Which graph represents the solution of x2 + y2 < 25 and y2 <6x?

Answer:

33.51 cm

Step-by-step explanation:

240/360 = 2/3 (Arc length is 2/3 of the total circumference)

C = 2[tex]\pi[/tex]r             ( Calculate the total circumference)    

C = 2(8)[tex]\pi[/tex]

C = 50.265

2/3(50.265)      (Take 2/3 of the circumference. times 2 divide by 3)

33.51

Use a calculator and leave the answer to C and then multiply and divide. You get a more precise answer.

The exact arc length is [tex]\frac{32\pi}{3}[/tex] radians.

The arc length in approximate form is 33.49 radians.

[tex]s = r\times \theta[/tex]

where r is the radius of the circle and [tex]\theta[/tex] is the central angle in radians.

Radians = Degrees ×[tex]\frac{\pi}{180^{\circ}}[/tex]

For given question,

We have been given a circle with a 8-cm radius associated with a central angle of 240 degrees.

[tex]r=8~cm,~\theta=240^{\circ}[/tex]

First we convert angle in radians.

[tex]\theta=240^{\circ}\\\\\theta=240^{\circ} \times \frac{\pi}{180^{\circ}}\\\\ \theta=\frac{4\pi}{3}[/tex]

Using the formula of the arc length,

[tex]s=8\times \frac{4\pi}{3} \\\\s=\frac{32\pi}{3}[/tex]

The exact answer of the arc length is [tex]s=\frac{32\pi}{3}[/tex]

Substitute the value of [tex]\pi = 3.14[/tex]

So, the arc length would be,

[tex]\Rightarrow s=\frac{32\times \pi}{3}\\\\\Rightarrow s=\frac{32\times 3.14}{3}\\\\\Rightarrow s=33.49[/tex]radians

Therefore, the exact arc length is [tex]\frac{32\pi}{3}[/tex] radians.

the arc length in approximate form is 33.49 radians.

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Answer:

Bob had 25 cars

Step-by-step explanation:

10+15=25

Answer: 5%

Step-by-step explanation:

In 2006, there were 160 teachers in College A, and ¾ of them had their own vehicles, the number of people who had their own vehicles will be:

= 3/4 × 160

= 120

In 2007, 20 new teachers came to the school and 6 of them had own vehicles. This means the number if people with vehicles will be:

= 120 + 6

= 126

The percentage increase will be:

= Increase / Old vehicle owners × 100

= 6/120 × 100

= 1/20 × 100

= 5%

The Percentage increase is 5%.

Answer:

Step-by-step explanation:

21,753

at unit place=3 not an even number,not equal to 5 and not equal to 0

so 21,753 is not divisible by 2,5 and 10

again

2+1+7+5+3=18 divisible by 3 and 9.

so 21,753 is divisible by 3 and 9.

Answer:

The right answer is "0.3193".

Step-by-step explanation:

According to the question,

Mean,

[tex]\frac{1}{\lambda} = 13[/tex]

[tex]\lambda = \frac{1}{13}[/tex]

As we know,

The cumulative distributive function will be:

⇒ [tex]1-e^{-\lambda x}[/tex]

hence,

In the first 5 years, the probability of failure will be:

⇒ [tex]P(X<5)=1-e^{-\lambda\times 5}[/tex]

                    [tex]=1-e^{-(\frac{1}{13} )\times 5}[/tex]

                    [tex]=1-e^(-\frac{5}{13})[/tex]

                    [tex]=1-0.6807[/tex]

                    [tex]=0.3193[/tex]

Answer:

45 km por galón

60 galones en 2700 Km

Step-by-step explanation:

180 / 4

45 km por galón

900 / 45

20 galones

2700 / 45

60 galones en 2700 Km

Answer: (8x8x9)/3=192

Answer:

The margin of error for her confdence interval is of 0.3757.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 18 - 1 = 17

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.8982

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

Standard deviation of 0.55 meters.

This means that [tex]s = 0.55[/tex]

What is the margin of error for her 99% confidence interval?

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

[tex]M = 2.8982\frac{0.55}{\sqrt{18}}[/tex]

[tex]M = 0.3757[/tex]

The margin of error for her confdence interval is of 0.3757.

Margin of error is the distance between the mean and the limit of confidence intervals. The margin of error for the given condition is 3.28 approximately.

Suppose that we have:

Sample size n  < 30

Then the margin of error(MOE) is obtained as

Margin of Error = [tex]MOE = T_{c}\dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]MOE = T_{c}\dfrac{s}{\sqrt{n}}[/tex]

where [tex]T_{c}[/tex] is critical value of the test statistic at level of significance

For the given case, taking the random variable X to be tracking the height of trees in the sample taken of trees from the considered forest.

Then, by the given data, we get:

[tex]\overline{x} = 4.8[/tex], [tex]s = 4.8[/tex], n = 18

The degree of freedom is n-1 = 17

Level of significance = 100% - 99% = 1% = 0.01

The critical value of t at level of significance 0.01 with degree of freedom 17 is obtained as T = 2.90 (from the t critical values table)

Thus, margin of error for 99% confidence interval for considered case is:

[tex]MOE = T_{c}\dfrac{s}{\sqrt{n}}\\\\MOE = 2.9 \times \dfrac{4.8}{\sqrt{18}} \approx 3.28[/tex]

Thus, the margin of error for the given condition is 3.28 approximately.

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Answer:

0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose a large shipment of televisions contained 9% defectives

This means that [tex]p = 0.09[/tex]

Sample of size 393

This means that [tex]n = 393[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.09[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{393}} = 0.0144[/tex]

What is the probability that the sample proportion will differ from the population proportion by less than 3%?

Proportion between 0.09 - 0.03 = 0.06 and 0.09 + 0.03 = 0.12, which is the p-value of Z when X = 0.12 subtracted by the p-value of Z when X = 0.06.

X = 0.12

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.12 - 0.09}{0.0144}[/tex]

[tex]Z = 2.08[/tex]

[tex]Z = 2.08[/tex] has a p-value of 0.9812

X = 0.06

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.06 - 0.09}{0.0144}[/tex]

[tex]Z = -2.08[/tex]

[tex]Z = -2.08[/tex] has a p-value of 0.0188

0.9812 - 0.0188 = 0.9624

0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%

Answer:

Step-by-step explanation:

B

Answer:

[tex]\mu = 5.2[/tex]

[tex]\sigma = 2.257[/tex]

Step-by-step explanation:

Given

[tex]n = 260[/tex] -- samples

[tex]p = \frac{1}{50}[/tex] --- one in 50

Solving (a): The mean

This is calculated as:

[tex]\mu = np[/tex]

[tex]\mu = 260 * \frac{1}{50}[/tex]

[tex]\mu = 5.2[/tex]

Solving (b): The standard deviation

This is calculated as:

[tex]\sigma = \sqrt{\mu * (1-p)}[/tex]

[tex]\sigma = \sqrt{5.2 * (1-1/50)}[/tex]

[tex]\sigma = \sqrt{5.2 * 0.98}[/tex]

[tex]\sigma = \sqrt{5.096}[/tex]

[tex]\sigma = 2.257[/tex]

Answer:

21.4 m

Step-by-step explanation:

Let x represent the sum of the tall metal, medium metal and short metal heights. Since the tall metal has a length of 1.44 m, and the ratio is in 9:8:7, hence:

(9/24) * x = 1.44

x = 3.84 m

For the medium metal pieces:

(8/24) * 3.84 = medium metal height

medium metal height = 1.28 m

For the short metal pieces:

(7/24) * 3.84 = short metal height

short metal height = 1.12 m

Total horizontal metal piece length  = 3 * 1.8 m = 5.4 m

Total tall metal piece length  = 2 * 1.44 m = 2.88 m

Total medium metal piece length  = 5 * 1.28 m = 6.4 m

Total short metal piece length  = 6 * 1.12 m = 6.72 m

Total length of metal = 5.4 + 2.88 + 6.4 + 6.72 = 21.4 m

Answer:

Step-by-step explanation:

-2

Answer:

f(4) = 31

f(0) = 7

f(-1) = 1

Step-by-step explanation:

f(x) = 6x + 7

f(4) = 6(4) + 7

f(4) = 24 + 7

f(4) = 31

f(0) = 6(0) + 7

f(0) = 0 + 7

f(0) = 7

f(-1) = 6(-1) + 7

f(-1) = -6 + 7

f(-1) = 1

Answer:

The price elasticity of demand is -10

Step-by-step explanation:

Given

[tex]p_1,p_2 = 50,40[/tex]

[tex]q_1,q_2 = 400,500[/tex]

Solving (a): The coefficient of price elasticity of demand (k)

This is calculated as:

[tex]k = \frac{\triangle q}{\triangle p}[/tex]

So, we have:

[tex]k = \frac{500 - 400}{40 - 50}[/tex]

[tex]k = \frac{100}{-10}[/tex]

[tex]k = -10[/tex]

Because |k| > 0, then we can conclude that the company made a wise decision.

Answer:

Step-by-step B represents the $14 John earned in the 2 hours he worked.

explanation:

(3.1) … … …

[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{2x-y}{x-2y}[/tex]

Multiply the right side by x/x :

[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{2-\dfrac yx}{1-\dfrac{2y}x}[/tex]

Substitute y(x) = x v(x), so that dy/dx = x dv/dx + v :

[tex]x\dfrac{\mathrm dv}{\mathrm dx} + v = \dfrac{2-v}{1-2v}[/tex]

This DE is now separable. With some simplification, you get

[tex]x\dfrac{\mathrm dv}{\mathrm dx} = \dfrac{2-2v+2v^2}{1-2v}[/tex]

[tex]\dfrac{1-2v}{2-2v+2v^2}\,\mathrm dv = \dfrac{\mathrm dx}x[/tex]

Now you're ready to integrate both sides (on the left, the denominator makes for a smooth substitution), which gives

[tex]-\dfrac12\ln\left|2v^2-2v+2\right| = \ln|x| + C[/tex]

Solve for v, then for y (or leave the solution in implicit form):

[tex]\ln\left|2v^2-2v+2\right| = -2\ln|x| + C[/tex]

[tex]\ln(2) + \ln\left|v^2-v+1\right| = \ln\left(\dfrac1{x^2}\right) + C[/tex]

[tex]\ln\left|v^2-v+1\right| = \ln\left(\dfrac1{x^2}\right) + C[/tex]

[tex]v^2-v+1 = e^{\ln\left(1/x^2\right)+C}[/tex]

[tex]v^2-v+1 = \dfrac C{x^2}[/tex]

[tex]\boxed{\left(\dfrac yx\right)^2 - \dfrac yx+1 = \dfrac C{x^2}}[/tex]

(3.2) … … …

[tex]y' + \dfrac yx = \dfrac{y^{-3/4}}{x^4}[/tex]

It may help to recognize this as a Bernoulli equation. Multiply both sides by [tex]y^{\frac34}[/tex] :

[tex]y^{3/4}y' + \dfrac{y^{7/4}}x = \dfrac1{x^4}[/tex]

Substitute [tex]z(x)=y(x)^{\frac74}[/tex], so that [tex]z' = \frac74 y^{3/4}y'[/tex]. Then you get a linear equation in z, which I write here in standard form:

[tex]\dfrac47 z' + \dfrac zx = \dfrac1{x^4} \implies z' + \dfrac7{4x}z=\dfrac7{4x^4}[/tex]

Multiply both sides by an integrating factor, [tex]x^{\frac74}[/tex], which gives

[tex]x^{7/4}z'+\dfrac74 x^{3/4}z = \dfrac74 x^{-9/4}[/tex]

and lets us condense the left side into the derivative of a product,

[tex]\left(x^{7/4}z\right)' = \dfrac74 x^{-9/4}[/tex]

Integrate both sides:

[tex]x^{7/4}z=\dfrac74\left(-\dfrac45\right) x^{-5/4}+C[/tex]

[tex]z=-\dfrac75 x^{-3} + Cx^{-7/4}[/tex]

Solve in terms of y :

[tex]y^{4/7}=-\dfrac7{5x^3} + \dfrac C{x^{7/4}}[/tex]

[tex]\boxed{y=\left(\dfrac C{x^{7/4}} - \dfrac7{5x^3}\right)^{7/4}}[/tex]

(3.3) … … …

[tex](\cos(x) - 2xy)\,\mathrm dx + \left(e^y-x^2\right)\,\mathrm dy = 0[/tex]

This DE is exact, since

[tex]\dfrac{\partial(-2xy)}{\partial y} = -2x[/tex]

[tex]\dfrac{\partial\left(e^y-x^2\right)}{\partial x} = -2x[/tex]

are the same. Then the general solution is a function f(x, y) = C, such that

[tex]\dfrac{\partial f}{\partial x}=\cos(x)-2xy[/tex]

[tex]\dfrac{\partial f}{\partial y} = e^y-x^2[/tex]

Integrating both sides of the first equation with respect to x gives

[tex]f(x,y) = \sin(x) - x^2y + g(y)[/tex]

Differentiating this result with respect to y then gives

[tex]-x^2 + \dfrac{\mathrm dg}{\mathrm dy} = e^y - x^2[/tex]

[tex]\implies\dfrac{\mathrm dg}{\mathrm dy} = e^y \implies g(y) = e^y + C[/tex]

Then the general solution is

[tex]\sin(x) - x^2y + e^y = C[/tex]

Given that y (1) = 4, we find

[tex]C = \sin(1) - 4 + e^4[/tex]

so that the particular solution is

[tex]\boxed{\sin(x) - x^2y + e^y = \sin(1) - 4 + e^4}[/tex]

Answer:

BC = 28

Step-by-step explanation:

The midsegment DF is half the measure of the third side BC , then

BC = 2 × DF = 2 × 14 = 28

Answer:

1000

Step-by-step explanation:

Answer:

310/[tex]3^{3}[/tex] = 310/27 =11.48

Step-by-step explanation:

Answer:

310/ = 310/27 =11.48

Step-by-step explanation:

Answer:

36 (maybe...)

Step-by-step explanation:

Technically there is no way to answer this question, it says that 120 ADULTS were surveyed and then asks how many STUDENTS rank themselves as introverts.  But if we a supposed to assume that all adults are students:

The ratio of 3:7 means that for every 3 introverts, there are 7 extroverts.

In other words for every 10 people (total introvert+extrovert) there are 3 introverts.

So to find the number of introverts in the group of 120, just multiply by 3/10 or 0.3

The answer would be 36

Answer:

Step-by-step explanation:

46.327=46 ( neaarest whole number)

-4.801=-5 (nearest whole number)

46-(-5)=46+5=51

Answer:

B

Step-by-step explanation:

Let the base of the triangle be b and the height be h.

The sum of the base and height is 14. Thus:

[tex]b+h=14[/tex]

Recall that the area of a triangle is given by:

[tex]\displaystyle A=\frac{1}{2}bh[/tex]

From the first equation, solve for either variable:

[tex]h=14-b[/tex]

Substitute:

[tex]\displaystyle A=\frac{1}{2}b(14-b)[/tex]

Distribute:

[tex]\displaystyle A=\frac{1}{2}(14b-b^2)[/tex]

Distribute:

[tex]\displaystyle A=-0.5b^2+7b[/tex]

Let b = x. Hence:

[tex]A=-0.5x^2+7x[/tex]

Therefore, our answer is B.

9514 1404 393

Answer:

  3/4

Step-by-step explanation:

It might be easier to start by expressing the ratios with AD as the denominator.

  AD/AC = 2/1   ⇒   AC/AD = 1/2

  AD/AB = 3/1   ⇒   AB/AD = 1/3

From the latter, we have ...

  (AD -AB)/AD = 1 -1/3 = 2/3 = BD/AD

Then the desired ratio is ...

  AC/BD = (AC/AD)/(BD/AD) = (1/2)/(2/3) = (3/6)/(4/6)

  AC/BD = 3/4

Answer:

5

Step-by-step explanation:

3-(-2) will become positive 5. so number line will go towards positive 5.

Step-by-step explanation:

here is the answer to your question

Answer:

g(x) = x^3 - 2

Step-by-step explanation:

As you can see on the graph, the line has been translated down 2 units.

If the graph of f has the same shape as the graph of g, then the slope remains the same. The y intercept (k) changes by -2 units, so the k value is -2

g(x) = x^3 - 2

Hope this helps!!

sinh(ln(4)) = (exp(ln(4)) - exp(-ln(4)))/2 = (4 - 1/4)/2 = 15/8 = 1.875

sinh(4) = (exp(4) - exp(-4))/2 ≈ 27.28992

Value of the expression in which each variable was swapped out with a number from its corresponding domain sinh⁡ (l5)

sinh (5)

=sinh(1.6094) =2.39990 rad

=sinh⁡(1.6094) =2.3

By doing the following, you may determine the numerical value of an algebraic expression: Replace each variable with the specified number. Then, enter your score in your team's table.

Value of the expression in which each variable was swapped out with a number from its corresponding domain. In the case of a number with only one digit, referring to the numerical value associated with a digit by its "value" is a convenient shorthand.

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9514 1404 393

Answer:

  y = 7√2

Step-by-step explanation:

We are given the side opposite the angle, and we want to find the hypotenuse. The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

  sin(45°) = 7/y

  y = 7/sin(45°) = 7/(1/√2)

  y = 7√2

__

Additional comment

In this 45°-45°-90° "special" right triangle, the two legs are the same length. Thus, ...

  x = 7