Write 3 2/5 as an improper fraction.

The area inside the curve r = 3 + sin(θ) is 4.5π square units.

To find the area inside the curve r = 3 + sin(θ), we can use double integrals in polar coordinates. The general formula for finding the area inside a polar curve is given by:

A = (1/2) ∫(θ2-θ1) ∫(r1^2)^(r2^2) r dr dθ

where θ1 and θ2 are the limits of integration for the angle θ, and r1 and r2 are the limits of integration for the radius r. In this case, since we want to find the area inside the curve r = 3 + sin(θ), we have r1 = 0 and r2 = 3 + sin(θ), and θ1 = 0 and θ2 = 2π (since we want to cover the full circle). Therefore, the double integral becomes:

A = (1/2) ∫(0)^(2π) ∫(0)^^(3+sinθ) r dr dθ

Evaluating the inner integral, we get:

∫(0)^^(3+sinθ) r dr = [1/2 r^2]_(0)^(3+sinθ) = 1/2 (9 + 6sinθ)

Substituting this into the double integral and evaluating the outer integral, we get:

A = (1/2) ∫(0)^(2π) 1/2 (9 + 6sinθ) dθ

= (1/4) (9(2π) + 6(∫(0)^(2π) sinθ dθ))

= (1/4) (18π) = 4.5π

Therefore, the area inside the curve r = 3 + sin(θ) is 4.5π square units.
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The airline fees was $41 each

The over the weight limit of the bag is 3 pounds

Number pounds of Natalie's bag = x

Airline 1:

29 + 4x

Airline 2:

23 + 6x

Equate airlines 1 and 2

29 + 4x = 23 + 6x

collect like terms

29 - 23 = 6x - 4x

6 = 2x

divide both sides by 2

x = 6/2

x = 3 pounds

Hence,

Airline 1:

29 + 4x

= 29 + 4(3)

= 29 + 12

= $41

Airline 2:

23 + 6x

= 23 + 6(3)

= 23 + 18

= $41

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In the given study comparing the effects of regular-fat cheese to reduced-fat cheese on LDL cholesterol levels, the dependent variable(s) refers to the outcome(s) that are being measured or observed. In this case, the dependent variable in this study is: b. LDL levels

The dependent variable is the variable that is measured or observed to assess the effect of the independent variable(s). In this case, the study is comparing the effects of regular-fat cheese and reduced-fat cheese on LDL cholesterol levels.

LDL cholesterol levels are the outcome being measured to determine the impact of the different types of cheese on cholesterol. Therefore, option b, LDL levels, is the dependent variable in this study. Options a (regular fat cheese) and c (reduced fat cheese) are not the dependent variables but rather the independent variables, as they are the different conditions being compared to assess their effect on LDL levels.

Option d (both a and b) and option e (both b and c) are incorrect because regular-fat cheese (option a) is an independent variable, not a dependent variable.

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Answer:

top right one

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. 2x + y

2. 48 +  60 = 108

3. 840 - 210 = 630

Question 3: True

Question 4: False

Question 5: True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c.

This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

Question 3: If f'(c) < 0 then f(x) is decreasing and the graph of f(x) is concave down when x = c.

True

When the derivative of a function, f'(x), is negative at a point c, it indicates that the function is decreasing at that point. Additionally, if the second derivative, f''(x), exists and is negative at x = c, it implies that the graph of f(x) is concave down at that point.

Question 4: A local extreme point of a polynomial function f(x) can only occur when f'(x) = 0.

False

A local extreme point of a polynomial function can occur when f'(x) = 0, but it is not the only condition. A local extreme point can also occur when f'(x) does not exist (such as at a sharp corner or cusp) or when f'(x) is undefined. Therefore, f'(x) being equal to zero is not the sole requirement for a local extreme point to exist.

Question 5: If f'(x) > 0 when x < c and f'(x) < 0 when x > c, then f(x) has a maximum value when x = c.

True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c. This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

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The probability that the mean weight of the sample babies would be less than 3174 grams is 0.1237 (rounded to four decimal places).

Given that the mean weight of babies born in a large hospital is 3215 grams and the variance is 84681. A sample of 67 babies is chosen at random from the hospital. We need to find the probability that the mean weight of the sample babies is less than 3174 grams.

To solve this, we can use the central limit theorem, which states that the sample means of a large sample (n > 30) taken from a population with a mean μ and a standard deviation σ will be approximately normally distributed with a mean μ and a standard deviation σ / √n.

Here,

n = 67,

μ = 3215 and

σ² = 84681.

σ = √σ² = √84681 = 290.8191

σ / √n = 290.8191 / √67 = 35.4465

To find the probability that the sample mean weight of the babies is less than 3174 grams, we need to find the z-score.

z = (x - μ) / (σ / √n) = (3174 - 3215) / 35.4465 = -1.1572

From the standard normal distribution table, we find that the probability of z being less than -1.1572 is 0.1237.

Therefore, the probability that the mean weight of the sample babies would be less than 3174 grams is 0.1237 (rounded to four decimal places).

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Answer:

B

Step-by-step explanation:

doesnt have an equals sign

Answer:

The second one, there is not = sign

2(4m+6)

Step-by-step explanation:

An equation is a mathematical statement that two things are equal. It consists of two expressions, one on each side of an 'equals' sign.

for it to be an equation there needs to be an equal sign

Answer:

6.5 × 3.1 = 20.15

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

\( \green{ \boxed{ \boxed{ \sf{Lusi \: Adriana} } } } \)

The probability that we dealt with two queens as private cards is = 0.0046 .

In the question ,

it is given that ,

the two cards are drawn as private cards,

we have to find the probability that you are dealt with two queens .

the total number of cards in deck is = 52 ,

total number of queens in the deck is = 4 ,

So , the number of ways 2 queens can be drawn from 4 queens is = ⁴C₂ ways .

So , the total number of ways 2 cards can be drawn is = ⁵²C₂

So , the required probability is = ⁴C₂ / ⁵²C₂ .

= 6/1326

= 0.0046

Therefore , the required probability is 0.0046  .

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Answer:

x = 14

Step-by-step explanation:

if the triangles are similar then

16/24 = x/21 cross multiply expressions

336 = 24x divide both sides by 24

14 = x

The expected value with a sample size of 20 and a probability of 0.25 will be 5.

The anticipated value is an extension of the weighting factor in statistical inference. Informally, the anticipated value is the simple average of a significant number of outcomes of a randomly selected variable that was separately chosen.

The expected value is given below.

E(x) = np

Where n is the number of samples and p is the probability.

If x is a binomial random variable with n = 20 and p = 0.25. Then the expected value is given below.

E(x) = 20 x 0.25

E(x) = 5

The expected value with n = 20 and p = 0.25 will be 5.

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Step-by-step explanation:

Answer:

{\color{#c92786}{6-4y}}=8

6−4y=8

−4+6=8

{\color{#c92786}{-4y+6}}=8

−4y+6=82

Subtract from both sides of the equation

=

−

1

2

The correct trigonometric, notation for z = 1+2i is √5 (cos 63.4° + i sin 63.4°).

The complex number z can be written in trigonometric form as z = r(cos θ + i sin θ), where r represents the magnitude of z and θ represents the argument (or phase) of z.

In this case, the magnitude of z is √(1² + 2²) = √5.

To find the argument θ, we can use the inverse tangent function:

θ = arctan(2/1) = 63.4°.

Therefore, the trigonometric notation for z is √5 (cos 63.4° + i sin 63.4°).

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Answer:

Dependent=35 Independent=1 minute

Step-by-step explanation:

Dependent variable is based on the independent variable, in this case, the amount of jumping jacks is the dependent variable.

Answer:i believe the jumping jacks are independent and the time is dependent

Step-by-step explanation:i say this because the time is depending on how many you do. some can do 35 in less than a minute or longer than a minute. therefore the time depends on how many you do.

Answer:

all you have to do is just re- arrange the angles and then add them up:0

Step-by-step explanation:

lol

Answer:

x = 2

Step-by-step explanation:

We'll start with this useful fact about triangles: equal angles in a triangle sweep out equal sides. If a 45 degree angle here sweeps out a length of x, the other one must do the same, so the legs of this right triangle must both be x.

Next, we can use the Pythagorean Theorem to tie all of the triangle's lenghts together:

x² + x² = (√8)²

Finally, we can solve for x:

2x² = 8

x² = 4

x = 2.

The total of oranges left by the taylor is about 10 3/4 pounds

To solve this problem, we will start by using adding the weights of the navel oranges and temple oranges to discover the total weight of oranges Taylor has, that's:

Next, we are able to subtract the weight of the navel oranges she uses from the total weight of navel oranges to discover how a lot she has left, which is:

In the end, we can add the weight of the navel oranges left to the weight of the temple oranges to find the overall weight of oranges Taylor has left, which is:

Therefore, the total of oranges left by the taylor is about 10 3/4 pounds

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Answer:

The height of the lightpost is 33.008 feet

Step-by-step explanation:

Refer the attached figure

Distance between lamp post and person = AB = 40 feet

Height of person = BC = 5 feet

The angle of elevation = ∠DCE =35°

Height of light post = AD

AB=CE=40 feet

In ΔDCE

\(\frac{Perpendicular}{Base}=Tan \theta \\\frac{DE}{CE}=tan 35^{\circ}\\\frac{DE}{40}=tan 35^{\circ}\\DE=40 \times tan 35^{\circ}\\DE=28.008\)

Height of light post = AD=DE+AE=28.008+5=33.008

Hence the height of the lightpost is 33.008 feet

Answer:

\(\frac{1}{16}, \frac{1}{4}, \frac{3}{16}\)

Step-by-step explanation:

Recall a probability: \(P=\frac{F}{T}\) , where F is a number of favorable outcomes and T is a number of total outcomes.

The probability to get tail is \(\frac{1}{2}\) as well as probability to get head.

The probability to choose number 7 of 8 numbers at total is equal to \(\frac{1}{8}\).

Therefore, the probability to get number 7 and a tail is:

\(\frac{1}{8}\cdot \frac{1}{2}=\frac{1}{16}\)

Prime numbers from 1 to 8 are: 2, 3, 5 and 7, so there are 4 numbers of 8 numbers in total, so the probability to get a prime number is  \(\frac{4}{8}=\frac{1}{2}\).

The second probability is equal to \(\frac{1}{2}\cdot \frac{1}{2}=\frac{1}{4}\).

The numbers greater than 5 are: 6,7,8, so there are 3 numbers of 8 in total, so the probability to get a number greater than 5 is \(\frac{3}{8}\).

The third probability is equal to:  \(\frac{3}{8}\cdot \frac{1}{2}=\frac{3}{16}\).

Answer:

$1.45

Step-by-step explanation:

Answer:

1/6

Since there are 6 faces and you're asking if 1 face is the probability, the probability is 1/6

Answer:

Dependent sample

Step-by-step explanation:

The sample: a data set includes the morning and evening temperature for the last 90 days.

The samples are dependent in that they are paired measurements on just one set of item which is the temperature.

These measurements are related in such a way that the each observation in one sample can be paired with an observation in the other sample.

The values between\(7 * 10^-6\) and \(6 * 10^-5 = 5.3 * 10^-5\)

The result of subtracting one number from another. How much one number differs from another.

Example: The difference between 8 and 3 is 5.Another example is the difference between 100 and 50= 100-50 = 50

The difference simply means subtracting a number from another

Similarly the difference between \(7 * 10^-6 and 6 * 10^-5 = 6 * 10^-5 - 7 * 10^-6\)

changing \(7 *10^-6 0.7 * 10^-5\)= \((6 * 10^-5) - (0.7 * 10^-5)= 5.3 * 10^-5\)

Therefore the values between \(7 * 10^-6\) and \(6 * 10^-5\) is \(5.3 * 10^-5\)

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Answer:

When rounding to the nearest ten, like we did with 1890 above, we use the following rules:

A) We round the number up to the nearest ten if the last digit in the number is 5, 6, 7, 8, or 9.

B) We round the number down to the nearest ten if the last digit in the number is 1, 2, 3, or 4.

C) If the last digit is 0, then we do not have to do any rounding, because it is already to the ten.

Step-by-step explanation:

Answer:

x=-1

Step-by-step explanation:

f (x)= -x + 8

Let f(x) = 9

9 = -x+8

Subtract 8 from each side

9-8 = -x+8-8

1 = -x

Multiply each side by -1

-1 = x

Answer: A! x=-1 2/5, y= 1 3/5

Step-by-step explanation:

First put -3x+3y=9 into slope-intercept form(y=mx+b)

3y=-3x+9

then solve for y

y=-1x+3

enter your y-intercept into the equation below..

2x-7(-1x+3)=-14

2x+7x-21=-14

2x+7x=-14+21(when changing sides it changes signs that's why 21 is now a positive)

2x-7x=7

-5x=7 divide -5 into 7

7/5

x=-1 and 2/5

then input x back into the first equation

-3(7/-5)+3y=9

21/5+3y=9

3y=9-21/5

3y=24/5

divide 3 into 24/5

=24/15=1 and 9/15 reduce it anddd

y=1 and 3/5

Answer:

Step-by-step explanation:

Formula

SA = 2*pi r^2 + 2*pi * r * h

Givens

pi = 3.14

r = d/2                   radius = diameter /2

r = 7/2 = 3.5

h = 10 cm

Solution

SA = 2*3.14 *3.5^2 + 2*3.14 * 3.5 * 10

SA = 76.93 + 219.8

SA = 296.73 cm^2

Answer

Surface Area = 296.73 cm^2

The value of R when A = {1, 2, 3, 4, 5, 6} and the distinct equivalence classes resulting from an equivalence relation R on A are {1, 4, 5}, {2, 6} and {3} is {(1,1), (4,4), (5,5), (1,4), (4,1), (1,5), (5,1), (4,5), (5,4), (2,2), (6,6), (2,6), (6,2), (3,3)}.

Given the distinct equivalence classes resulting from an equivalence relation R on A are {1, 4, 5},{2, 6} and {3}. We need to find R.

We know that the distinct equivalence classes of an equivalence relation on A, say R, will partition A.

Therefore we need to put every element of A in one of these three classes.

Now, we have to find out under what circumstances two elements in A belong to the same class.

We can do that by looking at the known equivalence classes.

Here we can assume that any two elements that are in the same class are equivalent.

Now we can write R as below;{(1,1), (4,4), (5,5), (1,4), (4,1), (1,5), (5,1), (4,5), (5,4), (2,2), (6,6), (2,6), (6,2), (3,3)}

Therefore, the relation R is: R={(1,1), (4,4), (5,5), (1,4), (4,1), (1,5), (5,1), (4,5), (5,4), (2,2), (6,6), (2,6), (6,2), (3,3)}.

Hence, the required answer is R={(1,1), (4,4), (5,5), (1,4), (4,1), (1,5), (5,1), (4,5), (5,4), (2,2), (6,6), (2,6), (6,2), (3,3)}.

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