A residual plot has data points that are all very close to the x-axis. What does this say about the data?

A) The line of best fit will be a horizontal line.

B) A linear model is appropriate.

C) There is not enough information to determine this.

D) A non-linear model is appropriate.

Answer:

(3) Jonah's graph has a steeper slope than Rowan's

Step-by-step explanation:

First we are going to write the equations for the amount of money that each one save

y = a+bx

 Where y: Amount of money in the jar

             a: Initial saving

             b: Money saved every week ( graph's slope )

             x: Number of week

Then, for Rowan

y = 50 + 5x

and for Jonah

y = 10 + 15x

Initially Rowan's graph lies above Jonah's graph but this situation change with time.

It is always true that Jonah's graph has a steeper slope than Rowan's, because for Rowan's graph the slope is 5 and for Jonah's graph the slope is 15

Then the answer is:  

(3) Jonah's graph has a steeper slope than Rowan's

3) Jonah's curve has a steeper slope than Rowan's is True, All others are false

Rowan Savings Equation = 50 + 5t , where t is weekly time

Rowan Savings = 10 + 15t , where t is weekly time

        1             50 + 5 (1) = 55           10 + 15 (1) = 25

        2            50 + 5 (2) = 60          10 + 15 (2) = 40

        3            50 + 5 (3) = 65          10 + 15 (3) =  55

        4            50 + 5 (4) = 70           10 + 15 (4) = 70

        5            50 + 5 (5) = 75           10 + 15 (5) = 85

At t weeks < 3 , Rowan savings > Jonah savings. At t weeks > 4, Jonah savings > Rowan savings. At t = 4 units, their savings are equal. So, none savings curve is above the other 'always'.

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Answer:

Susan payed $30 for her purchase

Step-by-step explanation:

Chicken: $12.36 per package (x2) = $24.72

Broccoli: $1.98 per pound (x1/2)   =   $0.99      +

Milk: $3.49 per gallon (x1)             =   $3.49

-and no added sales tax             ____________

                                                           $29.20

If Susan got $0.80 in return, then she must have payed $30 to begin with.

Answer:

The amount of money that Susan use to pay for the items = $30

Step-by-step explanation:

2×(12.36)+0.5×(1.98)+(3.49)+(0.8) = 30.

:)

Answer: the 55th stripe is white

Step-by-step explanation:

The first four stripes on a wall with 100 stripes are red , blue, white, and purple. The four colors repeat in the same order. This means that Red always follow blue which is followed by white and then purple. This means that red would always start each new and consecutive set of four stripes and purple will always end it

We want to determine the 55th stripe. The last four stripes that include 55 ends with the 56th stripe. This means that the 56th stripe is purple. Therefore, the 55th stripe would be white because it follows purple.

The color of the 55th stripe on the wall is white. The colors repeat every four stripes implying that the 55th, as per our calculation, falls on the third color in the pattern, white.

This is a repetition pattern problem in Mathematics. The pattern of colors (red, blue, white, purple) on the wall repeats every four stripes. To determine the 55th stripe color, we divide 55 by 4, getting a quotient of 13 and a remainder of 3. The remainder indicates that the 55th stripe is the third color in our repeating pattern which is white.

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Answer:

(x + 4) x 2

Step-by-step explanation:

x represents number of cookies Alice ate.

x + 4 represents the number of cookies Tim ate.

As Bob had eaten twice the number of cookies that Alice ate the expression should be

(x + 4) x 2

Answer:

B = 47°

Step-by-step explanation:

THe theorem to solve this is very simple. The angle created Angle B intercepts to arcs, one major, another minor.

The major arc is DE, 142 degrees.

The minor arc is AC, 48 degrees.

The two secants intersect outside the circle and creates a vertex angle, Angle B. The theorem tells us that the measure of that vertex angle would be ONE HALF of the difference of the two intercepted arcs. So, we have:

[tex]B=\frac{1}{2}(142-48)=47[/tex]

So, B = 47°

Answer: Comment: From the explanations below,

2x + y = 10

-6x = 3y + 7 had an infinite solution, while y = 14 -2x

6x + 3y = 42 has a fictitious solution, so also equation

2x + y = 17

-6x = 3y - 51.

Step-by-step explanation:

Answer:

(C) y = 14 - 2x

6x + 3y+ 42

(F) 2x + y = 17

-6x = 3y - 51

Step-by-step explanation:

Plato Correct answer.  Got them right.  Select the two boxes that have the equation written above.

Answer:

a. 53.20; 94.30

Step-by-step explanation:

Data given  

[tex]\mu =73.75[/tex] reprsent the population mean

[tex]\sigma=6.5[/tex] represent the population standard deviation

The Chebyshev's Theorem states that for any dataset

• We have at least 75% of all the data within two deviations from the mean.

• We have at least 88.9% of all the data within three deviations from the mean.

• We have at least 93.8% of all the data within four deviations from the mean.

Or in general words "For any set of data (either population or sample) and for any constant k greater than 1, the proportion of the data that must lie within k standard deviations on either side of the mean is at least: [tex] 1-\frac{1}{k^2}"[/tex]

We want the limits that have at least 90% of the population is include. And using the theorem we have this:

[tex]0.9 =1-\frac{1}{k^2}[/tex]

And solving for k we have this:

[tex]\frac{1}{k^2}=0.1[/tex]

[tex]k^2 =\frac{1}{0.1}=10[/tex]

[tex]k=\pm 3.162[/tex]

So then we need the limits between two deviations from the mean in order to have at least 90% of the data will reside.

Lower bound:

[tex]\mu -3.162\sigma=73.75-3.162(6.5)=53.195 \apporx 53.20[/tex]

Upper bound:

[tex]\mu +3.192\sigma=73.75+3.162(6.5)=94.304 \approx 94.30[/tex]

So the final answer would be between (53.20;94.30)

Using Chebyshev's theorem to find the range of life expectancy for Canadian women that includes at least 90% of the population, the lower and upper bounds are approximately 53.21 years and 94.29 years, respectively.

The question pertains to calculating bounds on life expectancy using Chebyshev's theorem, which is a statistical rule that applies to different types of distributions, regardless of their shape. To calculate the bounds that include at least 90% of the data for the life expectancy of Canadian women, where the mean is 73.75 years, and the standard deviation is 6.5 years, we need to use the formula k = 1/√(1-(1/p)), where p is the proportion of the population. In this case, since we want to include at least 90% of the population, p=0.9.

First, we solve for k:

k = 1/√(1-(1/0.9))
k ≈ 3.16

Then, we multiply k by the standard deviation and subtract it from and add it to the mean to find the bounds:

Lower Bound = Mean - k * Standard Deviation
Lower Bound = 73.75 - (3.16 * 6.5) ≈ 53.21

Upper Bound = Mean + k * Standard Deviation
Upper Bound = 73.75 + (3.16 * 6.5) ≈ 94.29

Therefore, the bounds are approximately 53.21 years and 94.29 years, which corresponds to option a. 53.20; 94.30.

Answer:

The farmer will need 7 crates.

Step-by-step explanation:

It is given that there are 71 pumpkins in total.

And each crate holds 19 pumpkins.

Let the number of crates required be "n".

The total number of pumpkins can be calculated by multiplying number of pumpkins in each crate with total number of crates.

Thus, the equation is

[tex]19(n) = 71[/tex]

[tex]n = \frac{71}{19} = 7[/tex]

Thus, the farmer needs 7 crates to hold total of 71 pumpkins.

The exponential growth function that models the data is: A(t) = 6.27 million * e^(0.0173t)

We can use the given information to solve for the parameters in the exponential growth model:

1. Set up the equation:

We know the initial population (A_0) is 6.27 million and the projected population after 40 years (t = 40) is 9 million. Therefore:

A(t) = 6.27 million * e^(kt)

2. Solve for k:

Substitute the final population value and time into the equation and solve for k:

9 million = 6.27 million * e^(40k)

e^(40k) = 9 million / 6.27 million

e^(40k) ≈ 1.433

Take the natural logarithm of both sides to isolate k:

40k ≈ ln(1.433)

k ≈ ln(1.433) / 40

k ≈ 0.0173

3. Write the complete function:

Now that we know k, we can substitute it back into the original equation to find the complete function:

A(t) = 6.27 million * e^(0.0173t)

Therefore, the exponential growth function that models the data is: A(t) = 6.27 million * e^(0.0173t)

Answer:

Step-by-step explanation:

You just need the distance formula here.  It's very simple to follow:

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2    }[/tex]

which, for us, looks like this:

[tex]d=\sqrt{(13-4)^2+(19-7)^2}[/tex] and

[tex]d=\sqrt{9^2+12^2}[/tex] and

[tex]d=\sqrt{81+144}[/tex] and

[tex]d=\sqrt{225}[/tex] so

d = 15

Answer:

He can take 5 Horses at max in his trailer at one time without going over the max weight his truck can tow. (Assuming the average weight of one horse to be equal to 1000 pounds)

Step-by-step explanation:

The no. of horses that can be carried by the truck can be found by simply dividing the maximum weight, that the truck can tow by the weight of a horse.

Max. No of Horses = (Max weight truck can tow)/(Average weight of one    horse)

The weight of a horse is not given in the question .Thus, we assume the average weight of one horse, to be equal to 1000 pounds, we get:

Max. No of Horses = 5000 pounds/ 1000 pounds

Max. No of Horses = 5

Answer:

[tex]Jade's\,score=5*right\,answers[/tex]

Step-by-step explanation:

Because all the questions have the same point, we can find the weight (value) of each question dividing the total points by the total number of answers questions:

[tex]\frac{100}{20}= 5[/tex]

Now with the weight of each question the only thing we should to do is to multiply it by the number of the questions she got right:

[tex]Jade's\,score=5*right\,answers[/tex]

Let check if our equation works, if Jade got all the answers right, we expect she got a 100 score. Let verify on the equation

[tex]Jade's\,score=5*(20)=100[/tex], that's what we expected

If she got 10 right answers, we expect 50 score and if she got 0 right answers, we expect 0 score, let check again:

[tex]Jade's\,score=5*(10)=50[/tex]

[tex]Jade's\,score=5*(0)=0[/tex]

Again, we obtain the expected scores, so we can conclude our equation works.

To find Jade's score on the math test, calculate the points per question by dividing the total points (100) by the number of questions (20). Each question is worth 5 points. Jade's score is the number of questions she got right multiplied by 5 points.

To calculate Jade's score on a math test with 20 questions that is worth a total of 100 points, we can start by finding out how many points each correct answer is worth. Since the total points are evenly distributed among the questions, we divide the total points by the number of questions.

Each question is worth 5 points (100 points total ÷ 20 questions).

Let x represent the number of questions Jade got right. The equation to calculate Jade's score is then:

Score = 5 × x

To find Jade's score, we simply multiply the number of questions she got right by 5. For example, if Jade answered 16 questions correctly, her score would be 80 points (5 points/question × 16 questions).

Answer: The bond has to go down.

Step-by-step explanation: A bond is a loan usually given by an issuer to an investor that pays back a fixed rate of return.

Although bonds have a fixed rate of return, bonds itself are not fixed which means when bond price can rise or fall. When bond rises, interest falls and when bond price falls, interest rises. A vice versa relationship.

What this means is that the investor has to pay more, take for example.

-If a bond of $100 has a return rate of 10%, this means investor will pay back $10.

-If bond price increases $120, investor will have to pay $12. Investor pays more

-However, if bond price decreases to $80, investor will pay $8. Investor pays less

Therefore, for an existing bond to compete with a new bond which has a higher interest rate, the existing bond price has to go down so that interest can go up.

Answer:

c

Step-by-step explanation:

In the experimental design we are choosing a random rats from both sets either male and female.

each set contains 2 elements (A,B), where A is a  Female i.e F1, F2,F3,F4

and B is a male i.e M1,M2,M3,M4.

none of the sets can have 2 male or 2 female.

Only option 'C' has sets which contains B (F3, F2) and D (M3, M4) which is impossible.

Hence c is the answer.

The  assignment of treatments that is impossible is given as

c.) A (F1, M1), B (F3, F2), C (F4, M1), D (M3, M4)

Treatment, the way by which someone acts towards someone else.

Generally, from the parameters, we see that

A is a  Female i.e F1, F2,F3,F4

B is a male i.e M1,M2,M3,M4.

In conclusion, the sets can't have 2 male or 2 female.

Therefore, we have

c.) A (F1, M1), B (F3, F2), C (F4, M1), D (M3, M4)

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Answer:

-2L² + 50L − 300 ≥ 0

Step-by-step explanation:

View Image

Perimeter is the sum of all the sides. She got 50 feet of fence work with. So our equation right now is:

y + y + x + x = 50

However, she used her house for one of the side, so we can remove one of the side. Our new equation is now:

y + y + x = 50

Solve for one of the side. I solved for x because it's easier to work with and substitute later. I got x = 50 - 2y.

Now I solve for area. Area of a rectangle is Length * Width.

A = LW

I used x and y for my sides so my area is this instead:

A = yx

Substitute in x.

A = y(50 - 2y)

A = 50y - 2y²

Area must be a minimum of 300ft², so

50y - 2y² ≥ 300

50y - 2y² - 300 ≥ 0

replace y with L because that's what they used in the answer choice

-2L² + 50L − 300 ≥ 0

Answer:

-2l^2+50l-300 ≥ 0

l(50 − 2l) ≥ 300

(l − 15)(l − 10) ≤ 0

Step-by-step explanation:

[I'm still thinking sorry]

I'm assuming 2x-12 is the angle measure of DAC in degrees.

Let p=AB=AD, q=AC

By the Law of Cosines,

22² = p² + q² - 2pq cos 48°

q² - 2pq cos 48° + p² - 22² = 0

We also require by the triangle inequality

CD+AD < AC

16 + p < q

Let's set them equal and see where we are.

q=p+16

(p+16)² - 2p(p+16) cos 48° + p² - 22² = 0

p≈12.2125,

q≈28.2125

16² = p² + q² - 2 pq cos DAC

16² = 12.2125² + 28.2125² - 2 (12.2125)(28.2125) cos DAC

cos DAC = (12.2125² + 28.2125²  - 16²)/(2 (12.2125)(28.2125) ) = 1

That's a surprise, DAC maxes out at a right angle

90 = 2x - 12

102 = 2x

x = 51

Answer: 6 < x < 51

Answer:

Step-by-step explanation:

Let B divides AB in the ratio K:1

[tex]x=\frac{nx1+mx2}{m+n} \\y=\frac{ny1+my2}{m+n} \\\frac{-4}{5} =\frac{1*\frac{2}{3}+k*4}{k+1} \\-4k-4=\frac{10}{3} +20k\\-12 k-12=10+60k\\72k=-22\\36k=-11\\k=-\frac{11}{36} \\[/tex]

so B divides AB in the ratio 11:-36

[tex]x=\frac{-36*1+11 *\frac{-1}{2} }{11-36} \\x=\frac{83}{50}[/tex]

Answer:

[tex]\large \boxed{1.66}[/tex]

Step-by-step explanation:

1. Calculate the equation of the straight line joining A and C.

The equation for a straight line is

y = mx + b

where m is the slope of the line and b is the y-intercept.

The line passes through the points (-½, 4) and (1, ⅔)

(a) Calculate the slope of the line

[tex]\begin{array}{rcl}m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\ & = & \dfrac{\frac{2}{3} - 4}{1 - (-\frac{1}{2})}\\\\& = & \dfrac{-\frac{10}{3}}{\frac{3}{2}}\\\\& = & \dfrac{-10}{3}\times{\dfrac{2}{3}}\\\\& = & \dfrac{-20}{9}\\\\\end{array}[/tex]

(b) Find the y-intercept

Insert the coordinates of one of the points into the equation

[tex]\begin{array}{rcl}y & = & mx + b\\4 & = & \dfrac{-20}{9}\left(-\dfrac{1}{2}\right) + b \\\\4 & = & \dfrac{10}{9} + b\\\\b & = & \dfrac{36}{9} - \dfrac{10}{9}\\\\b & = & \dfrac{26}{9}\\\\\end{array}[/tex]

(c) Write the equation for the line

[tex]y = -\dfrac{20}{9}x + \dfrac{26}{9}[/tex]

2. Calculate the value of x when y = -⅘

[tex]\begin{array}{rcl}y & = & -\dfrac{20}{9}x + \dfrac{26}{9}\\\\-\dfrac{4}{5} & = & -\dfrac{20}{9}x+ \dfrac{26}{9}\\\\36 & = & 100x -130\\100x & = & 166\\x & = & 1.66\\\end{array}\\\text{The value of x is $\large \boxed{\mathbf{1.66}}$}[/tex]

The graph below shows your three collinear points.

Answer:

63 degrees

Step-by-step explanation:

add 4x + 23 and 6x + 7, then equal that to 130. When you find x, plug it into 4x+23 and get 63.

Answer:

Size C can is the best buy.

Step-by-step explanation:

The given question is incomplete; here is the complete question.

One brand of canned salmon is sold in four different sizes.

Size A The 7 1/5 -ounce can costs $3.49.

Size B The 16 1/2 -ounce can costs $6.49.

Size C The 24 3/4 -ounce can costs $8.49.

Size D The 30 2/3 -ounce can costs $10.99. What is the unit rate for each size to the nearest cent? If the cost is less than a dollar, put a zero to the left of the decimal point.

Size Unit rate

A (Blank)

B (Blank)

C (Blank)

D (Blank)

What size is best to buy? explain how you know.

For Size A - [tex]7\frac{1}{5}[/tex] ounce or [tex]\frac{36}{5}[/tex] ounce can costs $3.49

Therefore, per ounce cost = [tex]\frac{\text{Total cost}}{\text{Size of can}}[/tex]

= [tex]\frac{3.49}{\frac{36}{5}}[/tex]

= [tex]\frac{3.49\times 5}{36}[/tex]

= $0.48

For Size B - [tex]16\frac{1}{2}[/tex] or [tex]\frac{33}{2}[/tex] ounce can costs $6.49

Per ounce cost = [tex]\frac{6.49}{\frac{33}{2}}[/tex]

= [tex]\frac{6.49\times 2}{33}[/tex]

= 0.39

For size C - [tex]24\frac{3}{4}[/tex] ounce or [tex]\frac{99}{4}[/tex] ounce can costs $8.49

Per ounce cost = [tex]\frac{8.49}{\frac{99}{4}}[/tex]

                         = [tex]\frac{8.49\times 4}{99}[/tex]

                         = $0.34

For size D - [tex]30\frac{2}{3}[/tex] or [tex]\frac{92}{3}[/tex] ounce can for $10.99                                                              

Per ounce cost = [tex]\frac{10.99}{\frac{92}{3} }[/tex]

                         = [tex]\frac{10.99\times 3}{92}[/tex]

                         = $0.36

For size C, per ounce cost of the can is the least. Therefore, size C can is the best buy.

Answer:

[tex]z=\frac{0.21 -0.2}{\sqrt{\frac{0.2(1-0.2)}{400}}}=0.5[/tex]  

[tex]p_v =2*P(Z>0.5)=0.617[/tex]  

So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.1[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 10% of significance the true proportion of defectives it's not significant different from 0.2.  

Step-by-step explanation:

1) Data given and notation

n=400 represent the random sample taken

X=84 represent the number of items defective

[tex]\hat p=\frac{84}{400}=0.21[/tex] estimated proportion of defectives

[tex]p_o=0.2[/tex] is the value that we want to test

[tex]\alpha=0.1[/tex] represent the significance level

Confidence=90% or 0.90

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.2 or 20%:  

Null hypothesis:[tex]p=0.2[/tex]  

Alternative hypothesis:[tex]p \neq 0.2[/tex]  

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.21 -0.2}{\sqrt{\frac{0.2(1-0.2)}{400}}}=0.5[/tex]  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided [tex]\alpha=0.1[/tex]. The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

[tex]p_v =2*P(Z>0.5)=0.617[/tex]  

So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.1[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 10% of significance the true proportion of defectives it's not significant different from 0.2.  

Answer:

Step-by-step explanation:

a) Steps to prove that two triangles are similar are

1) AA(angle angle)if two angles of each triangle is congruent to two angles of another triangle, then the third angles of both triangles must be congruent since the sum of angles in the triangle is 180 degrees

2) SSS(side side side) if the three sides of both triangles are proportional to each other, then the triangles are similar.

3) SAS(side angle side) if two sides of a triangle are proportional to two sides of another triangle and and the angle formed by both lines in the two triangles are equal, then the third sides of both triangles are proportional. Therefore, the triangles are similar.

b) triangle ABC would be similar to triangle QRS if

1) angle A is congruent to angle Q and angle B is congruent to angle R

2)if the ratio of AB to QR is proportional to the ratio of AC to QS, and to BC to RS

3) if AC is proportional to QS, AB is proportional to QR and angle A = angle Q

c) AC/AB = QS/QR

60/50 = 6/QR

6/5 = 6/QR

6QR = 6×5 = 30

QR = 30/6 = 5 cm

Answer:

  x = -4

Step-by-step explanation:

Vertical asymptotes are found where the denominator has a zero that is not cancelled by a numerator zero. Here, the expression simplifies to ...

  [tex]f(x)=\dfrac{x^2+7x+10}{x^2+9x+20}=\dfrac{(x+5)(x+2)}{(x+5)(x+4)}=\dfrac{x+2}{x+4} \qquad x\ne -5[/tex]

The function is undefined at x=-5, but has a vertical asymptote at x=-4.

Answer:

B) [tex]j=32m[/tex]

Step-by-step explanation:

Given:

Ayanna jumps at the rate of = 32 times/minute

To find the algebraic equation to express the function of the total number of time Ayanna jumped the rope.

Solution:

Let [tex]j[/tex] represent the total jumps made by Ayanna.

Let Ayanna jump for [tex]m[/tex] minutes.

Using unitary method to calculate total number of jumps made by Ayanna in [tex]m[/tex] minutes.

In 1 minute, Ayanna jumps = 32 times

Thus, in [tex]m[/tex] minutes Ayanna will jump = [tex]32\times m=32m[/tex] times

Thus, the function can be represented as;

[tex]j=32m[/tex]  (Answer)

Answer: b

Step-by-step explanation:

Answer:

Yamal can move the ice to 82 km in approximately 15 hrs.

Step-by-step explanation:

Given:

Speed  = 5.5 km/hr

Distance = 82 km

Let time be represented as 'x'.

We need to find the number of hours required to travel 82 km.

We know that Distance can be calculated by the product of Speed and time.

Framing above sentence in equation form we get;

Distance = Speed × Time

Substituting the given value we get;

[tex]82 = 5.5x[/tex]

Hence The expression for number of hours is [tex]82 = 5.5x[/tex]

Solving the equation to find the value of x we get;

[tex]82 = 5.5x\\\\x=\frac{82}{5.5} = 14.90 \approx 15\ hrs[/tex]

Hence Yamal can move the ice to 82 km in approximately 15 hrs.

Answer:

Dh/dt  = 0.082 ft/min

Step-by-step explanation:

As a perpendicular cross section of the trough is in the shape of an isosceles triangle the trough has a circular cone shape wit base of  1 feet and height     h = 2 feet.

The volume of a circular cone is:

V(c)  = 1/3 * π*r²*h

Then differentiating on both sides of the equation we get:

DV(c)/dt   = 1/3* π*r² * Dh/dt   (1)

We know that DV(c) / dt   is  1 ft³ / 5 min      or     1/5  ft³/min

and  we are were asked how fast is the water rising when the water is 1/2 foot deep. We need to know what is the value of r at that moment

By proportion we know

r/h  ( at the top of the cone  0,5/ 2)   is equal to  r/0.5  when water is 1/2 foot deep

Then      r/h   =   0,5/2   =  r/0.5

r  =  (0,5)*( 0.5) / 2        ⇒   r  =  0,125 ft

Then in equation (1) we got

(1/5) / 1/3* π*r² =  Dh/dt

Dh/dt  = 1/ 5*0.01635

Dh/dt  = 0.082 ft/min

Answer:

$28,600

Step-by-step explanation:

Probably of 0.7 = 46000

Probability of 0.3 = 12000

The average profit = Sum of (x*Pr(x)

=0.7(46000) + 0.3(-12000)

= 32200 - 3600

= $28,600

The contractor should expect to earn $28,600 on the average

Answer:

The graph of the inverse function is the same that the graph of the original function

Step-by-step explanation:

step 1

Find the equation of the function in the graph

Let

f(x) ---> the function in the graph

we know that

Is a linear function

take the points (0,6) and (6,0)

Find the slope of the linear function

[tex]m=(0-6)/(6-0)\\m=-1[/tex]

Find the the equation of the linear function in slope intercept form

[tex]f(x)=mx+b[/tex]

we have

[tex]m=-1[/tex]

[tex]b=6[/tex] ---> the y-intercept is given

substitute

[tex]f(x)=-x+6[/tex]

step 2

Find the inverse of the function f(x)

Let

y=f(x)

[tex]y=-x+6[/tex]

Exchange the variables (x for y and y for x)

[tex]x=-y+6[/tex]

Isolate the variable y

[tex]y=-x+6[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=-x+6[/tex]

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

In this problem the graph of the inverse function is the same that the graph of the original function

Graphing the inverse of a function is achieved by flipping the graph over the line y = x. In science, graphs of inversely proportional variables like P and V form a hyperbola, but these can be 'linearized' for clarity and accuracy. Often, a regression analysis is utilized to find the best fitting line within a set of data plots.

To graph the inverse of a function, you observe the function as a set of points in a 2D space (on a graph) and flip each point over the line y = x. This results in a new function, which is the inverse. When it comes to more specific functions like pressure and volume relationships, this is shown when plotting the inverse of the pressure (P^-1) versus the volume (V), or the inverse of volume (V^-1) versus the pressure (P).

Scientists often linearize data when graphs have curved lines because they're difficult to read accurately at low or high values. If you plot P (pressure) versus V (volume), you will get a hyperbola. This kind of function can be 'linearized' to make it easier to understand and interpret.

Finally, in many cases, such as plotting data points of inflation rate versus unemployment rate, the resulting graph can be analysed using a statistical process called regression. This helps to find the best fitting line for the set of data plots, which can often not perfectly fit the line.

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The 500th digit from 1 to 500 in a row will be;

A: 0 or 1

The double digit numbers are; 10 to 99 = 90 numbers × 2 = 180 digits

This is a total of 180 + 9 = 189 digits

Thus, after 99, we are looking for the;

500 - 189 digit = 311th digit

(100 + x)3 = 312

100 + x = 312/3

100 + x = 104

x = 104 - 100

x = 4

The 104th term after 99 is;

104 + 99 = 203

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As per the question, the 500th digit would be:

a). 0 or 1

To write,

Numbers from [tex]1 to 500[/tex]

The numbers containing 1 digit [tex]= 9[/tex] digits  (1 to 9)

The numbers containing 2 digits [tex]= 90[/tex] × [tex]2 = 180[/tex]   (from 10 to 99)

To find,

[tex]500th[/tex] digit

Remaining [tex]= 500 - (180 + 9)[/tex]

[tex]= 311th[/tex]

As we know, 311 can not be divided by 3, and therefore, we will look for the nearest number that is divisible by 3 i.e. 312

So, assuming the x as 100 + nth digit

[tex](100 + x)3 = 312[/tex]

[tex]100 + x = 312/3[/tex]

[tex]100 + x = 104[/tex]

[tex]x = 104 - 100[/tex]

∵[tex]x = 4[/tex]

Now,

[tex]100 + 4 = 104th digit[/tex]

∵ [tex]104 + 99 = 203[/tex]

Since the [tex]312th[/tex] term is employed rather than the [tex]311th[/tex], it implies that[tex]203 - 3 = 200[/tex]. Thus, 0 would be the [tex]500th[/tex] digit.

Thus, option a is the correct answer.

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There are 4 numbers possible 156, 257, 358 and 459.

The value a digit in a number represents based on where it is in the number is known as place value.

Let 25 is a number, then the place value of 2 is 20.

Let the three-digit number is x5y,

Then the number whose digits are switched is y5x,

The number x5y can be written according to its place value = 100x + 50 + y

Similarly, y5x can be written according to its place value = 100 y + 50 + x

The number y5x is 495 more than the number x5y

Implies that,

100 y + 50 + x - (100x + 50 + y) = 495

99y-99x - 495

99(y-x) = 495

y-x = 5

The numbers can be 156, 257, 358 and 459.

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Final answer:

To find the three-digit number with the tens digit being 5 and the number increasing by 495 when the hundreds and ones digits are switched, set up an equation using placeholders for the hundreds and ones digits, solve the equation to find these digits, and deduce the original number, which is 459.

Explanation:

The question involves finding a three-digit number based on given conditions about digits and their positions. We know that the tens digit is 5. If we switch the hundreds and the ones digits, the number increases by 495. This implies that the ones digit must be less than the hundreds digit, as switching them results in a larger number. Let's denote the hundreds digit by 'a' and the ones digit by 'c'.

The original number can be represented as 100a + 50 + c, and after switching, the number becomes 100c + 50 + a. The problem states that the latter is 495 units larger than the original number. So, we can set up the following equation:

100c + 50 + a = (100a + 50 + c) + 495

Simplifying the equation gives us:

99c - 99a = 495

This simplifies to:

c - a = 5

Since 'a' and 'c' are digits, the only possibility is that a = 4 and c = 9. Therefore, the original number is 459.