The points (0,5), (1,6), (2,9), and (3,14) are on the graph of a function. Write an equation in standard form that represents the function

Answer:

36720 different desserts

Step-by-step explanation:

(1020x3)x12=36720

Answer:

  1/60 gallon

Step-by-step explanation:

You want to know what is left of 4/5 gallon of paint if 3/4 gallon was used to paint a doghouse, and 2/3 of the remaining amount was used to paint a door.

To find the amount remaining we subtract the amount used for the doghouse from the original amount:

  4/5 -3/4 = (16 -15)/20 = 1/20 . . . . . gallon

2/3 of that was used, so 1/3 of it remains:

  (1/3)(1/20 gallon) = 1/60 gallon

There is 1/60 of a gallon of paint left in the can.

__

Additional comment

In a standard size gallon paint can, that's about 0.11 inches of paint in the bottom.

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Answer:

Step-by-step explanation:

Let assume that the volume = 88 cubic feet

Then:

\(L = 3w --- (1)volume = l \times w \times h \\ \\ 88 = (3w) \times w \times h \\ \\ 3w^2 h= 88 \\ \\ h = \dfrac{88}{3w^2}--- (2) \\ \\\)

The construction cost now is:

\(C = 4(l \times w) + 2 ( w \times h) + 2(l \times h) \\ \\ C = 4(3w^2) + 2(w \times \dfrac{88}{3w^2}) + 2(3w \times \dfrac{88}{3w^2}) \\\\ C = 12w^2 + \dfrac{176}{3w} + \dfrac{176}{w}\)

Now, to determine the minimum cost:

\(\dfrac{dC}{dw}= 0 \\ \\ \implies 24 w - \dfrac{176}{3w^2}- \dfrac{176}{w^2}=0 \\ \\ 24 w ^3 = \dfrac{176}{w^2}(\dfrac{1}{3}+1) \\ \\ 24 w ^3 = \dfrac{176(4)}{3} \\ \\ w^3 = \dfrac{88}{3(3)}\)

\(w = \dfrac{88}{3(3)}^{1/3} \ feet\)

Now;

\(length = 3 ( \dfrac{88}{3(3)})^{1/3} \ feet\)

\(height = ( 88})^{1/3} (3)^{1/3} \ feet\)

Answer:

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

The number is n.

The equation we can set:

Solve it:

The interquartile range of Victor's lemonade sale is A = 7

The distance between the upper and lower quartiles is known as the interquartile range. Half of the interquartile range corresponds to the semi-interquartile range. Finding the values of the quartiles in a small data set is straightforward.

The spread of the data, or statistical dispersion, is measured by the interquartile range. The middle 50%, fourth spread, or H-spread are further names for the IQR. It is described as the spread between the data's 75th and 25th percentiles.

Given data ,

Let the interquartile range of sales of Victor's lemonade be A

Now , the equation will be

Let the 75th percentile data = 29

Let the 25th percentile data be = 22

Now , the IQR is calculated by spread between the data's 75th and 25th percentiles

On simplifying , we get

The IQR = 29 - 22 = 7

Hence , the interquartile range is 7

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The complete question is :

Victor is selling lemonade to raise money for his school the amount of money he collected from his sales each day is summarized on the box plot below.

What is the interquartile range of the data?

For picture 1:

YES: 2x + 14 = 36 (2 · x) + (2 · 7) = 36 NO: The rest of the answer choices.

For Picture 2:

That equation is right.

Good luck Noal, and have a great day.

Answer:

15 nights

Step-by-step explanation:

187+26n=577

-187          -187

     26n=390

divide 26 on both sides

         n=15

The length of the string in cm is; 20 cm

We are told that the string is wound symmetrically around a circular rod.

Now, the circumference of the rod is 4 cm and length is 15 cm.

Now, circumference is also the length of a circle. Thus, one wound of the string will be equal to the circumference of the rod.

Thus, one wound = 4 cm

Since the string makes 5 turns about the rod, then;

Length of string = 5 × 4 = 20 cm

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The needed number of days at 10 degrees is given as follows:

11 days.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

For this problem, we have that when x decreases by 5, y increases by 2, hence the slope m is given as follows:

m = -2/5

m = -0.4.

Hence the time needed for a temperature of 10 degrees is given as follows:

9 + 2 = 11 days.

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As given in the equation,

The line is horizontal.

For a horizontal line, 'y' is always constant, while x keeps on changing.

Therefore, y will always be 2.

In contrast, x will keep on changing. Therefore, the equation of x would be x = a; while, a = ......, -3, -2, -1, 0, 1, 2, 3, .....

Hence

Answer:

A requested task is subject to be reported when it has been completed according to the instructions provided.

To demonstrate this with chain of thought reasoning:

1. The task requested will have details outlining what needs to be done.

2. To fulfill the request of the task, the instructions outlined must be followed.

3. Once all instructions are met, the task is complete.

4. Completion of the task means it is subject to be reported.

Step-by-step explanation:

The end behavior of the function is as x tends to infinity, f(x) tends to zero. It is power function.

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function given is determine the end behavior of the graph.

Given that function has a vertical asymptote at x = -5 and x = 3 , a point discontinuity at x = 2.

The end behavior of f(x) goes to 0 as x goes to negative infinity and f(x) goes to 0 as x goes to positive infinity.

The domain is (-inf, -5)U(-5, 2)U(2, 3) U (3,inf).

Hence, we can conclude that the end behavior of the function is as x tends to infinity, f(x) tends to zero.

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Answer:

220

Step-by-step explanation:

Circumference of a circle is=diameter times pi

70=diameter because diameter is twice the radius

(22/7)70 is your answer

Answer:

Triangle Area = ½ × b × h b = base h = vertical height

Rectangle Area = w × h w = width h = height

Parallelogram Area = b × h b = base h = vertical height

Step-by-step explanation:

:)

Answer:

area

triangle = 1/2 x base x height

rectangle = base x height

parallelogram = base x height

Step-by-step explanation:

Answer:

There's 3 questions which one do I answer?

Step-by-step explanation:

Answer:

D. 19

Step-by-step explanation: I got it correct, if you need more of an explanation go ahead and contact me by commenting below. (If you have any complaints, go ahead and tell me). Thank you & have a great day! :)

The volume of the cylindrical shaped pool with water is V = 75.4 feet³

Given data ,

Let the diameter of the pool be d = 8 feet

So , radius r = 4 feet

And , the height of the cylindrical pool is h = 3 feet

Now , the water is half full

So , Volume of Cylindrical pool is V = ( 1/2 ) πr²h

V = ( 1/2 ) ( 3.14 ) ( 4 )² ( 3 )

On simplifying , we get

V = 75.4 feet³

Hence , the amount of water in pool is V = 75.4 feet³

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182865658888835438469

Answer:

a. The 95% C.I. is approximately -5.83 < μ₁ - μ₂ < -0.57

b. Yes

c. The power of the test is 0.03836

d. The sample size can be considered adequate

Step-by-step explanation:

a. The given data in the study

Catalyst 1: 57.9, 66.2, 65.4, 65.4, 65.2, 62.6, 67.6, 63.7, 67.2, 71.0

Catalyst 2: 66.4 , 71.7, 70.3, 69.3, 64.8, 69.6, 68.6, 69.4, 65.3, 68.8

Using the Average, Standard Deviation function from Microsoft Excel, we have;

The mean for Catalyst 1, \(\overline x_1\) = 65.22

The standard deviation for catalyst 1, σ₁ = 3.444416

The mean for Catalyst 2, \(\overline x_2\) = 68.42

The standard deviation for catalyst 2, σ₂ = 2.22401

The 95% confidence interval on the difference in mean is given as follows;

\(\left (\bar{x}_1-\bar{x}_{2} \right ) \pm z_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}} + \dfrac{\sigma_{2}^{2}}{n_{2}}}\)

The critical-z for a 95% confidence interval = 1.96

Therefore, we have;

\(\left (65.22-68.42 \right ) \pm 1.96 \times \sqrt{\dfrac{3^{2}}{10} + \dfrac{3^{2}}{10}}\)

Therefore, we have;

The 95% C.I. is approximately -5.83 < μ₁ - μ₂ < -0.57

The test statistics is given as follows;

\(z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}\)

Therefore we have;

\(z=\dfrac{(65.22-68.42)}{\sqrt{\dfrac{3^{2} }{10}+\dfrac{3^{2}}{10}}} = -2.385\)

The p-value = P(Z<-2.39 or Z > 2.39) = 2P(Z<-2.39) = 2 × 0.00842 = 0.01684

b. From the confidence interval which range from approximately -5.83 to -0.57 and does not include 0, therefore, there is a difference in mean active concentration which depends on the choice of catalyst

c. The power of the test

 The sample mean difference is given as follows;

\(\left (\bar{x}_1-\bar{x}_{2} \right ) = \pm z_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}} + \dfrac{\sigma_{2}^{2}}{n_{2}}}\)

Therefore, we have;

\(\left (\bar{x}_1-\bar{x}_{2} \right ) = \pm 1.96 \times \sqrt{\dfrac{3^{2}}{10} + \dfrac{3^{2}}{10}} = \pm 2.6296\)

The z-value is given as follows;

\(z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}\)

μ₁ - μ₂ = 5

When \(\bar{x}_1-\bar{x}_{2} = 2.6296\)

\(z=\dfrac{2.6296-5}{\sqrt{\dfrac{3^{2} }{10}-\dfrac{3^{2}}{10}}} \approx -1.7667918\)

When \(\bar{x}_1-\bar{x}_{2} = -2.6296\)

\(z=\dfrac{-2.6296-5}{\sqrt{\dfrac{3^{2} }{10}-\dfrac{3^{2}}{10}}} \approx -5.686768\)

The power of the test is given by P = P(Z<-5.69) + P(Z>-1.77) = 0 + 0.03836 = 0.03836

The power of the test = 0.03836

d. The sample size is statistically adequate because the confidence interval of -5.83 < μ₁ - μ₂ < -0.57 has a value of -5 as a possible population difference in mean

The assumption of normality seems adequate because the confidence interval obtained by using the sample standard deviation is given as follows;

(-5.74, -0.66) which also contains -5 which is the difference in the population mean

Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.

Let's assume the number of miles driven is represented by 'm'. The cost of renting a moving truck for one day at Rentals Plus can be calculated using the equation:

Cost at Rentals Plus = $5.24 + $4.46 * m

Similarly, the cost of renting a moving truck for one day at Speedy Move can be calculated using the equation:

Cost at Speedy Move = $85.24 + $0.46 * m

To find the number of miles that makes the costs equal, we can set up the equation:

$5.24 + $4.46 * m = $85.24 + $0.46 * m

By rearranging the equation, we can solve for 'm':

$4.46 * m - $0.46 * m = $85.24 - $5.24

$4 * m = $80

m = $80 / $4

m = 20

Therefore, Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.

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Answer:

1)

P(X = 0) = 0.125

P(X = 1) = 0.375

P(X = 2) = 0.375

P(X = 3) = 0.125

2)

E(X) = 1.5

Step-by-step explanation:

For each coin, there are only two possible outcomes. Either it is heads, or it is tails. The probability of a toss being heads or tails is independent of any other toss. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

The expected value of the binomial distribution is \(E(X) = np\).

A fair coin is flipped 3 times.

Fair means that it is equally as likely to be heads or tails, so \(p = 0.5\).

3 times means that \(n = 3\)

(1) Find the pmf for X;

Probability of each outcome. So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{3,0}.(0.5)^{0}.(0.5)^{3} = 0.125\)

\(P(X = 1) = C_{3,1}.(0.5)^{1}.(0.5)^{2} = 0.375\)

\(P(X = 2) = C_{3,2}.(0.5)^{2}.(0.5)^{1} = 0.375\)

\(P(X = 3) = C_{3,3}.(0.5)^{3}.(0.5)^{0} = 0.125\)

(2) calculate the expected value of X.

\(E(X) = np = 3*0.5 = 1.5\)

Answer:

Step-by-step explanation:

we know the sum in an triangle will be 180-(47+39)=94

Answer:

X n Y , X n Y

Step-by-step explanation:

1) Use Associative law:

X n (X n Y) =  (X n X) n Y

Idempotent law:

= X n Y

2) it is in the 'distributed' form, thus we need to reverse the distribution,

akin to 'factorization':

(X n Y) u (X n Y) = (X n (Y u Y))

which can be further simplified using idempotent law:

= X n Y

Graph B is correct and shows the rectangular opening.

Looking at the text the question, I notice that each unit means 1 inch. After looking at all the graphs, I found out that B was the correct answer because of the sides. The sides are five inches by two inches and it was the only graph that had these units.

—————

Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle

—————

Answer: Option B.

Step-by-step explanation:

     With the scale of one unit equalling one inch, the only answer option that meets the given requirement of having side lengths that are 5 inches and 2 inches is option B.

     Answer A is 4 units by 2 units, Answer B is the needed 5 units by 2 units, Answer C is 7 units by 2 units, and Answer D is 6 units by 2 units. This leaves us with Answer B.

Step-by-step explanation:

To find an angle that is coterminal with an angle measuring -720°, we need to add or subtract multiples of 360° until we get an angle between 0° and 360°.

We can start by adding 360° multiple times until we get a positive angle:

-720° + 360° = -360° (still negative) -360° + 360° = 0°

So, -720° is equivalent to an angle of 0° plus a full rotation of 360°.

Since we want an angle that is between 0° and 360°, we can just take a = 0°.

Therefore, an angle that is coterminal with an angle measuring -720° and between 0° and 360° is a = 0°.

The solution to the system of equation is as follows:

x = 5 and y = 1

System of equation can be solved using different method such as elimination method and substitution method.

Therefore, let's solve the system of equation using elimination method as follows:

4x + 2y = 22

-2x + 2y = -8

subtract equation(ii) form equation(i)

6x = 30

divide both sides by 6

x = 30 / 6

x = 5

Hence, let's find the value of y

4x + 2y = 22

4(5) + 2y = 22

20 + 2y = 22

2y = 22 - 20

2y = 2

y = 2 / 2

y = 1

let's check whether or solution is correct.

-2(5) + 2(1) = -8

4(5) + 2(1) = 22

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Answer:

4 paintings in a full hour

Work:

Carly painted 6/7 of a picture in 3/14 hours:

6/7=3/14

Which means Carly painted 2/7 of a picture in 1/14 hours:

2/7=1/14

We need to find how many paintings she can paint in 1 full hour, or 14/14 of an hour, how do you get from 1/14 to 14/14? You do multiplication:

1/14 x 14 = 14/14

but there is a rule that says what you do to one side of the equation, you need to do it to the other side too so:

2/7 x 14=1/14 x 14

28/7=14/14

28/7=4  

Answer:

6/11, 11/2, 5.77, 5.772

Step-by-step explanation: