np = 12*0.2 = 2.4[/tex]

And the deviation is given by:

[tex] \sigma_X = \sqrt{np(1-p)}=\sqrt{12*0.2*(1-0.2)}=1.386[/tex]

Random variable Y

For this case the expected value is given by:

[tex] E(Y) = \mu_Y = np = 12*0.8 = 9.6[/tex]

And the deviation is given by:

[tex] \sigma_Y = \sqrt{np(1-p)}=\sqrt{12*0.8*(1-0.8)}=1.386[/tex]

For this case the expected value of people lying is 2.4 and the complement is 9.6 and that makes sense since we have a total of 12 poeple.

And the deviation for both variables are the same.

Answer:

dfbustos is correct! But I wanted to add a bit more to part b, specifically why the standard deviation makes sense.

Step-by-step explanation:

Y = # of people who the lie detector says are telling the truth.

X = # of people who the lie detector says are telling being deceptive.

This leads to the following conclusion:

Y = 12 - X

(We are given that 12 people answered.)

Because the standard deviation is not affected by adding or subtracting a constant, it makes sense for the σY = σX.

Answer:

c i did the test

Step-by-step explanation:

Answer: The mean of this binomial distribution is 53.36.

Step-by-step explanation:

We know that , the mean of this binomial distribution is given by :_

[tex]\mu = np[/tex]

, where n = sample size or the number of possible trials .

p = probability of getting success in each trial.

We are given that , the probability of success in each of the 58 identical engine tests is p = 0.92.

i.e. n= 58

p=0.92

Then, the mean of this binomial distribution = [tex]58\times0.92=53.36[/tex]

Hence , the mean of this binomial distribution is 53.36.

Answer:

B )  -2

Step-by-step explanation:

slope of given points

slope [tex]m= \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }[/tex]

The given points are

[tex]m = \frac{-4-8}{5-(-1)}[/tex]

[tex]m=\frac{-12}{6}[/tex]

[tex]m=-2[/tex]

final answer :-

slope of the line is m=-2

Answer: A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of cashews should he use?

a 3

b 4

c 6

d 7

Step-by-step explanation:

3lbs of Cashews

Answer:

Step-by-step explanation:

4x+(10-x)*6.5 =4.75*10

4x+65-6.5x=47.5

6.5 x-4 x=65-47.5

2.5 x=17.5

x=7

peanuts=7 -pound

cashews=10-7=3 -pound

Answer:

To empty the aquarium it takes 26 minutes

Step-by-step explanation:

step 1

Find the volume of the aquarium

The volume of rectangular prism is

[tex]V=LWH[/tex]

we have

[tex]L=33\ in\\W=26\ in\\H=12\ in[/tex]

substitute the given values

[tex]V=(33)(26)(12)=10,296\ in^3[/tex]

step 2

Divide the volume by the rate of 396 in^3 per minute

[tex]10,296/(396)=26\ minutes[/tex]

therefore

To empty the aquarium it takes 26 minutes