a store sells two different brands of lemonade mix. for brand a 1/2 cup if mix makes a pitcher. for brand b 1/4 cup of mix makes a pitcher. the container for brand a contains 4 more cups of mix than the container for brand b. both containers make the same number of pitchers of lemonade. how many pitchers of lemonade can each container make?

Answer:

[tex]\frac{ds}{dt} = 39.586 km/h[/tex]

Step-by-step explanation:

let distance between farmhouse and road is 2 km

From diagram given

p is the distance between road and past the intersection of highway

By using Pythagoras theorem

[tex]s^2 = 2^2 +p^2[/tex]

differentiate wrt t

we get

[tex]\frac{d}{dt} s^2 = \frac{d}{dt} (4 + p^2)[/tex]

[tex]2s \frac{ds}{dt}  =2p \frac{dp}{dt} [/tex]

[tex]\frac{ds}{dt} = \frac{p}{s}\frac{dp}{dt}[/tex]

[tex]\frac{ds}{dt} = \frac{p}{\sqrt{p^2 +4}} \frac{dp}{dt}[/tex]

putting p = 3.7 km

[tex]\frac{ds}{dt} = \frac{3.7}{\sqrt{3.7^2 +4}} 45[/tex]

[tex]\frac{ds}{dt} = 39.586 km/h[/tex]

The distance between the automobile and the farmhouse is increasing at the automobile's constant speed of 45 km/h, which is the same as the car's rate of change of distance as it moves away from the farmhouse.

The question asks us to determine how fast the distance is increasing between an automobile and a farmhouse when the car is 3.7 km past a certain intersection, given the car's speed is 45 km/h. This is a problem that can be solved using the concepts of rates of change and kinematics.

Given that the car is moving in a straight line away from the farmhouse and there are no other factors altering the speed, the rate at which the distance between the car and farmhouse is increasing is constant and is equal to the speed of the car.

Since the car's speed is constant at 45 km/h, and it moves directly away from the farmhouse without any acceleration or deceleration, the rate at which the distance increases is exactly the car's speed. Therefore, when the car is 3.7 km past the intersection, the distance between the car and the farmhouse is still increasing at 45 km/h.

This straightforward problem shows that when an object moves away from a point at constant speed, the rate at which the distance between the object and the point increases is simply the speed of the object. This concept is very useful in solving more than 100 questions involving rates of change in kinematics, which is a part of classical mechanics.

Final answer:

The problem is solved by finding the prime factorization of 16,000 and assigning the factors to the chips based on their point values, resulting in there being 3 red chips.

Explanation:

The student's question is a typical problem in combinatorics, a field of mathematics concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. This problem also involves prime factorization as a method to solve for the number of chips.

To solve the problem, let us denote by R, B, and G the number of red, blue, and green chips respectively. Since the blue chips and green chips have the same quantity, the problem can be solved by first finding the prime factorization of the point value product of 16,000, which is 2⁷ × 5³, and then distributing these prime factors to match the point values of the chips.

Since the point values of blue and green chips are 4 (2²) and 5 respectively and their quantities are equal, we match the prime factors of 5 first. There are 3 factors of 5, so we assign one to each blue and green chip, resulting in 1 remaining.

Then, we match 2² or 4 to each blue and green chip, using 4 out of 7 factors of 2, leaving us with 3 factors of 2, which can be matched with 3 red chips since they have a value of 2 each.

Therefore, we have 3 red chips which is answer option C.

Answer:

Step-by-step explanation:

the formular for distance between two points is: [tex]\sqrt{(x2-x1)^2+(y2-y1)^2} \\\\\sqrt{4^{2}+1^{2} } \\\sqrt{17}\\ = 4.12[/tex]

Answer: Distance = 4.123

Step-by-step explanation:

The given coordinates are P(-1,5) and Q (3,4)

- 1 = x1 = the horizontal coordinate(along the x axis) at P

3 = x2 = the horizontal coordinate (along the x axis) at Q

5 = y1 = vertical coordinate( along the y axis) at P

4 = y2 = vertical coordinate(along the y axis) at Q

The distance between points P and Q is expressed as square root of the sum of the square of the horizontal distance and the square of the vertical distance. It becomes

Distance = √(x2 - x1)^2 + (y2 - y1)^2

Distance = √(3 - - 1)^2 + (4 - 5)^2

Distance = √ 4^2 + (-1)^2

Distance = √16+1 = √17

Distance = 4.123

Answer: 0.0142

Step-by-step explanation:

Given : The mean height of women in a country​ (ages 20 - ​29) is 64.2 inches.

i.e. [tex]\mu=64.2[/tex]

Also, [tex]\sigma=2.58[/tex]

Sample size : n= 50

Let x denotes the height of women.

Then, the probability that the mean height for the sample is greater than 65​ inches :-

[tex]P(x>65)=1-P(x\leq 65)\\\\=1-P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}\leq\dfrac{65-64.2}{\dfrac{2.58}{\sqrt{50}}})\\\\=1-P(z\leq2.193)\ \ [\because z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-0.9858463\ \ [\text{By using z-value table or calculator}]\\\\=0.0141537\approx0.0142[/tex]

Hence, the the probability that the mean height for the sample is greater than 65​ inches = 0.0142

Explanation:

Define points D, E, F as the midpoints of AB, BC, and AC, respectively. Point D is the midpoint of both AB and MN, so AMBN is a parallelogram, and side AM is parallel to and congruent with side NB.

Point E is the midpoint of both BC and NK, so BNCK is a parallelogram with side NB parallel and congruent to side CK, and by the transitive property of congruence, also to segment AM.

Point F is the midpoint of both AC and KL, so AKCL is a parallelogram with side CK parallel and congruent to side LA. By the transitive properties of congruence and of parallelism, sides AM, NB, CK, and LA are all congruent and parallel. Since AM and LA are congruent to one another and parallel, and share point A, point A must be their midpoint.

Answer:

$208,000

Step-by-step explanation:

For 50 years of marriage, Barry and Mary accumulated over $3.5million.

They have 3 children and 5 grandchildren which gives a total of 8.

You are allowed to give up $13,000 each year to a person without incurring tax liability.

This means Barry and Mary can give $13,000 to anyone each

For the 3 children and 5 grandchildren, Barry and Mary can gift $(13000 * 8) each

= $104,000 each

Therefore, Barry and Mary can gift $208,000 (104,000*2) to their children in 2017 without gift tax liability

Answer:

atleast 52

Step-by-step explanation:

Given that an employment agency requires applicants average at least 70% on a battery of four job skills tests.

An applicant scored 70%, 77%, and 81% on the first three exams,

Since weightages are not given we can assume all exams have equal weights

Let x be the score on the 4th test

Then total of all 4 exams = [tex]70+77+81+x\\= 228+x[/tex]

Average should exceed 70%

i.e.[tex]\bar X \geq 70\\Total\geq 70(4) =280[/tex]

Comparing the two totals we have

[tex]228+x\geq 280\\x\geq 280-228 = 52[/tex]

Hemust  score on the fourth test a score atleast 52 to maintain a 70% or better average.

Answer:

c

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

16*12 is 192. Plus the 6 for the bride and groom, and you get a total of 198.

Amy will need between 16 to 22 round tables for her wedding reception, accounting for a total guest range of 198 to 270, and considering that the head table seats 8 people. We calculate the number of tables by dividing the remaining guests by 12 and rounding up.

Let's solve the problem of determining the number of round tables Amy will need for her wedding reception. First, we know that the head table can sit the bride, groom, and their 6 attendants, totaling 8 people. Next, we calculate the number of guests that can be seated at the round tables, by subtracting the 8 people at the head table from the total number of guests:

Each round table can sit 12 guests, so we divide the numbers of remaining guests by 12 to find the range of tables needed:

Since we can't have a fraction of a table, we round up because each table can only seat whole numbers of guests. Therefore, Amy will need at least 16 tables for the minimum number of guests and at most 22 tables for the maximum number of guests.

The range for the number of round tables Amy will need for her reception, therefore, is 16 to 22 tables.

After reviewing the options, we can see that Option D matches our calculated range and is the correct choice for Amy’s wedding reception planning.

Answer:

Meningitis

Step-by-step explanation:

Meningitis is a inflammation of the membrane surrounding your brain and spinal cord.

In most cases it is caused by viral infection.

Some cases it improve without treatment in few days

Symptoms include:

As 17 year old had some symptoms such as headache,stiff neck, chills and vomiting o might be he have been suffered from Meningitis.

The simplified expression is -19/12.

First, the least common multiple (LCM) of the denominators, which in this case is 24.

Now, convert the fractions to have a denominator of 24:

-2/3 = -16/24

20/24 remains the same

-1.75 can be written as -42/24

Now we can add and subtract the fractions:

-16/24 + 20/24 - 42/24 = -38/24

Finally, we can simplify the fraction:

-38/24 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2.

-38/24 ÷ 2/2 = -19/12

Therefore, the simplified expression is -19/12.

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Answer:

By using hypothesis test at α = 0.01, we cannot conclude that the proportion of high school teachers who were single greater than the proportion of elementary teachers who were single

Step-by-step explanation:

let p1  be the proportion of elementary teachers who were single

let p2 be the proportion of high school teachers who were single

Then, the null and alternative hypotheses are:

[tex]H_{0}[/tex]: p2=p1

[tex]H_{a}[/tex]: p2>p1

We need to calculate the test statistic of the sample proportion for elementary teachers who were single.

It can be calculated as follows:

[tex]\frac{p(s)-p}{\sqrt{\frac{p*(1-p)}{N} } }[/tex] where

Using the numbers, we get

[tex]\frac{0.2-0.15}{\sqrt{\frac{0.15*0.85}{180} } }[/tex] ≈ 1.88

Using z-table, corresponding  P-Value is ≈0.03

Since 0.03>0.01 we fail to reject the null hypothesis. (The result is not significant at α = 0.01)

The proportion of single high school teachers (0.20) is greater than the proportion of single elementary school teachers (0.15). However, further statistical testing would be required to determine if this difference is significant.

To answer the student's question regarding proportions, we first need to calculate the proportion of single teachers in both samples. For elementary school teachers, the proportion is 15 out of 100, or 0.15. For high school teachers, the proportion is 36 out of 180 or 0.20.

Now, to determine if the proportion of high school teachers who were single is statistically greater than the proportion of elementary school teachers, we would typically perform a hypothesis test for the difference in proportions. However, in this simplified comparison, we can see that the proportion of single high school teachers (0.20) is indeed greater than the proportion of single elementary school teachers (0.15).

It's important to note that this does not mean there is a significant difference, we would need to conduct a significance test (like a Z-test for two proportions at the α = 0.01 level ) to determine this.

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Answer:

a) 0.394

b) 0.430

c) 0.981

Step-by-step explanation:

Use binomial probability:

P = nCr pʳ (1−p)ⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

and p is the probability of success.

Here, n = 3 and p = 4/15.

r is the number of defective tablets.

a) If r = 0:

P = ₃C₀ (4/15)⁰ (1−4/15)³⁻⁰

P = 1 (1) (11/15)³

P = 0.394

b) If r = 1:

P = ₃C₁ (4/15)¹ (1−4/15)³⁻¹

P = 3 (4/15) (11/15)²

P = 0.430

c) If r ≠ 3:

P = 1 − ₃C₃ (4/15)³ (1−4/15)³⁻³

P = 1 − 1 (4/15)³ (1)

P = 0.981

To find the probability of selecting no defective tablets, multiply the probabilities of selecting non-defective tablets.

a) To find the probability of selecting no defective tablets, we need to find the probability of selecting 3 non-defective tablets. There are 11 non-defective tablets out of the total of 15 tablets. So, the probability is:

Multiplying these probabilities together:

(11/15) * (10/14) * (9/13) = 990/2730 ≈ 0.362 = 36.2%

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Answer: it’s easy your teacher should’ve taught this in 9th

Step-by-step explanation:

Answer:

The answer to your question is  2 x 10¹⁴

Step-by-step explanation:

Process

1.- Divide the whole numbers

                                                [tex]\frac{4}{2}  = 2[/tex]

2.- Apply rule of exponents

                                              8 - (-6) = 8 + 6 = 14

3.- Write the answer

                                              2 x 10¹⁴

Answer:

0.028

Step-by-step explanation:

Let sample space, S, be the trucks.

Hence, n(S)= number of trucks=9750

Let E be the event of the truck failing within the first two years of operation.

Hence, n(E)=273

Therefore by classical definition of probability, the probability of occurrence of the event E, denoted by P(E), is

P(E)=[tex]\frac{n(E)}{n(S)}[/tex]=[tex]\frac{number of trucks failed within two years of operation}{Total number of trucks}[/tex]

⇒P(E)=[tex]\frac{273}{9750}[/tex]=0.028

The probability that an Ajax truck will develop transmission problems within the first two years is 2.8%, calculated by dividing the number of trucks with transmission problems (273) by the total number of trucks (9,750).

To calculate the probability that an Ajax truck will develop transmission problems within the first two years, we can use the formula for simple probability:

P(event) = Number of favorable outcomes / Total number of possible outcomes

Given that 273 out of 9,750 Ajax trucks developed transmission problems, the probability P is calculated as:

P(transmission problems) = 273 / 9,750

P(transmission problems) = 0.028 or 2.8%

The probability is 0.028, which means there is a 2.8% chance that an Ajax truck will develop transmission problems within the first two years of operation.

Answer:

Step-by-step explanation:

A recipe for a pan of brownies requires 1 ½ cups of milk. Converting the 1 1/2 to improper fraction, it becomes 3/2 cups of milk

The recipe also requires 2/3 cups of sugar

It also requires 1 1/5 cups of oil. Converting to improper fraction, it becomes 6/5 cups of sugar

Total number of cups of ingredients in the mixing Bowl will be sum of the amount if milk, sugar and oil. It becomes

3/2 + 2/3 + 6/5 = (45 + 20 + 36)/30

= 101/30 cups of ingredients

Answer:

$22,508

Step-by-step explanation:

Edmentum

The total cost that she pays for car will be $22,508.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

A = P + (PRT)/100

Where P is the principal, R is the rate of interest, and T is the time.

Mia as of late purchased a vehicle worth $20,000 borrowed with a financing cost of 6.6%. She made an initial investment of $1,000 and needs to reimburse the credit in the span of two years (two years).

Then the total cost that she pays will be calculated as,

A = $20,000 + ($19,000 x 6.6 x 2) / 100

A = $20,000 + $2,508

A = $22,508

The total cost that she pays will be $22,508.

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You can use variables to model the situation and convert the description to mathematical expression.

The time that the fountain will take to get drained completely with both valves open is approximately 2.27 hours.

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on  methods can be used to convert description to mathematical expressions.

Let the fountain contains V amount of water

Let the first valve emits x liter of water per hour

Let the second valve emits y liter of water per hour

Then, from the given description, we have:

With only the first valve open, the fountain completely drains in 4 hours

or

[tex]x \times 4 = V\\\\x = \dfrac{V}{4}[/tex] (it is since V volume of water is drained when we let x liter of water drained for 4 hours, thus adding x 4 times which is equivalent of x times 4)

Similarly,

With only the second valve open, the fountain completely drains in 5.25 hours
or

[tex]y \times 5.25 = V\\y = \dfrac{V}{5.25}[/tex]

Let after h hours, the fountain gets drained, then,

[tex]x \times h + y \times h = V\\\\\dfrac{V}{4}h + \dfrac{V}{5.25}\times h = V\\\\\text{Multiplying both the sides with} \: \dfrac{4 \times 5.25}{V}\\\\5.25 \timses h + 4 h = 4 \times 5.25\\9.25h = 21\\\\h = \dfrac{21}{9.25} \approx 2.27[/tex]

Thus,

The time that the fountain will take to get drained completely with both valves open is approximately 2.27 hours.

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Final answer:

By adding the work rates of the two valves and then calculating the reciprocal of the combined rate, it is estimated that it will take approximately 2.27 hours for the fountain to drain with both valves open.

Explanation:

To find out how long it will take for the fountain to drain with both valves open, you can use the rate of work formula, which states that work is the product of rate and time. When dealing with two independent work rates that contribute to completing a single job, we can add their work rates together to find the combined work rate.

Valve 1's rate of work is draining the fountain in 4 hours, which means its rate is 1/4 fountain per hour. Valve 2's rate of work is draining the fountain in 5.25 hours, which means its rate is 1/5.25 fountain per hour.

To find the combined rate, we add these two rates together:

1/4 + 1/5.25 = 0.25 + 0.19 = 0.44 (approximately)

This combined rate is 0.44 fountain per hour. Now, to find the total time to drain the fountain with both valves open, we take the reciprocal of the combined rate:

1 / 0.44 = 2.27 hours (approximately)

Therefore, it will take approximately 2.27 hours for the fountain to drain with both valves open.

the correct answer is C. The interval estimate is above 70%, so infer that it will be supported.The 95% confidence interval (0.75, 0.85) indicates that we can expect around 75% to 85% of students to support the fee increase, which is more than the presumed 70%. So, we can infer that the fee increase will be supported.

In the scenario given, the 95% confidence interval for the proportion of students supporting the fee increase is [0.75, 0.85].

This means that we are 95% confident that the true proportion of students who support the fee increase falls within this interval. Since the entire range is above 70%, we can be pretty confident that more than 70% of the student population supports the fee increase.

The confidence interval is a statistical method that gives us a range in which the true parameter likely falls based on our sample data. This shows us that statistical inference can give us insights about a population based on a sample.

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Answer:

a) The debris was 256 feet  into the air after 2 seconds of the explosion.

b)

[tex]h(t) = -16t(t-10)[/tex]

Step-by-step explanation:

We are given the following in the question:

Initial Velocity =  160 feet per second

[tex]h(t) = 160t-16t^2[/tex]

The above function gives the height in feet and t is seconds after the explosion.

a) Height of the debris 2 second(s) after the explosion.

We put t = 2 in the above function

[tex]h(2) = 160(2)-16(2)^2 = 256[/tex]

Thus, the debris was 256 feet  into the air after 2 seconds of the explosion.

b) Factor the polynomial

[tex]h(t) = 160t-16t^2\\= 16t(10-t)\\=-16t(t-10)[/tex]

Final answer:

The height of the debris 2 seconds after the explosion is 256 feet. The given polynomial can be factored completely as -16t(t - 10)

Explanation:

To find the height of the debris 2 seconds after the explosion, we can substitute t = 2 into the equation h(t) = 160t - 16t^2.

So, h(2) = 160(2) - 16(2)^2 = 320 - 16(4) = 320 - 64 = 256 feet.

Therefore, the height of the debris 2 seconds after the explosion is 256 feet.

To factor the given polynomial completely, we can rewrite it as:

h(t) = -16t^2 + 160t.

Now, we can factor out a common factor of -16t:

h(t) = -16t(t - 10).

This gives us the completely factored form of the polynomial.

Answer:

  2485

Step-by-step explanation:

The number of seats in row n is given by the explicit formula for an arithmetic sequence:

  an = a1 +d(n -1)

  an = 20 +3(n -1)

The middle row is row 18, so has ...

  a18 = 20 + 3(18 -1) = 71 . . . . seats

The total number of seats is the product of the number of rows and the number of seats in the middle row:

  capacity = (71)(35) = 2485

The seating capacity is 2485.

Answer:

B. [tex]P=l+w[/tex]

Step-by-step explanation:

Let l represent length of rectangle and w represent width of rectangle.

We have been given four formulas for the perimeter of rectangle. We are asked to choose the formula that displays a common student error for finding the perimeter.

We know that perimeter of a polygon is sum of all sides of the polygon. We also know that rectangle is polygon having two sets of equal sides.

The perimeter, P, of rectangle will be sum of its all sides that is:

[tex]P=l+w+l+w[/tex]

Combine like terms:

[tex]P=2l+2w[/tex]

Factor out 2:

[tex]P=2(l+w)[/tex]

Upon looking at our given choices, we can see that formula represented by option B displays a common student error for finding the perimeter.

Answer:

Ashley and her 4 friends would required 5.33 hours to repair 1575 bags of sample.

Step-by-step explanation:

75% is written as 0.75 as a decimal or 3/4 as a fraction.

Her friends take 75% longer, so multiply the time it takes Ashley by 1 + the percentage: 1.75 as a decimal or [tex]1 \frac{3}{4} \ \ or \ \ \frac{7}{4}[/tex] as a fraction.

[tex]\frac{2}{3} \times \frac{7}{4} =\frac{14}{12} = 1 \frac{2}{12} = 1 \frac{1}{6} minutes[/tex].

1 hour = 60 minutes.

Divide minutes in an hour by minutes per pack:

Ashley can pack: [tex]\frac{60}{\frac{2}{3}} = 90 \ bags\ per \ hour[/tex]

1 friend can pack: [tex]\frac{60}{1\frac{1}{6}}=\frac{360}{7} = 51 \frac{3}{7} \ bags \ per \ hour.[/tex]

multiply the amount 1 friend can pack by 4 friends: [tex]51 \frac{3}{7} \times 4 = \frac {1440}{7} = 205 \frac{5}{7} \ bags \ per \ hour[/tex]

Ashley and her friends can pack [tex]90 + 205 \frac{5}{7} = 295 \times \frac{5}{7} \ bags \ per \ hour.[/tex]

Now divide the total bags by bags per hour:

[tex]\frac{1575}{295 \frac{5}{7}} = 5.33 \ hours[/tex] ( Round answer as needed.)

Hence, Ashley and her 4 friends would required 5.33 hours to repair 1575 bags of sample.

Answer:

We conclude that  the mean transaction time exceeds 60 seconds.

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 60 seconds

Sample mean, [tex]\bar{x}[/tex] = 67 seconds

Sample size, n = 16

Alpha, α = 0.05

Sample standard deviation, s = 12 seconds

First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 60\text{ seconds}\\H_A: \mu > 60\text{ seconds}[/tex]

We use One-tailed(right) t test to perform this hypothesis.

Formula:

[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }[/tex] Putting all the values, we have

[tex]t_{stat} = \displaystyle\frac{67 - 60}{\frac{12}{\sqrt{16}} } = 2.34[/tex]

Now, [tex]t_{critical} \text{ at 0.05 level of significance, 15 degree of freedom } = 1.753[/tex]

Since,                  

[tex]t_{stat} > t_{critical}[/tex]

We fail to accept the null hypothesis and reject it. Thus, we conclude that  the mean transaction time exceeds 60 seconds.

Final answer:

The hypothesis test for the mean ATM transaction time given a sample mean of 67 seconds and a standard deviation of 12 seconds involves a one-tailed Z-test, where the null hypothesis H0: μ = 60 is rejected in favor of the alternative hypothesis Ha: μ > 60 since the test statistic of 2.33 exceeds the critical value of 1.645 at an α = .05 significance level.

Explanation:

Conducting a Hypothesis Test for Mean Transaction Time

For the sample of 16 ATM transactions with a mean of 67 seconds and a standard deviation of 12 seconds, the goal is to test the hypothesis that the mean transaction time exceeds 60 seconds.

a. Determine your hypotheses

The null hypothesis (H0) is that the mean transaction time is 60 seconds (H0: μ = 60). The alternative hypothesis (Ha) is that the mean transaction time is greater than 60 seconds (Ha: μ > 60).

b. Compute the test statistic

To compute the test statistic, we use the following formula for a sample mean with a known standard deviation: Z = (Xbar - μ0) / (s / sqrt(n)) where Xbar is the sample mean, μ0 is the hypothesized population mean, s is the sample standard deviation, and n is the sample size. Plugging in the values we get: Z = (67 - 60) / (12 / sqrt(16)) = 7 / (12 / 4) = 2.33.

c. Rejection rule

The rejection rule is if the computed test statistic is greater than the critical value at α = .05 significance level, we reject H0.

d. Critical Value at α = .05

The critical value for a one-tailed Z-test at α = .05 is approximately 1.645.

e. Conclusion

Because our test statistic of 2.33 exceeds the critical value of 1.645, we reject the null hypothesis, concluding that there is sufficient evidence at the 0.05 significance level to suggest that the mean transaction time exceeds 60 seconds.

Answer: $66

Step-by-step explanation:

Area of a rectangular =length*breadth

= 3.2 km * 3.0 km = 9.6km(squared)

Note, 1.6km = 1 mile

Cost of a hiking trail = $11 per mile

Converting kilometer to kill = 9.6km/1.6km = 6 miles

Hence, cost of a hiking trail to surround the rectangular shaped wilderness = $11 * 6 = $66

In case the cost is $11,000 per mile; total cost of hiking trails to surround the wilderness equals $66,000

You can find the cost of the trail by first calculating the perimeter of the rectangular wilderness area in kilometers, converting this into miles, and then multiplying by the given cost per mile. The total cost to install the trail would be approximately $85,250.

To calculate the cost of installing the hiking trail, we first need to find the perimeter of the rectangular forest, which will represent the length of the trail. In a rectangle, the perimeter is calculated as 2*(length + width).

Thus, the perimeter of the forest is 2*(3 km + 3.2 km) = 2*6.2 km = 12.4 km.

Next, we need to convert this into miles, as the cost is given in dollars per mile. We know that 1 mile is approximately equivalent to 1.6 km, so to convert km to miles, we can divide the distance in kilometers by 1.6.

The length in miles is therefore 12.4 km / 1.6 = 7.75 miles.

Finally, to find the total cost, we multiply the length of the trail in miles by the cost per mile: $11,000*7.75 miles = $85,250.

So, the cost to install the trail surrounding the wilderness area would be approximately $85,250.

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The computed value of the test statistic is 4.06 when using a sample size of 25 observations and a correlation coefficient of 0.60. Since this value is greater than 2.045 (the critical value for a two-tailed test at an alpha level of 0.05), we conclude that the population correlation is significantly different from zero.

In the context of this question, the student is conducting a hypothesis test to examine whether the population correlation is significantly different from zero. Given that the student has a sample size of 25 observations with a correlation coefficient of 0.6, we can calculate the test statistic. Our first step is to find the t value using the formula: t = r*sqrt[(n-2)/(1-r²)], where n is the sample size and r is the correlation coefficient.

Substituting the given values, t=0.6*sqrt[(25-2)/(1-0.6²)].

Solving this gives a t-value that can be rounded to 4.06. Since this value is greater than the critical value of 2.045 for a two-tailed test at an alpha level of 0.05, we reject the null hypothesis and conclude that the sample correlation coefficient is statistically significant, meaning it is unlikely that the correlation in the population is zero.

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Answer:

The total number of men is 32. Of these men, 25 wore a watch. So, the number of men who didn’t wear a watch is 7, because 32 − 25 = 7.

Step-by-step explanation:

Answer:

a) Cost (h,x)  =  12*x*h + 5*x²

b)

V =  V(max) = 355.5 ft³

Dimensions of the hut:

x = 9.48 ft       (side of the base square)

h = 3.95 ft      ( height of the hut)

Step-by-step explanation:

Let x be the side of the square of the base

h the height of the hut

Then the cost of the hut as a function of "x"  and "h" is

Cost of the hut = cost of 4 sides + cost of roof

cost of side  = 3* x*h   then for four sides cost is   12*x*h

cost of the roof = 5 * x²

Cost(h,x)  =  12*x*h + 5*x²

If the troll has only 900 $

900 = 12xh + 5x²        ⇒ 900 - 5x² = 12xh      ⇒(900-5x²)/12x  = h

And the volume of the hut   is  V  =  x²*h       then

V (h)  =  x² * [(900-5*x²)]/12x

V(h)  = x (900-5x²) /12      ⇒ V(h) = (900*x - 5*x³) /12

Taking derivatives (both sides of the equation):

V´(h) =  (900 - 10* x²)/12                V´(h) =  0

900 - 10*x² = 0          ⇒ x² = 90         x =√90      

x = 9.48 ft

And h

h = (900-5x²)/12x       ⇒  h = [900 - 90(5)]/12*x    ⇒ h = 450/113,76

h = 3.95 ft

And finally the volume of the hut is:

V(max) = x²*h             ⇒   V(max) = 90*3.95

V(max) = 355.5 ft³

A hut will consist of four walls and one roof. The figures needed evaluates to:

Let the three dimensions(height, length, width) be x, y,z units respectively.

Then the volume of the cuboid is given as

[tex]V = x \times y \times z \: \rm unit^3[/tex]

To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.

Putting those values of x in the second rate of function, if results in negative output, then at that point, there is maxima. If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.

For this case, we're specified that:

Four walls are attached to sides of floor. Thus, their one edge's length = length of side of floor = [tex]x \: \rm ft[/tex]

Thus, we get:

Thus, cost of four walls' material = [tex]3 \times 4 \times h \times x = \$ 12hx[/tex]

Thus, cost of roofing material for this roof = [tex]5 \times x^2 = \$5x^2[/tex]

Thus, cost of hut = cost for walls + cost for roof = [tex]12hx + 5x^2 = x(12h+5x) \: \rm (in \: dollars)[/tex]

The volume of the hut is: [tex]x\times x\times h =x^2.h \: \rm ft^3[/tex]

If troll has got only $960, then,

[tex]12hx + 5x^2 \leq 960\\\\\text{Multiplying x on both the sides}\\\\12x^2h + 5x^3 \leq 960x\\\\x^2h \leq \dfrac{960x-5x^3}{12}[/tex]

Let we take [tex]f(x) =\dfrac{960x-5x^3}{12}[/tex]

Then, taking its first and second derivative, we get:
[tex]f(x) =\dfrac{960x-5x^3}{12}\\\\f'(x) = 80 -1.25x^2\\\\f''(x) = -2.5x[/tex]

Putting first derivative = 0, we get critical points as:

[tex]80-1.25x^2 = 0\\\\x = 8 \text{\:(positive root as x denotes side length, thus a non-negative quantity)}[/tex]

At x = 8, the second derivative evaluates to:

[tex]f''(8) = -2.5(8) < 0[/tex]

Thus, we obtain maxima at x = 8.

Thus, we get the maximum value of function when x = 8.

Since we have:

[tex]V = x^2h \leq f(x)[/tex] (V is volume of the hut)

and [tex]max(f(x)) = f(8) = \dfrac{960(8) - 5(8)^3}{12} = 640-213.3\overline{3} \approx 426.67[/tex]

Thus, max(V) = 426.67 sq. ft approximately.

Thus, the figures needed evaluates to:

Learn more about maxima and minima here:

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Answer:

  B.  2010.62 ft³

Step-by-step explanation:

The formula for the volume of a cylinder is ...

  V = πr²h . . . . . where r is the radius and h is the height

Filling in the numbers and doing the arithmetic, we get ...

  V = π(8 ft)²(10 ft) = 640π ft³ ≈ 2010.6193 ft³ ≈ 2010.62 ft³

The volume of the cylinder is about 2010.62 ft³.

Answer:

Mrs. Wright's paycheck is $630

Step-by-step explanation:

Let x = Mrs. Wright's paycheck.

Mrs. Wright spent 2/9 of her paycheck on food. This means that the amount of money spent on food is 2/9 × x = 2x/9

She spent 1/3 on rent. This means that the amount spent on rent is

1/3 ×x x = x/3

Amount she spent on food and rent is x/3 + 2x/9 =3x + 2x /9

= 5x/9

The remainder is her pay check - the amount that she spent on food and rent. It becomes

x - 5x/9 = (9x- 5x)/9 = 4x/9

She spent 1/4 of the remainder on transportation. It means that she spent 1/4 × 4x/9 = x /9 on transportation.

Amount left = 4x /9 - x/9= 3x/9

She had $210 left. Therefore,

210 = 3x/9

3x = 9×210 = 1890

x = 1890/3

x = $630