Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4x2 + y2 = 4 and the plane x + y + z = 9.

Final answer:

Explanation of sampling distributions and probabilities for different sample sizes in relation to the population proportion in St. Paulites.

Explanation:

In part a, when selecting a sample of 540 St. Paulites, the sampling distribution of p would have a mean of 0.32 and a standard error of 0.0201.

The probability that the sample proportion will be within 0.05 of the population proportion is 0.9871.

In part c, with a sample of 170 St. Paulites, the sampling distribution of p has a mean of 0.32 and a standard error of 0.03145.

The probability that the sample proportion will be within 0.05 of the population proportion is 0.9907.

The gain in precision by taking the larger sample is substantial, with the probability increasing from 0.9907 to 0.9871, reducing the error by a factor of 0.9999.

The required simplification of function for the a is given as a = -2b / l +  s / l.

Given that,
To simplify the expression  S=la + 2b for a.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
s = la + 2b
Transposition of 2b on right side
s - 2b = la
dividing both sides by l
a = s / l  - 2b / l

Thus, the required simplification of function for the a is given as a = -2b / l +  s / l.

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Answer:

The answer is the next table:

x    y

0   1

3   0

6   -1

9   -2

Step-by-step explanation:

In order to determine the table with ordered pairs, we have to know about replacing values.

In a linear function, there are two variables, the dependent variable (y) and the independent variable (x). If we replace any value in the "x" variable, we get the "y" value. The process is called "replacing value".

To get the table, we choose some value to replace in the "x" variable:

[tex]x=0\\y=-\frac{1}{3}(0)+1=1\\[/tex]

[tex]x=3\\y=-\frac{1}{3}(3)+1=-1+1=0[/tex]

[tex]x=6\\y=-\frac{1}{3}(6)+1=-2+1=-1[/tex]

[tex]x=9\\y=-\frac{1}{3}(9)+1=-3+1=-2[/tex]

The table with some ordered pairs is:

x    y

0   1

3   0

6   -1

9   -2

I have attached an image that shows a graph with the ordered pairs.

Answer:

Wee is the independent variable, and deposit is the dependent variable

Step-by-step explanation:

Given that Olivia started her banking account with $100 and is increasing the account $20 per month.

Here the variable which changes independently is the independent variable

Hence no of weeks elapsed would be the independent variable

The dependent variable would be the variable which changes whenever number of weeks changes.

Here dependent variable is the total balance in the account in a particular week

D=100+20n wbere n= no of weeks that eapsed

and D= depositisin in the bank

At 4:00 PM, the distance between the ships is changing at a rate of 6160 km/h.

To find the rate at which the distance between the ships is changing, we can use the concept of relative velocity. At 4:00 PM, ship A has been sailing east for 4 hours, covering a distance of 40 km/h * 4 h = 160 km. Ship B has been sailing north for 4 hours, covering a distance of 20 km/h * 4 h = 80 km.

To find the distance between the ships at 4:00 PM, we can use the Pythagorean theorem. The distance between the ships is the hypotenuse of a right triangle with legs of 170 km and 80 km. Using the theorem, we find that the distance between the ships is √(170^2 + 80^2) ≈ 186.45 km.

To find the rate at which the distance is changing, we can use the derivative of the distance formula. Let D be the distance between the ships. Then, D^2 = (170 + 40t)^2 + (80 + 20t)^2, where t is the time in hours. Taking the derivative of D^2 with respect to t and solving for dD/dt, we get: dD/dt = (170 + 40t)(40) + (80 + 20t)(20).

Substituting t = 4 into the expression, we find that dD/dt = (170 + 40(4))(40) + (80 + 20(4))(20) = 6160 km/h. Therefore, the distance between the ships is changing at a rate of 6160 km/h at 4:00 PM.

Answer

0.5

Explanation

0.05 is 1/10 the value of?

In other words the question is asking, what must be multiplied by 1/10 to give 0.05.

let that value be X.

1/10 × X = 0.05

X/10 = 0.05

X = 0.05 × 10

    = 0.5

The value that must be multiplied by 1/10 which gives 0.05 would be 0.5.

If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We need to find the value that must be multiplied by 1/10 which gives 0.05.

Let that value be X.

1/10 × X = 0.05

X/10 = 0.05

X = 0.05 × 10

   = 0.5

Thus, the value that must be multiplied by 1/10 which gives 0.05 would be 0.5.

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The florist can design the bouquet in 700 unique ways, using 3 different types of flowers and 3 different types of greenery chosen from 7 types of flowers and 6 types of greenery respectively.

The subject of this question is within the realm of Mathematics, specifically combinatorics, which studies the various ways in which objects can be selected, arranged, and combined. To find the total number of ways the florist can design the bouquet given 7 types of flowers and 6 types of greenery, we can employ the combination (or 'choose') formula given by n choose r, where n is the total number of objects and r is the number of objects selected. Hence, the number of ways to choose 3 flowers out of 7 is '7 choose 3', and similarly for the greenery we have '6 choose 3'.

Using the formula for combinations, we have:

Combinations of flowers = 7 choose 3 = 7! / (3!(7-3)!) = 35

Combinations of greenery = 6 choose 3 = 6! / (3!(6-3)!) = 20

Since the flowers and the greenery are selected independently of each other, we multiply the two results to get the total number of combinations. Therefore, the number of unique ways in which the florist can design the bouquet is 35 * 20 = 700.

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Answer:

The answer is 12

Step-by-step explanation:

For 2 1/2 times the doubled recipe, starting with an initial amount of 3 1/3 cups of heavy cream, the total amount needed would be 16 2/3 cups of heavy cream.

To calculate how much heavy cream is needed, we must first understand the initial amount required and then apply the necessary adjustments to upscale the recipe.

If the original recipe calls for 3 1/3 cups of heavy cream and we want to double the recipe, we would need 2 x 3 1/3 cups which is 2 x (10/3) cups = 20/3 cups or 6 2/3 cups.

Now, if we want to make 2 1/2 times the amount of the doubled recipe, we multiply 6 2/3 cups by 2 1/2 (5/2), resulting in (20/3) x (5/2) cups. Simplifying this, we get:

(20/3) x (5/2) = (100/6) cups = 16 2/3 cups.

Therefore, for 2 1/2 times the doubled recipe, you would need 16 2/3 cups of heavy cream.

The probability of rolling a 2 on a die and then rolling an odd number on a second roll is 1/12.

The probability of rolling a 2 on a die is 1/6 because there are six sides on a die, each with an equal chance of landing face up. When rolling the dice a second time, there are three odd numbers (1, 3, and 5), so the probability of rolling an odd number is 3/6, or 1/2. To find the combined probability of both events occurring in sequence (rolling a 2 first and then an odd number), we multiply the individual probabilities: (1/6) × (1/2) = 1/12.

Answer:

Triangle GHI is rotating 180° counterclockwise .

Step-by-step explanation:

Given : Triangles.

To find : Which is the image of Triangle ABC for a 180° counterclockwise rotation about P.

Solution : We have triangle ABC .

If we Rotate GHI triangle in counterclockwise 180 degree we get triangle ABC.

We can prove it by rotating triangle ABC in clockwise direction 180° We get triangle GHI.

Therefore, Triangle GHI is rotating 180° counterclockwise .

Final answer:

The total cost for fixing a drain that takes 7 hours is $226. If the plumber charges a total of $310, he spent 11 hours fixing the drain.

Explanation:

The cost function given by the plumber is C(h) = 79 + 21h, where C represents the total cost and h represents the number of hours spent fixing the drain.

John needs to use the inequality 72 + 78 + 70 + x ≥ 289 to determine the minimum number of additional test points required to pass his math class.

The student, John, needs to determine how many more test points he requires to pass his math class. Given his current test scores, the inequality to represent this scenario should account for the minimum points he needs to achieve the threshold.

Therefore, the inequality should include an 'at least' condition, meaning the total points must be greater than or equal to the pass mark of 289. Adding his current scores of 72, 78, and 70 gives a total of 220, so the inequality will include an unknown variable, x, which represents the additional points needed. The correct inequality is D. 72 + 78 + 70 + x ≥ 289.

Final answer:

John needs to use the inequality 72 + 78 + 70 + x ≥ 289, which simplifies to x ≥ 69, to determine he requires at least 69 more points to pass. Option D

Explanation:

John needs to determine how many more points he requires to pass his math class, with a target score of at least 289 points. He already has test scores of 72, 78, and 70. To find out the least number of additional points he needs, he should use an inequality that allows for the sum of his scores and an unknown quantity x (representing the points he needs) to be at least as great as 289. This is represented by the inequality 72 + 78 + 70 + x ≥ 289. This can be simplified to x ≥ 69, which means John needs at least 69 more points to pass the class.

Answer:

The tax will be $42,750.

Step-by-step explanation:

Mel Company has a net income, before taxes, of $95,000.

The treasurer of the company estimates 45% of net income will have to be paid for federal and state taxes.

So, the tax for both federal and state is:

[tex]0.45\times95000=42750[/tex] dollars

Therefore, the tax will be $42,750.

Answer:

90 degrees

Step-by-step explanation:

The like radicals to 3x√5 from the given options is: D. y√5.

Like radicals can be defined as radicals having the same root number (i.e. square) and also have the same radicand.

Given, 3x√5, the root here is a square, while the radicand is 5. Thus, like radicals to 3x√5 will have same root and radicand.

Therefore, the like radicals to 3x√5 from the given options is: D. y√5.

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The like radical to 3x sqrt 5 is y sqrt 5.

Given the expression 3x sqrt 5, we can see that the square root is applied only to 5 and not to 3x. To find a like radical, we need to find an expression in which the square root is also applied only to the same number.

Looking at the options, the only expression that matches this criterion is y sqrt 5. The square root is applied only to 5, just like in the original expression. Therefore, y sqrt 5 is the like radical to 3x sqrt 5.

Answer:

On Zira's birthday Lizzy, Amy Wilson Amara, and Ria want only 3/4 inches of the cake how much cake do you need for all of them?

Solutions 5 x3/4 = 3.75 inches of cake

Step-by-step explanation:

Answer: 5:7

Step-by-step explanation:

The person above is right

I just did the test