Homework: Section 15.1 Homework Question 14, 15.1.74 Part 1 of 2 > Find an equation for the family of level surfaces corresponding to f. Describe the level surfaces. 13 f(x,y,z)= x² + y² + 2? Write an equation for the family of level surfaces where is constant.

The domain of the function is {R} and the range of the function is {R}. where R are all the real numbers.

The range of values that we are permitted to enter into our function is known as the domain of a function.

The x values for a function like f make up this set (x).

A function's range is the collection of values it can take as input. The values in this set

Hence, once we input an x value, the function returns. The y values are those.

The given function is:

f(x) = -log(5 - x) + 5

The domain of the function is the input value or the x-coordinates of the function, and the range of the function are the output values that are obtained when the input value is plugged in the function.

For the function:

f(0) = - log (5 - 0) + 5

f(0) = 4.30

f(1) = 4.39

f(2) = 4.69

The domain is {0, 1, 2, ....} and the range of the function is {4.30, 4.39, 4.69...}.

Hence, the domain of the function is {R} and the range of the function is {R}. where R are all the real numbers.

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area is just length times width ! so u do 90 x 100 = 90,000cm^2 :)

Answer:

60%

Step-by-step explanation:

(4-2.5):2.5*100 =

(4:2.5-1)*100 =

160-100 = 60

Age will be 40 years old.

R, in beats per minute, can be approximated by the formulas, where a represents the person's age.

where R= 143 - 0.65a for women.... (1)

and R= 165 - 0.75a for men,..... (2)

So by implementing these two equation we get a = 40

If the sum of ages is X and Y, and the ratio of their ages is p:q, then the age of Y can be calculated using the formula shown below: Y's age = Y's ratio/Sum of ratios x sum of ages The age dependency ratio is the ratio of dependents (people under the age of 15 or over the age of 64) to the working-age population (people between the ages of 15 and 64). The proportion of dependents per 100 working-age population is shown in the data.

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The required value of y for the unit circle is: 2/3

The circle is defined as the locus of a point whose distance from a fixed point is constant i.e center (h, k).

The equation of the circle is given by:

(x - h)² + (y - k)² = r²

where:

h, k is the coordinate of the center of the circle on coordinate plane.

r is the radius of the circle.

Here,

Equation of the unit circle is given as,

x² + y² = 1

Now substitute the given value in the equation,

5/9 + y² = 1

y² = 1 - 5/9

y² = 4/ 9

y = √(4/9)

y = 2/3

Thus, the required value of y for the unit circle is 2/3

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The given equation, 16x² - y² + 16z² = 4, represents a quadric surface known as an elliptic paraboloid.

To determine the classification, we can examine the coefficients of the squared terms. In this case, the coefficients of x², y², and z² are positive, indicating that the surface is bowl-shaped. Additionally, the signs of the coefficients are the same for x² and z², indicating that the bowl opens upward along the x and z directions.

The negative coefficient of y², on the other hand, means that the surface opens downward along the y direction. This creates a cross-section in the shape of an elliptical parabola.

Considering these characteristics, the given equation represents an elliptic paraboloid.

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Answer:

704 kilolitres (3 s.f.)

Step-by-step explanation:

First, we'll work out the volume of the cylinder tank in \(m^3\).

\(V_{cylinder}=\pi r^2h\\=\pi*4^2*14\\=224\pi (m^3)\)

Then, we'll convert this into kilolitres.

We know that 1 cubic metre is 1 kilolitre.

So \(224\pi\) cubic metres is approximately 704 kilolitres (3 s.f.)

Answer:

1/38

Step-by-step explanation:

12/20 × 5/19 × 3/18 = 1/38

Using the permutation formula, it is found that the number of ways to distribute the books is given by:

c. 8,204,716,800

The order is important, as the books are different, hence the permutation formula is used to solve this question.

The number of possible permutations of x elements from a set of n elements is given by:

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

In this problem, 8 books are distributed among 21 children, hence the number of ways is given by:

\(P_{21,8} = \frac{21!}{13!} = 8,204,716,800\)

Which means that option c is correct.

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Null hypothesis: The average lifespan of the heaters is equal to or greater than 5 years

Alternative hypothesis: The average lifespan of the heaters is less than 5 years.

In hypothesis testing, the null hypothesis (H0) is a statement that assumes no significant difference between a sample statistic and a population parameter. The alternative hypothesis (Ha) is a statement that contradicts the null hypothesis and asserts that there is a significant difference between the sample statistic and the population parameter.

In this scenario, the company claims that its heaters last less than 5 years. We can express this claim as the alternative hypothesis (Ha), which states that the average lifespan of the heaters is less than 5 years.

On the other hand, the null hypothesis (H0) is a statement that assumes that the average lifespan of the heaters is equal to or greater than 5 years. This is the default assumption until evidence is found to support the alternative hypothesis.

To test these hypotheses, we would collect a sample of heaters and measure their lifespans. We would then calculate the sample mean and compare it to 5 years. If the sample mean is significantly less than 5 years, we would reject the null hypothesis and conclude that the average lifespan of the heaters is less than 5 years.

In summary, the null and alternative hypotheses for this scenario are:

Null hypothesis (H0): The average lifespan of the heaters is equal to or greater than 5 years.

Alternative hypothesis (Ha): The average lifespan of the heaters is less than 5 years

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Answer:

Step-by-step explanation:

\(\angle R+\angle S+ \angle T =180\)       (angle sum of a triangle is 180°)

\(2x+11+3x+23+x+42=180\)

                              \(6x+76=180\)

                                      \(6x=104\)

                                        \(x=17.667\)

\(\text{So we get: } \angle R= 46.33,\angle S=76,\angle T=59.667\)

In ascending order:

   \(\angle R= 46.33,\angle T=59.667,\angle S=76\)

Answer:

c) 7x² + 16x +39

Step-by-step explanation:

g(x) = 6(x + 2)² + (x - 3)(x - 5)

g(x) = 6(x² + 2*2x + 2²) + (x² - 3x - 5x + 15) =

= 6x² + 24x + 24 + x² - 8x + 15 = 7x² + 16x + 39

The product of 2 and 1/10 times -7 times 5/12 is -7/12, which is a fraction.

The product of 2 and 1/10 times -7 times 5/12 can be found stepwise by multiplying the numbers together.
1. Convert the mixed fraction 1/10 to an improper fraction: 1/10 = 1 ÷ 10 = 1/10.
2. Multiply the numbers together: 2 × 1/10 × -7 × 5/12 = -70/120.
3. Simplify the fraction: -70/120 = -7/12.
Therefore, the product of 2 and 1/10 times -7 times 5/12 is -7/12.

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a)

The perimeter is given by

b)

Then we simplify by summing similar terms we obtain that the expression of the perimeter is

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

If rounded to the nearest tenth of a cubic foot, would be: 927587.2

Step-by-step explanation:

The equation of finding the equation of the volume of a sphere is "4π\(\frac{radius^{3} }{3}\)"

If values are inserted in for radius as 60.5, the answer will be 927587.2 when rounded to the nearest tenths.

Hope this helps!

Solution

Given that cos θ= 3/5 and cot x < 0, then tanθ = ?

Using trigonometric function and angle

USING PYTHAGORAS therorem

Tanθ = opposite/adjacent

Answer:

Terry needs to buy 7 packages

Step-by-step explanation:

Terry has invited 31 people, meaning she needs 31 party favors

If they come in groups of five, we have to find how many packages(of 5) equal 31. Because 5 does not evenly multiply into 31, (it fits evenly inti 30) we have to add an extra package, meaning she will need 7 packages because 7×5 is 35, which is enough for each guest

The product of 73 and 4.4 x 10^6 expressed in scientific notation is as - 3.212 × 10^8 .

A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10^8.

The 4 rules of scientific notation -

Based on the given condition formulate 73  x 4.4  x 10^6

= 73  x 4.4  x 10^6

= 321.2 x 10^6

= 3.212 × 10^8

Hence , In scientific notation, the result of 73 and 4.4 x 106 is written as 3.212 × 10^8 .

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There are 5354 people were in the arena.

Percentage:

The term percentage is referred as a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

The formula for calculating the percentage is,

Percentage = (Actual value/Total value) x 100

Given,

Here we have that, 4550 men in the arena comprised 85% of the people in the arena.

Now we need to find how many people were in the arena.

Let p be the number of people in Arena.

So, based on the percentage formula,

It can be written as,

=> 85% = (4550 / p) x 100

=> 85/100 = 4550 /p

=> 0.85 = 4550/p

=> 4550/0.85 = p

=> p = 5354

Therefore, there are 5354 people were in the arena.

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There are 6 donut with sprinkles and 7 with filling. if there are 3 donut that have both sprinkles and filling, 10 have sprinkles or filling

Let S represent the set for donut with Sprinklers.

Let F represent the set for donut with Filling.

To find :- How many have sprinkles or filling?

i.e. n ( S ∪ F )

Formula,

n ( S ∪ F ) = n ( S ) + n ( F ) + n ( S ∩ F )

Given,

n ( S ) = 6

n ( F ) = 7

n ( S ∩ F ) = 3

Putting in formula

n ( S ∪ F ) = n ( S ) + n ( F ) - n ( S ∩ F )

                = 6 + 7 - 3

                = 10

Donuts with Sprinklers or Filling = 10

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If r is < 0, then lambda must be:  Less than 0, Less than 1, Greater than 1  and Greater than 0. The correct answers are: A), B), C), and D).

Recall that the exponential growth or decay model is given by the function:

\(y = y0 * e^(rt)\)

where y0 is the initial value of the function, r is the rate of change (growth or decay), t is the time, and e is the mathematical constant approximately equal to 2.71828.

If r < 0, then the function represents exponential decay, and we have:

\(y = y0 * e^(rt)\)

y/y0 = e^(rt)

Taking the natural logarithm of both sides, we get:

ln(y/y0) = rt

r = (1/t) * ln(y/y0)

Since ln(y/y0) is the natural logarithm of a ratio, it can take any real value. Therefore, r can take any negative value, and there is no restriction on the value of lambda (which is\(e^r\)).

So, the correct answers are: A), B), C), and D).

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Answer: D, (1,3)

Hope this helped

Answer:

b. (0, 1.5)

Step-by-step explanation:

\((x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\\(3,7)\\(-3,-4)\\3+(-3)/2 , 7+(-4)/2\\(0, 1.5)\)

Answer:

m=36×20

Step-by-step explanation:

A hybrid SUV uses 36 miles per gallon in the city.

The equation that could be used to find how many miles a hybrid SUV can travel in the city on 20 gallons of gas is m=36×20.

The equation of a radical function can be determined by using the transformation rules for x- and y- shifts, stretches/compressions, reflections, and rotations.

The equation of a radical function can be determined by applying various transformation rules. The most common transformations are shifts, stretches/ compressions, reflections, and rotations. For example, a radical function that is shifted left two units would have an equation of y = sqrt(x + 2). This is because the function is shifted two units to the left of the origin, so the equation must include an x + 2 term. Similarly, if the function is reflected in the x-axis, the equation would be y = -sqrt(x). This is because the reflection inverts the sign of the y-coordinate, so the equation must include a negative sign in the radical. For stretches and compressions, the equation must include a coefficient in front of the radical. For example, if the function is stretched horizontally by a factor of 3, then the equation would be y = 3 sqrt(x). This is because the function is stretched by a factor of three, so the equation must include a coefficient of 3 in front of the radical. Finally, for rotations, the equation must include a term for the angle of rotation. For example, if the function is rotated counterclockwise by 45 degrees, then the equation would be y = sqrt(x + y/tan45). This is because the angle of rotation is 45 degrees, so the equation must include a tan45 term.

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Answer:

9

Step-by-step explanation:

Since one place to the right is greater than or equal to 5 you round up.

Yes, it would be possible to use 14C age dating to estimate the age of a dinosaur bone.

Explanation:14C dating is a method used to determine the age of once-living organisms based on the radioactive decay of carbon-14 in their tissues. However, 14C dating is only effective for samples that are less than 50,000 years old. Therefore, it is not possible to use 14C dating to directly date dinosaur bones as they are much older than 50,000 years, and all the carbon-14 would have already decayed.

However, indirect dating methods such as radiometric dating can be used to estimate the age of the rocks in which the dinosaur bones were found. This method is based on the radioactive decay of isotopes in the rocks and can be used to determine the age of the rocks to within a few million years. By association, the age of the dinosaur bones can also be estimated, providing an indirect method of dating them. Therefore, while 14C dating is not useful for directly dating dinosaur bones, it can be used indirectly to estimate their age.

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A higher percentage of people who did not wear wrist guards (41.67%) experienced wrist injuries compared to those who did wear wrist guards (11.32%).

Based on the information provided, we can analyze the data on injuries to in-line skaters. Let's break down the given numbers:

Total number of people interviewed: 161

Number of people wearing wrist guards: 53

Number of people wearing wrist guards with wrist injuries: 6

Number of people not wearing wrist guards: 108

Number of people not wearing wrist guards with wrist injuries: 45

From this information, we can calculate the following:

Percentage of people wearing wrist guards with wrist injuries:

(Number of people wearing wrist guards with wrist injuries / Number of people wearing wrist guards) × 100

= (6 / 53)× 100 ≈ 11.32%

Percentage of people not wearing wrist guards with wrist injuries:

(Number of people not wearing wrist guards with wrist injuries / Number of people not wearing wrist guards)×100

= (45 / 108) ×100 ≈ 41.67%

These calculations provide insights into the likelihood of wrist injuries in relation to wearing wrist guards while inline skating. The data suggests that the percentage of wrist injuries among those wearing wrist guards is lower (11.32%) compared to those not wearing wrist guards (41.67%). This indicates that wearing wrist guards may offer some protection against wrist injuries while inline skating.

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A) Pr(o,e) is the probability of an event o and event e occurring. B) Pr(e) is the probability of an event e occurring.C) Pr(o|e) is the probability of an event o given that event e has occurred.

Risk analysis is a quantitative assessment of risk. It is a method for estimating the likelihood of an adverse event occurring and the possible negative consequences if it does occur. Risk analysis has many applications, including finance, insurance, healthcare, and engineering.

It is a critical component of decision-making processes, such as business planning and policy development. The probability of occurrence is one of the key inputs to risk analysis, and it is essential to understand its meaning in this context.

Pr(o,e) is the probability of an event o and event e occurring.

This is the joint probability of two events. (o,e) represents the occurrence of two events together.

Pr(e) is the probability of an event e occurring.

This is the marginal probability of an event. Finally,

Pr(o|e) is the probability of an event o given that event e has occurred.

This is the conditional probability of an event.

This equation is known as Bayes' theorem, and it is the foundation of risk analysis. It describes how we can update our beliefs about the likelihood of an event occurring as new information becomes available.

By applying Bayes' theorem, we can estimate the likelihood of an adverse event occurring and the possible consequences of that event.

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