by considering the curve traced by the parametrisation z(t) = t 2 it3 with −1 ≤ t ≤ 1, show why the condition that z ′ (t) never vanishes is necessary to ensure that smooth curves have no cusps.

The greatest number of 27-inch pieces that she can cut from three pieces of ribbon is found to be 19. So, option B is the correct answer choice.

Each yard is equal to 36 inches, so 5 yards are equal to 180 inches. Therefore, each piece of ribbon is 180 inches long.

To find out how many 27-inch pieces Lucia can cut from each piece of ribbon, we divide 180 by 27.

180/27 = 6.67

Since Lucia can only cut whole pieces, she can cut 6 pieces of ribbon from each piece of ribbon.

Therefore, she can cut a total of 6 x 3 = 18 pieces of ribbon from the three separate pieces of ribbon.

Learn more about Division :

https://brainly.com/question/19871608

#SPJ4

If the area of the base is 19. 6 ft^2 and the height of the pyramid is 11. 6 ft, the volume of the pyramid is approximately 79.1 cubic feet.

The formula for the volume of a pyramid is given by:

V = (1/3) × base area × height

In this case, we are given that the pyramid has a square base, so the base area is simply the area of a square with side length s:

base area = s^2 = 19.6 ft^2

We are also given the height of the pyramid:

height = 11.6 ft

Substituting these values into the formula for the volume of a pyramid, we get:

V = (1/3) × base area × height

= (1/3) × 19.6 ft^2 × 11.6 ft

≈ 79.1 ft^3 (rounded to the nearest tenth)

To learn more about volume click on,

https://brainly.com/question/23861754

#SPJ4

Step-by-step explanation:

vf = vo + at      vo = 0 in this case  ( you dropped it from 'at rest')

4 f/s = 32 t

t = 1/8 s

df = do + vot + 1/2 at^2                  df = final position = 0 ft (on the ground)

0 = do  + 0   + 1/2 (-32)(1/8)^2

   solve for do = 1/4 foot

There are 120 different ways to award the gold, silver, and bronze medals to the 10 women in the 100 meters race.

The number of ways that the gold, silver, and bronze medals can be awarded to 10 women is a combination problem.

We can use the formula for combinations to determine the number of ways to choose 3 women out of 10 for the medals:

[tex]nCr = n! / (r! * (n - r)!)[/tex]

Where n is the total number of women (10) and r is the number of medals (3).

So, the number of ways to award the gold, silver, and bronze medals to the 10 women is:

[tex]10C3 = 10! / (3! * (10 - 3)!) = 120[/tex]

Therefore, there are 120 different ways to award the gold, silver, and bronze medals to the 10 women in the 100 meters race.

To learn more about combination problem. refer the below link

https://brainly.com/question/4658834

#SPJ4

In the given equation r = 2/5 t "r" is the dependent variable.

In mathematics, a variable is a symbol that represents a quantity that can take on different values. In many cases, variables can be divided into two types: dependent variables and independent variables.

An independent variable is a variable that can be changed freely, and its value is not dependent on any other variable in the equation.

A dependent variable is a variable whose value depends on the value of one or more other variables in the equation

Here we have

Lin notices that the number of cups of red paint is always  2/5 of the total number of cups.

She writes the equation r = 2/5 t to describe the relationship.

In the equation, r = 2/5 t, "t" represents the total number of cups, while "r" represents the number of cups of red paint.

Here "t" is the independent variable because it represents the total number of cups, which can be changed arbitrarily.

The value of "r" depends on the value of "t" because the number of cups of red paint is always 2/5 of the total number of cups.

Therefore,

In the given equation r = 2/5 t "r" is the dependent variable.

Learn more about Variables at

https://brainly.com/question/1479694

#SPJ1

Complete Question:

Lin notices that the number of cups of red paint is always  2/5 of the total number of cups. She writes the equation r = 2/5 t to describe the relationship. Which is the independent variable? Which is the dependent variable? Explain how you know.

By Pythagorean , Eli's home is thus roughly **11.4 miles** from Salem when viewed from a straight line.

A fundamental relationship between a right triangle's three sides in Euclidean geometry is known as the Pythagorean theorem. The hypotenuse is the side that forms the right angle, and the rule says that the square of its length is equal to the sum of the squares of the lengths of the other two sides. In other words, if the hypotenuse is length c and the legs of a right triangle are lengths a and b, then a²+ b² = c² .

Call Yardley Y, Salem S, and Eli's home E. As far as we are aware, Y is located 7 miles from E and 9 miles from S.

We can check that the distance between Eli's house and Salem is the hypotenuse of a right triangle with Yardley as one of the vertices because Eli's house is located due west of Yardley and due south of Salem. The Pythagorean theorem can be used to determine this distance.

Eli's home is 11.4 miles from Salem at a distance of√(7 + 9 ) = √(130).

√(130) = 11.4miles

Eli's home is thus roughly **11.4 miles** from Salem when viewed from a straight line.

To know more about Pythagorean theorem visit:

brainly.com/question/14930619

#SPJ1

Answer:

Step-by-step explanation:

6 greater than a number is 24.

This means adding 6 to a number, x, will equal 24.

6 + x = 24

subtract 6 from both sides of the equation, and you are left with x=18

18 is your answer!!

The result for the appropriate measure, relative risk, is approximately 0.515.

This indicates that the risk of death within 5 years is about 51.5% lower in the new procedure group compared to the standard procedure group.

This suggests a strong association between the surgical procedure and the reduction in the risk of death.

To determine the strength of the association between the surgical procedures and death, we can calculate the relative risk.
Identify the numbers given in the question.
- Total participants: 550
- New procedure group: 275 (half of 550)
- Deaths in new procedure group: 98
- Standard procedure group: 275 (half of 550)
- Deaths in standard procedure group: 190
Calculate the death rate (proportion of deaths) in each group.
- Death rate in new procedure group = (Number of deaths in new procedure group) / (Total in new procedure group) = 98/275 ≈ 0.356
- Death rate in standard procedure group = (Number of deaths in standard procedure group) / (Total in standard procedure group) = 190/275 ≈ 0.691
Calculate the relative risk.
- Relative risk = (Death rate in new procedure group) / (Death rate in standard procedure group) = 0.356/0.691 ≈ 0.515.

For similar question on standard.

https://brainly.com/question/187506

#SPJ11

According to the equation, a person who weighs 63 kg is predicted to be approximately 141 centimeters tall.

The equation given is Y = 0.91X - 65.5, where X represents the height in centimeters and Y represents the weight in kilograms. To predict the height of a person who weighs 63 kg, we need to solve for X, the height in centimeters.

To do this, we can plug in the given weight of 63 kg for Y in the equation and then solve for X. So, we have:

63 = 0.91X - 65.5

Adding 65.5 to both sides, we get:

63 + 65.5 = 0.91X

Simplifying, we have:

128.5 = 0.91X

Finally, to solve for X, we divide both sides by 0.91, giving:

X = 141.21

To know more about equation here

https://brainly.com/question/10413253

#SPJ4

The property used to simplify the expression is the Commutative Property of Addition, which states that changing the order of addends does not change the sum.

The Commutative Property is a property of operations that states that the order in which two numbers are added or multiplied does not affect the result. In other words, the property says that changing the order of the terms being added or multiplied will not change the final answer.

The property that was used to simplify the expression is the Commutative Property of Addition. This property states that the order in which we add two numbers does not affect the result. In other words, if we have two numbers a and b, then a + b is equal to b + a.

In the given expression, we have two terms, 3c and 4c, that are being added together. By applying the Commutative Property of Addition, we can rearrange the terms to get 4c + 3c. This gives us the simplified expression 7c + 9.

To know more about Commutative Property visit:

https://brainly.com/question/778086

#SPJ1

Answer:

The given function is k(t) = cos(2πt/3).

The general form of a cosine function is A*cos(Bx - C) + D, where:

Comparing this form to the given function, we can see that:

Therefore, the amplitude of k(t) is 1, the period of k(t) is 3, the phase shift of k(t) is 0, and the vertical shift of k(t) is 0.

There are 67,108,863 outcomes in which at least one head occurs if a fair coin is tossed 26 times.

The probability of getting tails on any given toss is 1/2, so the probability of getting tails on all 26 tosses is (1/2)^26. Therefore, the probability of getting at least one head is

1 - (1/2)^26 ≈ 0.999999999996

So there are almost 100% chance of getting at least one head in 26 coin tosses. To find the number of outcomes that satisfy this condition, we can use the formula for combinations

ⁿCₓ = n! / (x! * (n-x)!)

where n is the total number of trials (26 in this case), x is the number of successes (at least 1 head), and ! denotes the factorial function (e.g., 5! = 54321).

Using this formula, we get

26C1 + 26C2 + ... + 26C26

which simplifies to

2^26 - 1 = 67,108,863

So there are 67,108,863 outcomes in which at least one head occurs in 26 coin tosses.

To know more about fair coin here

https://brainly.com/question/29503598

#SPJ4

The probability that the weight of a randomly selected newborn baby boy born at the local hospital will be greater than 2620 grams is 0.9099 (rounded to four decimal places).

The probability can be calculated using the standard normal distribution as follows:

P(Z > (2620 - 3245) / 625) = P(Z > -1.335)

Using a standard normal distribution table, we find that the probability of Z being greater than -1.335 is 0.9099.

We use the standard normal distribution because we know the mean and standard deviation of the population of newborn baby boys' weights. We convert the raw score of 2620 grams to a z-score, which tells us how many standard deviations the raw score is away from the mean.

Learn more about probability

https://brainly.com/question/24756209

#SPJ4

Step-by-step explanation:

24 times, as there are no orange marbles in the set.

so, every pull will produce a marble that is not orange with 100% certainty.

in general, we have 12 marbles.

let's change the problem description into picking a marbles that is not blue.

we have 6 blue marbles.

the chance to pick a blue marble is therefore 6/12 = 1/2.

and the probability to not pick a blue marbles is 1 - 1/2 = 1/2.

so, in 24 pulls, we expect 24× 1/2 = 12 times to get a marble that is not blue.

or change it to "not green" marbles.

5 green marbles.

the probability to pick a green marble is 5/12.

the probabilty to not pick a green marble = 1 - 5/12 = 7/12.

in 24 pulls we expect 24 × 7/12 = 14 times to get a marble that is not green.

it change it to "not purple" marbles.

1 purple marble.

the probability to pick a purple marble is 1/12.

the probabilty to not pick a purple marble = 1 - 1/12 = 11/12.

in 24 pulls we expect 24 × 11/12 = 22 times to get a marble that is not purple.

The best prediction possible for the number of times the spinner will land on green or blue is given as follows:

30 spins.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Out of six regions, three are green and two are blue, hence the probability of one spin resulting in green or blue is given as follows:

p = (3 + 2)/6

p = 5/6.

Thus the expected number out of 36 trials of spins resulting in green or blue is given as follows:

E(X) = 5/6 x 36

E(X) = 30 spins.

More can be learned about probability at https://brainly.com/question/24756209

#SPJ1

The pair of required complementary angles are 26.2° and 63.8° respectively.

Two angles are said to be supplementary angles because they combine to generate a linear angle when their sum is 180 degrees.

When two angles add up to 90 degrees, however, they are said to be complimentary angles and together they make a right angle.

If the total of two angles is 90o (ninety degrees), then the angles are complementary.

A 30-angle and a 60-angle, for instance, are two complementary angles.

So, to find the 2 angles which are complementary:

x + x + 37.6 = 90

Now, solve it as follows:

x + x + 37.6 = 90

2x = 90 - 37.6

2x = 52.4

x = 52.4/2

x = 26.2

Now, x = 26.2 and the second angle x + 37.6 is = 26.2 + 37.6 = 63.8°.

Therefore, the pair of required complementary angles are 26.2° and 63.8° respectively.

Know more about complementary angles here:

https://brainly.com/question/16281260

#SPJ1

$1000 is 71.43 percent of the credit limit.

To lower the debt to credit limit ratio by $1000, you have a few options. The first option is to increase your credit limit by requesting a higher limit from your credit card issuer. Alternatively, you can pay off some of your outstanding balance to reduce your debt. Either way, it's important to make sure you're not maxing out your credit limit, as this can negatively impact your credit score.

It's also a good idea to review your spending habits and create a budget to ensure you're not overspending and accumulating debt. By making responsible financial decisions and managing your credit wisely, you can improve your credit score and achieve your financial goals.

To calculate the percentage of $1000 in terms of the credit limit of $1400, we need to divide $1000 by $1400 and multiply the result by 100. This gives us,

($1000 / $1400) x 100 = 71.43%

Therefore, $1000 is approximately 71.43% of the credit limit of $1400.

To learn more about percent here:

https://brainly.com/question/30704720

#SPJ4

Triangle PQR's perimeter is **60 inches**.

The lengths of a triangle's sides added together form its perimeter.

The Pythagorean theorem asserts that in a right-angled triangle, the square of the hypotenuse's length (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides 1. A Pythagorean triplet is a group of three positive integers that satisfies this condition.

Triangle PQR has sides PQ = 15 inches, QR = 20 inches, and PR = 25 inches.

A triangle's perimeter is equal to the sum of its sides. Triangle PQR's perimeter is 15 + 20 + 25= **60 inches**.  as a result.

To know more about perimeter of triangle visit:

brainly.com/question/29507476

#SPJ1

The minimum value of V occurs at x ≈ 0.93, which means that the volume of the box is smallest when the height is about 0.93 units.

To find the extreme values of V, we need to take the derivative of V and set it equal to zero. So, let's begin:

[tex]V(x) = x(10-2x)(16-2x)[/tex]
Taking the derivative with respect to x:
[tex]V'(x) = 10x - 4x^2 - 32x + 12x^2 + 320 - 48x[/tex]
Setting V'(x) = 0 and solving for x:
[tex]10x - 4x^2 - 32x + 12x^2 + 320 - 48x = 0\\8x^2 - 30x + 320 = 0[/tex]
Solving for x using the quadratic formula:
[tex]x = (30 ± \sqrt{(30^2 - 4(8)(320))) / (2(8))\\x = (30 ± \sqrt{(1680)) / 16\\x = 0.93 or x =5.07[/tex]
So, the extreme values of V occur at x ≈ 0.93 and x ≈ 5.07. To determine whether these are maximum or minimum values, we need to examine the second derivative of V. If the second derivative is positive, then the function has a minimum at that point. If the second derivative is negative, then the function has a maximum at that point. If the second derivative is zero, then we need to use a different method to determine whether it's a maximum or minimum.

Taking the second derivative of V:
V''(x) = 10 - 8x - 24x + 24x + 96
V''(x) = -8x + 106

Plugging in x = 0.93 and x = 5.07:
V''(0.93) ≈ 98.36 > 0, so V has a minimum at x ≈ 0.93.
V''(5.07) ≈ -56.56 < 0, so V has a maximum at x ≈ 5.07.

Now, to interpret these values in terms of the volume of the box, we need to remember that V(x) represents the volume of a box with length 2x, width 2x, and height x. So, the maximum value of V occurs at x ≈ 5.07, which means that the volume of the box is greatest when the height is about 5.07 units. The minimum value of V occurs at x ≈ 0.93, which means that the volume of the box is smallest when the height is about 0.93 units.

learn more about extreme values

https://brainly.com/question/1286349

#SPJ11

a) The extreme values of V are:

Minimum value: V(0) = 0

Relative maximum value: V(3) = 216

Absolute maximum value: V(4) = 128

b) The absolute maximum value of V at x = 4 represents the case where the box has a square base of side length 4 units, height 2 units, and width 8 units, which has a volume of 128 cubic units.

a) To find the extreme values of V, we first need to find the critical points of the function. This means we need to find where the derivative of the function equals zero or is undefined.

Taking the derivative of V(x), we get:

[tex]V'(x) = 48x - 36x^2 - 4x^3[/tex]

Setting this equal to zero and solving for x, we get:

[tex]48x - 36x^2 - 4x^3 = 0[/tex]
4x(4-x)(3-x) = 0

So the critical points are x = 0, x = 4, and x = 3.

We now need to test these critical points to see which ones correspond to maximum or minimum values of V.

We can use the second derivative test to do this. Taking the derivative of V'(x), we get:

[tex]V''(x) = 48 - 72x - 12x^2[/tex]

Plugging in the critical points, we get:

V''(0) = 48 > 0 (so x = 0 corresponds to a minimum value of V)
V''(4) = -48 < 0 (so x = 4 corresponds to a maximum value of V)
V''(3) = 0 (so we need to do further testing to see what this critical point corresponds to)

To test the critical point x = 3, we can simply plug it into V(x) and compare it to the values at x = 0 and x = 4:

V(0) = 0
V(3) = 216
V(4) = 128

So x = 3 corresponds to a relative maximum value of V.
b) In terms of the volume of the box, the function V(x) represents the volume of a rectangular box with a square base of side length x and height (10-2x) and width (16-2x).
The minimum value of V at x = 0 represents the case where the box has no dimensions (i.e. it's a point), so the volume is zero.
The relative maximum value of V at x = 3 represents the case where the box is a cube with side length 3 units, which has a volume of 216 cubic units.
for such more question on extreme values

https://brainly.com/question/30886356

#SPJ11

Answer:

The third equation is equal to 2.

Step-by-step explanation:

6 times one third is equal to 6 divided by three, which equals two. Using order of operations, 5 times 2 equals 10, and that divided by 5 is 2, so that equation is equal to 2.

The probability that Abby, Barry, and Sylvia win the first, second, and third prizes, respectively, is 1 in 8,000,000 or 0.0000125%

Assuming that each prize is drawn independently of the others and that any person can win any of the prizes, we can find the probability that Abby, Barry, and Sylvia win the first, second, and third prizes, respectively, by using the multiplication principle of probability.

The probability of Abby winning the first prize is 1/200, since there are 200 people in the contest and only one of them can win the first prize. Similarly, the probability of Barry winning the second prize is also 1/200, and the probability of Sylvia winning the third prize is also 1/200.

Since winning more than one prize is allowed, the probability of all three of these events occurring simultaneously is simply the product of their individual probabilities:

P(Abby wins 1st prize AND Barry wins 2nd prize AND Sylvia wins 3rd prize) = (1/200) * (1/200) * (1/200) = 1/8,000,000

Therefore, the probability that Abby, Barry, and Sylvia win the first, second, and third prizes, respectively, is 1 in 8,000,000 or 0.0000125%

Learn more about probability

brainly.com/question/30034780

#SPJ11

Sample size and sample standard deviation are the key information needed for a single-sample t-test.

In the event that you need to compare the test cruel with the populace cruel, and you perform a single-sample t-test rather than a z-test, the vital piece of data that will be lost is the populace standard deviation.

Within the z-test, the populace standard deviation is known and the standard mistake of the cruel is calculated utilizing the populace standard deviation.

In a single-sample t-test, the populace standard deviation is obscure, and the standard mistake of the cruel is evaluated from the test standard deviation. 

Therefore, sample size and sample standard deviation are the key information needed for a single-sample t-test. 

learn more about standard deviation

brainly.com/question/23907081

#SPJ4

Answer:

To find the average rate of change of the function f(x) = 1.5x² over the interval [10, 11], we need to calculate the change in f(x) over the interval, and divide by the change in x.

The change in f(x) over the interval [10, 11] is:

f(11) - f(10) = (1.511^2) - (1.510^2) = 165 - 150 = 15

The change in x over the interval [10, 11] is:

11 - 10 = 1

Therefore, the average rate of change of the function over the interval [10, 11] is:

(15/1) = 15

This means that for every 1 cm increase in diameter (i.e., for every 1 unit increase in x), the number of calories in the pancake increases by an average of 15 calories per cm of diameter.

Therefore, the answer is (A) 150 calories per cm of diameter.

194 member voted against the bill whereas 241 members voted in favour of the bill.

A bill usually refers to a piece of paper money, such as a dollar bill or a euro bill.

To solve this problem, we can use algebra. Let's call the number of members who voted against the bill "x". Then, the number of members who voted in favor of the bill would be "x + 47" (since there were 47 more members voting in favor than against).

We know that the total number of members who voted (either for or against) was 435. So, we can write an equation:

x + (x + 47) = 435

Simplifying this equation, we get:

2x + 47 = 435

Subtracting 47 from both sides:

2x = 388

Dividing both sides by 2:

x = 194

So, 194 members voted against the bill, and the number of members who voted in favor would be:

x + 47 = 194 + 47 = 241

Therefore, 241 members voted in favor of the bill.

Learn more about equation here:

https://brainly.com/question/10413253

#SPJ1

If p is a prime number and a is a positive integer, then pa has (a+1) distinct positive divisors.

A prime number is a positive integer greater than 1, which is divisible only by 1 and itself. Divisors are the numbers that evenly divide a given number.

For a prime number p raised to the power of a (p^a), the number of distinct positive divisors can be found using the following formula:

Number of divisors = (a + 1)

This is because each power of p from 0 to a can divide p^a without any remainder, giving us a total of a + 1 distinct divisors. These divisors are:

1, p, p^2, p^3, ..., p^(a-1), p^a

For example, if p = 2 (a prime number) and a = 3 (a positive integer), then the number of distinct positive divisors for 2^3 (which is 8) would be:

Number of divisors = (3 + 1) = 4

The divisors for 2^3 (8) are 1, 2, 4, and 8.

Learn more about Prime numbers here: brainly.com/question/30358834

#SPJ11

The balance of the account after all the deposits is given as follows:

B = 800.25 + x + y + b.

The balance of an account refers to the amount of money that is currently in the account, taking into account all the transactions that have been made on the account, that is, adding all the money that has been deposited on the account.

Considering the initial balance of the account of b dollars, plus all the deposits listed on the problem, the expression is given as follows:

B = 750.25 + x + y + 100 + b

B = 800.25 + x + y + b.

More can be learned about the balance of an account at https://brainly.com/question/24914390

#SPJ1

The total areas of each composite shape are:

1) 121 in²

2) 150m²

3) 14.03 ft²

4) 538.36 cm²

1) Formula for area of a rectangle is:

Area = Length * width

Thus:

Area of composite shape = (9 * 8) + (7 * 7)

= 121 in²

2) Formula for area of rectangle is:

Area = Length * width

Area = 12 * 5 = 60 m²

Area of triangle = ¹/₂ * base * height

Area = ¹/₂ * 12 * 15

Area = 90 m²

Area of composite shape = 60 + 90 = 150m²

3) Area of triangle = ¹/₂ * 3 * 7 = 10.5 ft²

Area of semi circle = ¹/₂ * πr²

= ¹/₂ * π * 1.5²

= 3.53 ft²

Total composite area = 10.5 ft² + 3.53 ft²

Total composite area = 14.03 ft²

4) Total composite area = (¹/₂ * π * 7.5²) + (30 * 15)

= 538.36 cm²

Read more about Area of composite figure at: https://brainly.com/question/10254615

#SPJ1

The value of length XW and WV are 20 and 25 respectively.

Similar triangles are triangles that have the same shape, but their sizes may vary. The ratio of corresponding sides of similar triangles are equal.

Therefore XW/VW = XY/XZ

= XW/45 = 24/54

54(XW) = 45× 24

54(XW) = 1080

divide both sides by 54

XW = 1080/54

XW = 20

Therefore WV can be found by subtracting XW for VX

= 45-20 = 25

therefore the value of XW and WV are 20 and 25 respectively.

learn more about similar triangles from

https://brainly.com/question/14285697

#SPJ1