Use​ Green's Theorem to evaluate the following line integral. Assume the curve is oriented counterclockwise The circulation line integral of Fequalsleft angle 4 xy squared comma 2 x cubed plus y right angle where C is the boundary of StartSet (x comma y ): 0 less than or equals y less than or equals sine x comma 0 less than or equals x less than or equals pi EndSet

Answer:

they can get at most 6 drinks

Step-by-step explanation:

5 (17.5) + 2x ≤100

87.5 + 2x≤100

2x≤ 12.5

x≤6.25

Answer:

0 to 6 drinks, but no more.

Step-by-step explanation:

The requried, water depth is less than the minimum required depth of 4 inches, and the water is not deep enough for the flowers.

To determine if the water depth in the spherical vase is sufficient for the flowers, we need to compare the height of the water to the minimum required depth of 4 inches.

Given that the surface of the water forms a circle with a diameter of 5 inches, we can calculate the radius of this circle by dividing the diameter by 2.

Radius = Diameter / 2

Radius = 5 inches / 2

Radius = 2.5 inches

Since the shape of the vase is spherical, the water depth will be equal to the radius.

Therefore, the water depth in the spherical vase is 2.5 inches.

Since the water depth is less than the minimum required depth of 4 inches, the water is not deep enough for the flowers.

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Final answer:

Given that the spherical vase’s surface water diameter is 5 inches, translating to a radius of 2.5 inches at the water's surface level, the maximum depth at the center might be close to 2.5 inches, falling short of the 4 inches required for fresh cut flowers. Therefore, the water is not deep enough for the flowers.

Explanation:

The question asks if the water in a spherical vase, with a surface diameter of 5 inches, is adequate (at least 4 inches deep) for fresh cut flowers. To determine this, we need to consider the properties of a sphere and how the depth of water relates to its diameter.

Since the diameter of the water's surface is given as 5 inches, the radius of the spherical vase (at the water's surface level) is 2.5 inches. The depth of the water in a spherical vase does not evenly translate to its diameter because the shape curves upwards from every point on its surface. However, considering that the vase is filled to a level where the diameter is 5 inches, we must acknowledge that the depth in the very center might be more but decreases as we move towards the edge of the water's surface.

Given the spherical shape, the maximum depth of the water could be close to the radius of 2.5 inches in the center, assuming the vase is filled to exactly half its height. This depth is less than the required 4 inches for fresh cut flowers. Therefore, without a specific height indication of the water level relative to the vase's total height, and based on the central depth potentially being 2.5 inches at most, it is unlikely the flowers would have the required 4 inches of water depth across the entirety of the vase's base.

Answer:

QS + QR > RS

QR + RS > QS

RS + QS > QR    

Step-by-step explanation:

    ∧ ∧

( Ф∨Ф)

Answer:

hm here <3

Step-by-step explanation:

1 RS

2 QS

3 QR

<3

Answer:

The distribution of sample proportion Americans who can order a meal in a foreign language is,

[tex]\hat p\sim N(p,\ \sqrt{\frac{p(1-p)}{n}})[/tex]

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

 [tex]\mu_{\hat p}=p[/tex]

The standard deviation of this sampling distribution of sample proportion is:

[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]

The sample size of Americans selected to disclose whether they can order a meal in a foreign language is, n = 200.

The sample selected is quite large.

The Central limit theorem can be applied to approximate the distribution of sample proportion.

The distribution of sample proportion is,

[tex]\hat p\sim N(p,\ \sqrt{\frac{p(1-p)}{n}})[/tex]

Answer:

   £1800

Step-by-step explanation:

The lower price is 80% of the original, so the original price is ...

   £1440 = 0.80×original

   £1440/0.80 = original =  £1800

The price before the decrease was  £1800.

Answer:

£155

Step-by-step explanation:

look at the formula

first solve 12 minutes per light switches

12*10(lightswitches)= 120 minutes

we know that 120 minutes = 2 hours

the task says that she charges £30 per hour

so, 2 hours+ 2 hours= 4 hours

now do

4*30= £120

120+35(call-out fee)= £155

I really hope this helped.

Given:

The graph of [tex]f(t)=4 \cdot 2^t[/tex] shows the value of a rare coin in year t.

We need to determine the meaning of the y - intercept.

Meaning of the y - intercept:

Here, t represents the x - axis and f(t) represents the y - axis.

The value of y - intercept is the value of y when x = 0.

Hence, the the value of f(t) can be determined by substituting t = 0 in the function [tex]f(t)=4 \cdot 2^t[/tex]

Thus, we have;

[tex]f(0)=4 \cdot 2^0[/tex]

[tex]f(0)=4[/tex]

Thus, the value of the y - intercept is 4.

The y - intercept represents the value of the rare coin in year 0.

Therefore, the meaning of the y - intercept is "When it was purchased (year 0), the coin was worth $4".

Hence, Option B is the correct answer.

Answer:

B

Step-by-step explanation:

Answer:

in fraction form: -1/36, 1/216, -1/1296

in decimal form: -.03, .005, -.0008

Step-by-step explanation:

Each term is the previous term divided by -6:

-36 ÷ -6= 6

6 ÷ -6= -1

and so on...

-1/36

The numbers divide by -6 each time

Answer:

82%

Step-by-step explanation:

Final answer:

The probability that Sophia was assigned Golem given that her software crashed is approximately 82%, calculated using Bayes' Theorem.

Explanation:

When software crashes and we want to know the likelihood Sophia was using Golem, we need to consider both the probability of being assigned Golem and the probability of that software crashing. This is known as the application of Bayes' Theorem, which is a way to find conditional probabilities. In this case, we calculate as follows:

We want to find the probability that Sophia was assigned Golem given that her software crashed (P(G|C)). We use the formula:

P(G|C) = (P(C|G) * P(G)) / (P(C|G) * P(G) + P(C|F) * P(F))

Inserting the above probabilities yields:

P(G|C) = (0.10 * 7/10) / ((0.10 * 7/10) + (0.05 * 3/10))

P(G|C) = 0.07 / (0.07 + 0.015)

P(G|C) = 0.07 / 0.085

P(G|C) = 0.8235 or approximately 82%

Expressed as a whole-number percentage, the probability that Sophia was using Golem is 82%.

Answer:

Check the explanation

Step-by-step explanation:

The fundamentals

A continuous random variable can take infinite values in the range associated function of that variable. Consider [tex]f\left( x \right)f(x)[/tex] is a function of a continuous random variable within the range [tex]\left[ {a,b} \right][a,b][/tex] , then the total probability in the range of the function is defined as:

[tex]\int\limits_a^b {f\left( x \right)dx} = 1 a∫b​ f(x)dx=1[/tex]

The probability of the function [tex]f\left( x \right)f(x)[/tex] is always greater than 0. The cumulative distribution function is defined as:

[tex]F\left( x \right) = P\left( {X \le x} \right)F(x)=P(X≤x)[/tex]

The cumulative distribution function for the random variable X has the property,

[tex]0 \le F\left( x \right) \le 10≤F(x)≤1[/tex]

The probability density function for the random variable X has the properties,

[tex]\\\begin{array}{c}\\{\rm{ }}f\left( x \right) \ge 0\\\\\int\limits_{ - \infty }^\infty {f\left( x \right)dx} = 1\\\\P\left( E \right) = \int\limits_E {f\left( x \right)dx} \\\end{array} f(x)≥0[/tex]

Kindly check the attached image below to see the full explanation to the question above.

Complete question:

CHECK ATTACHMENT FOR THE DIAGRAM.

Answer:

Angle 7 is 76°

Step-by-step explanation:

From the diagram, notice that angle 4 = angle 5

That is,

Δ4 = Δ2

Because vertically opposite angles are equal.

Δ4 = 7x

Δ2 = 126

So

126 = 7x

Divide both sides by 7

x = 126/7 = 18

Again, angle 5 = angle 7

Δ5 = Δ7

Because vertically opposite angles are equal.

Since Δ5 = (4x + 4)°

And x = 18

Then

Δ7 = 4(18) + 4 = 72 + 4 = 76°

Answer:

[tex]\bar X =\frac{2.3+3.1+2.8+1.7+0.9+4+2.1+1.2+3.6+0.2+2.4+3.2}{12}=2.29[/tex]

[tex] s=1.09[/tex]

Step-by-step explanation:

For this case we have the following data given:

2.3 3.1 2.8

1.7 0.9 4.0

2.1 1.2 3.6

0.2 2.4 3.2

Since the data are assumedn normally distributed we can find the standard deviation with the following formula:

[tex]\sigma =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n}}[/tex]

And we need to find the mean first with the following formula:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

And replacing we got:

[tex]\bar X =\frac{2.3+3.1+2.8+1.7+0.9+4+2.1+1.2+3.6+0.2+2.4+3.2}{12}=2.29[/tex]

And then we can calculate the deviation and we got:

[tex] s=1.09[/tex]

Answer:

X ~ Norm ( 2.29167 , 1.09045^2 )

Step-by-step explanation:

Solution:-

- The (GPA) for 12 randomly selected college students are given as follows:

            2.3 , 3.1 , 2.8 , 1.7 , 0.9 , 4.0 , 2.1 , 1.2 , 3.6 , 0.2 , 2.4 , 3.2

- We are to assume the ( GPA ) for the college students are normally distributed.

- Denote a random variable X: The GPA secured by the college student.

- The normal distribution is categorized by two parameters:

- The mean ( u ) - the average GPA of the sample of n = 12. Also called the central tendency:

                        [tex]Mean ( u ) = \frac{\sum _{i=1}^{\ 12 }\: Xi }{n}[/tex]

Where,

           Xi : The GPA of the ith student from the sample

           n: The sample size = 12

          [tex]Mean ( u ) = \frac{2.3 + 3.1 + 2.8 + 1.7 + 0.9 + 4.0 + 2.1 + 1.2 + 3.6 + 0.2 + 2.4 + 3.2}{12} \\\\Mean ( u ) = \frac{27.5}{12} \\\\Mean ( u ) = 2.29167[/tex]

- The other parameter denotes the variability of GPA secured by the students about the mean value ( u ) - called standard deviation ( s ):

          [tex]s = \sqrt{\frac{\sum _{i=1}^{\ 12 }\: [ Xi - u]^2}{n} } \\\\\\\sum _{i=1}^{\ 12 }\: [ Xi - u]^2 = ( 2.3 - 2.29167)^2 + ( 3.1 - 2.29167)^2 + ( 2.8 - 2.29167)^2 + ( 1.7\\\\ - 2.29167)^2+ ( 0.9 - 2.29167)^2 + ( 4 - 2.29167)^2 + ( 2.1 - 2.29167)^2 + ( 1.2 - 2.29167)^2 +\\\\ ( 3.6 - 2.29167)^2 + ( 0.2 - 2.29167)^2 + ( 2.4 - 2.29167)^2 + ( 3.2 - 2.29167)^2 \\\\\\\sum _{i=1}^{\ 12 }\: [ Xi - u]^2 = 14.26916 \\\\\\s = \sqrt{\frac{ 14.26916 }{12} } \\\\s = \sqrt{1.18909 } \\\\s = 1.09045[/tex]

- The normal distribution for random variable X can be written as:

                 X ~ Norm ( 2.29167 , 1.09045^2 )

Answer:

36 degrees.

Step-by-step explanation:

Total Sum of the Exterior Angle of a Regular Polygon[tex]=360^0[/tex]

One Exterior Angle of a n-sided regular polygon[tex]=\dfrac{360^0}{n}[/tex]

A decagon has 10 sides.

One Exterior Angle of a decagon[tex]=\dfrac{360^0}{10}=36^0[/tex]

Therefore, the measure x of the angle between the house and the pool is 36 degrees.

Final answer:

To find the measure x of the angle between the house and a pool shaped as a regular decagon, calculate the exterior angle of the decagon, which is 36 degrees. This is the angle measure sought in the question.

Explanation:

The question involves finding the measure x of the angle between the house and the pool, where the pool is in the shape of a regular decagon.

First, let's recall that a regular decagon is a ten-sided polygon with all sides and angles equal. The sum of the interior angles of any polygon can be calculated using the formula (n-2) × 180, where n is the number of sides. For a decagon, n = 10, so the sum of the interior angles is (10-2) × 180 = 1440 degrees. Since all angles in a regular decagon are equal, each interior angle measures 1440 ° / 10 = 144 °.

Now, to find the measure x of the angle between the house and the pool, we need to understand that the exterior angle of the decagon will be involved, as this is the angle made between one side of the decagon (lying against the house) and an extension of an adjacent side. The measure of an exterior angle of a regular polygon is 360 ° / n. For our decagon, this is 360 ° / 10 = 36 °.

Therefore, the measure x of the angle between the house and the pool is 36 °, which is the measure of the exterior angle of the regular decagon.

Answer:95 degrees

Step-by-step explanation: That’s what it is closest to

Answer:

The lateral surface area of cube = 4

Step-by-step explanation:

Explanation:-

Given perimeter of the cube is 12

let 'a' be the base of cube

we know that the perimeter of cube formula = 12 a

        12 a= 12

           a = 1

The side of cube = 1cm

The lateral surface area of cube = 4 × a²

                                                      = 4 X (1)²

                                                      = 4

Final answer:-

The lateral surface area of cube = 4

Answer:

We accept H₀  the weaning weights of cows at this ranch is 610 lbs

Step-by-step explanation:

We assume normal distribution

Population mean      μ₀  = 610  lbs

Population standard deviation     unknown

sample size  n = 41

degree of fredom    df = n - 1    df  =  41 - 1   df = 40

Sample mean    X = 578  lbs

Sample standard deviation   s  =  87

As we don´t know standard deviation of the population we will use t- student test, furthemore, as  we are looking for any difference upper and lower we are in presence of a two tails test

Test Hypothesis    Null  hypothesis    H₀                X  =  μ₀

Alternative hypothesis                         Hₐ                X  ≠  μ₀

Now at α  = 0,01 ,   df  = 40   and two tail test we find   t = 2,4347

We have in t table

30 df           t  =  2,457        for       α  = 0,01

60 df           t  = 2,390         for      α   = 0,01

Δ = 30               0,067

     10                    x  ??       x = 0,022

then  2,457  -  0,022  =  2,4347

t = 2,4347

Now we compute the interval:

X ±  t * ( s/√n)    ⇒   578  ±  2,4347 * ( 87/√41)

578  ±  2,4347 * 13,59

578  ±  33,09

P [ 578 + 33,09  ;  578 - 33,09 ]

P ( 611,09 ; 544,91]

We can see that vale 610 = μ₀   is inside the iinterval , so we accept H₀ the weaning weight of cows in the ranch is 610 lbs

It's a goofy question.  These sides satisfy the triangle inequality, 7 < 4+5, so we can draw as many triangles as we care to with those sides.

The more interesting question is how many non-congruent triangles can we draw with those sides?   The answer is only 1, because by SSS all triangles with those sides will be congruent.

If we're asking about how many triangles with these sides cannot be mapped to each other through translation and rotation, the answer is two, basically a pair of reflected copies.

So much for deconstructing this lousy question.  Let's go with

Answer: 1

When two triangles are congruent, corresponding sides and angle both are equal.

Only one triangle can be drawn that fit the given description.

it is given that, A triangle has sides of length 7 cm, 4 cm, and 5 cm.

Two triangles that have corresponding congruent sides are congruent (SSS).

If triangle ABC has the sides AB=7 cm, AC=4 cm, BC=5 cm  and the triangle MNP has MN=7 cm, MP=4 cm, and PN=5 cm then

                    [tex]AB=MN=7 cm\\\\AC=MP=4 cm\\\\BC=PN=5cm[/tex]

Hence,  based on the axiom of congruent triangles side–side–side (SSS) triangle ABC is congruent with triangle MNP.

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