Passing through (3,3) and parallel to the line whose equation is 2x+y-2=0; slope intercept form.

Answer:

96sq ft. u just multiple the length by the height then square it

The equation that represents the graph of function g is: g(x) = 3f(x).

A linear function is often expressed as y = mx + b (slope-intercept form), where the slope of the function is the value of "m", while the y-intercept, which is the point where the line cuts the y-axis is the value of "b".

To find the linear function equation for the graph of g, find the slope (m) and determine the point on the y-axis where the line intercepts it, b.

Slope of function g (m) = rise/run = 3/1

Slope of function g (m) = rise/run = 3

The graph of the function of g intersects the y-axis at 0. b = 0

The slope of function .f = 1. This means the slope of function g is three times the slope of the function of .f.

Therefore, the best representation for the graph of function g is: g(x) = 3f(x).

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The area of the sector with a central angle of 60 degree and radius of 8 units is approximately 33.5 sqaure units.

A sector of a circle is simply part of a circle made up of an arc and two radii.

The area of a sector of a circle can be expressed as:

Area = (θ/360º) × πr²

Where θ is the sector angle in degrees, and r is the radius of the circle.

From the image:

Measure of central angle θ = 60 degrees

Radius r = 8 units

Plug these values into the above formula and solve for the area:

Area = (θ/360º) × πr²

Area = (60°/360°) × π × 8²

Area = 1/6 × π × 64

Area = 1/6 × π × 64

Area = 33.5 sqaure units.

Therefore, the area is approximately 33.5 sqaure units.

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Answer:

18.266

Step-by-step explanation:

The functions 7 are inverse functions while the functions 8 are not inverse functions

To verify that f and g are inverse functions, we need to show that:

Let's apply these conditions to the given functions:

f(x) = 5x + 2; g(x) = (x−2)/5

f(g(x)) = f((x−2)/5) = 5((x−2)/5) + 2 = x − 2 + 2 = x

g(f(x)) = g(5x + 2) = ((5x + 2) − 2)/5 = 5x/5 = x

Since f(g(x)) = x and g(f(x)) = x, we can conclude that f and g are inverse functions.

f(x) = ½x − 7; g(x) = 2x + 14

f(g(x)) = f(2x + 14) = ½(2x + 14) − 7 = x

g(f(x)) = g(½x − 7) = 2(½x − 7) + 14 = x − 7 + 14 = x + 7

Since f(g(x)) = x and g(f(x)) ≠ x, we can conclude that f and g are not inverse functions.

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Answer:

5.6235567 * \(10^{7}\) as scientific notation

A  single digit times a power of ten is called a scientific notation.

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The area of trapezoid $ABCD$ is $\frac{1}{2}h(a+b)$, where $h$ is the height of the trapezoid and $a$ and $b$ are the lengths of the bases $\overline{AB}$ and $\overline{CD}$, respectively.

To find the area of trapezoid $ABCD$, we need to know the lengths of the bases and the height. Let's assume that the lengths of the bases are $a$ and $b$, where $a > b$. The extensions of the legs of the trapezoid intersect at point $P$.

To calculate the area of the trapezoid, we need to find the height. Let's consider triangle $APB$ formed by the extension of the leg $\overline{AB}$, the extension of the leg $\overline{CD}$, and the line segment $\overline{AP}$. Since $\overline{AB}$ and $\overline{CD}$ are parallel, triangle $APB$ is similar to triangle $CPD$.

Using the similarity of triangles, we can set up the following proportion: $\frac{h}{a} = \frac{h+x}{b}$, where $x$ is the length of $\overline{PD}$. Cross-multiplying gives us $bh = ah + ax$. Rearranging the equation, we have $ax = (b-a)h$. Dividing both sides by $a$, we get $x = \frac{b-a}{a}h$.

Now, the height of the trapezoid, $h$, is the sum of the lengths of $\overline{AP}$ and $\overline{PD}$: $h = \overline{AP} + \overline{PD} = x + \frac{b-a}{a}h$. Simplifying the equation, we have $\frac{a}{a}h = x + \frac{b-a}{a}h$, which gives us $\frac{h}{a} = x + \frac{b-a}{a}h$.

Substituting the value of $x$, we have $\frac{h}{a} = \frac{b-a}{a}h + \frac{b-a}{a}h$. Simplifying further, we get $\frac{h}{a} = \frac{2(b-a)}{a}h$. Dividing both sides by $\frac{2(b-a)}{a}$, we find that $h = \frac{a}{2(b-a)}h$.

Finally, we can substitute the value of $h$ in the formula for the area of the trapezoid to find:

$[ABD] = \frac{1}{2}h(a+b) = \frac{1}{2}\left(\frac{a}{2(b-a)}h\right)(a+b) = \frac{a(a+b)}{4(b-a)}$.

The area of trapezoid $ABCD$ with bases $\overline{AB}$ and $\overline{CD}$ is given by $\frac{a(a+b)}{4(b-a)}$, where $a$ and $b$ are the lengths of the bases and $h$ is the height of the trapezoid.

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We draw the conclusion that the results are significantly different since the null hypothesis was rejected, which means that a different proportion of people than 0.3 had clinical illness.

With the aid of a statistical test, researchers weigh the evidence in favor of and against the null and alternative hypotheses, which are two opposing claims: The null hypothesis (H0) states that there is no population impact. Alternative hypothesis (Ha or H1): The population is affected.

Given,

Among susceptible individuals exposed to a particular infectious agent 30% generally develop clinical disease. out of a random sample of 100 people suspected of exposure to the agent only 20 developed clinical disease.

Let X be the random variable to determine the proportion of people who have clinical illness.

n: The overall number of people who were exposed to a specific infectious pathogen.

p: The percentage of sample members who have a clinical illness.

Selected subjects who experience clinical disease are the experiment's success.

As a result, the variables are n = 100 and p = 0.30.

It is necessary to determine whether exposure to the agent outcome may be entirely accounted for by coincidence.

A P-value is a probabilistic indicator of the likelihood that an observed outcome effect is accidental.

Using the default level of significance = 0.05, the level of significance is not defined.

One percentage z-test is the best suitable test for the aforementioned assertion.

The alternate and null hypothesis is

H0: p = 0.3

H1:: p ≠ 0.3

Where p is the percentage of the population that develops a clinical illness.

R may be used to calculate the p-value and test statistic.

The instruction is as follows:

x = 20; n = 100; p = 0.3; prop.test

The result looks like this: - The p-value obtained from the output above is 0.03817.

Decision principle:

When significance is 5%,

If the p-value is below 0.05, reject the null hypothesis.

Accept the contrary.

Because the p-value was 0.03817 0.05

The null hypothesis is disproven.

In conclusion:

We draw the conclusion that the results are significantly different since the null hypothesis was rejected, which means that a different proportion of people than 0.3 had clinical illness.

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Answer:

0.15 repeating

Step-by-step explanation:

3 ft

Step-by-step explanation:

Answer:

To break-even, Zorah needs to play for 8 hours.

Step-by-step explanation:

To calculate the break-even point in hours, we need to use the following formula:

Break-even point in units= fixed costs/ contribution margin per unit

Break-even point in units= 120 / (25 - 10)

Break-even point in units= 8 hours

To break-even, Zorah needs to play for 8 hours.

Answer: (d)

Step-by-step explanation:

For option (a)

\(\sqrt[m]{x}\sqrt[m]{y}=\sqrt[m]{xy}\)

for the same exponent, numbers multiply keeping exponent the same.

for option (b)

\(a\sqrt[n]{x} +b\sqrt[n]{y} =\left(a+b\right)\sqrt[n]{x}\)

for option (c)

\(\Rightarrow \dfrac{\sqrt[m]{x} }{\sqrt[m]{y} }=\sqrt[m]{\dfrac{x}{y}}\)

for option (d)

exponent multiplies

\(\therefore \left(\sqrt[m]{x^a} \right)^b=\sqrt[m]{x^{ab}}\)

option (d) is correct

The given sequence converges to the limit -ln 3/2. The given sequence is an = \((-1)^{n/ 9\)√n.

We have to determine whether the sequence converges or diverges.

If it converges, find the limit. (If an answer does not exist, enter DNE.)

Let's calculate the first few terms of the given sequence:

n = 1; an = \((-1)^{1/9\)√1 = -1/9n = 2;

an = \((-1)^{2/9\)√2

= 1/9.3.

We notice that the terms of the sequence are oscillating in sign and decreasing in magnitude.

This suggests that the sequence might be converging.

Let's apply the alternating series test to confirm our conjecture.

Theorem (Alternating Series Test):

If an = \((-1)^{{n-1}bn\)

satisfies the following conditions:

1) bn > 0 for all n

2) bn is decreasing for all n

3) lim{n->∞} bn = 0

then the alternating series is convergent.

Moreover, the limit L lies between any two consecutive partial sums of the series.

Let's check the conditions for the given sequence.

1) bn = 1/9√n > 0 for all n

2) d/dn (1/9√n) = -1/(18n√n) < 0 for all n

3) lim{n->∞} 1/9√n = 0

We have checked all the conditions of the alternating series test, and hence the given sequence converges.

Let's find the limit using the formula for the sum of an infinite alternating series.

Limit = L = -ln 3/2.

So, the given sequence converges to the limit -ln 3/2.

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Answer:

-12 gal / min

Step-by-step explanation:

-60/5=-12

Using the z-distribution, as we have the population standard deviation, it is found that a sample of 83 people must be taken.

Given,

Estimation of number of minutes per day a person spends on the internet .

Margin of error in Z distribution,

M = z σ/\(\sqrt{n}\)

In which:

z is the critical value.

σ is the population standard deviation.

n is the sample size.

Here,

We have 90% confidence level ,

Thus ,

\(\alpha\) = 0.9

z is the value of Z that has a p-value

(1+0.9) / 2

= 0.95

so the critical value is z = 2.575

Also we have

standard deviation = 46 minutes

Population mean = 13 minutes

To find minimum sample size solve for n

M = z σ/\(\sqrt{n}\)

13 = 2.575 (46/\(\sqrt{n}\))

n = 83 .30

Rounding up, a sample of 83 people must be taken.

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The probability that a second call will not arrive in the next 20 seconds is approximately 0.2636 or 26.36%.

Poisson probability is a mathematical concept that describes the probability of a certain number of events occurring in a fixed interval of time or space, given a known average rate of occurrence. The Poisson probability distribution is named after French mathematician Siméon Denis Poisson, who introduced it in the early 19th century to model the occurrence of rare events, such as errors in counting or measurement, accidents, or phone calls.

The Poisson probability distribution is a discrete probability distribution that gives the probability of a certain number of events (x) occurring in a fixed interval (t), when the average rate of occurrence (λ) is known. The Poisson probability distribution assumes that the events occur independently and at a constant average rate over time or space. The formula for Poisson probability is:

P(x; λ) = (\(e^{-\lambda}\)) * λˣ) / x!

where:

P(x; λ) = the probability of x occurrences in a given interval, when the average rate is λ

e = a mathematical constant e (approximately 2.71828)

λ = it is the average rate of occurrence in the given interval

x = it is number of occurrences in the given interval

Given that calls for dial-in connections arrive at an average rate of four per minute and follow a Poisson distribution, we can use the Poisson probability formula to solve this problem. The Poisson probability formula is:

P(x; λ) =  (\(e^{-\lambda}\)) * λˣ) / x!

where:

P(x; λ) = the probability of x occurrences in a given interval, when the average rate is λ

e = a mathematical constant e (approximately 2.71828)

λ = the average rate of occurrence in the given interval

x = it is the number of occurrences in the given interval

In this problem, we are interested in finding the probability that a second call will not arrive in the next 20 seconds, given that a call has already arrived at the beginning of a one-minute interval. Since we are given the average rate of calls per minute, we need to adjust the interval to 20 seconds, which is 1/3 of a minute. Therefore, the average rate of calls per 20 seconds is:

λ = (4 calls/minute) * (1/3 minute) = 4/3 calls/20 seconds

Using the Poisson probability formula, we can calculate the probability of no calls arriving in the next 20 seconds:

P(0; 4/3) = ( \(e^{-4/3}\)* (4/3)⁰) / 0! = \(e^{-4/3}\) ≈ 0.2636

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Answer:

  P55,000

Step-by-step explanation:

The amount of commission is found by multiplying the commission rate by the value of the sale(s).

  commission = rate × sales

  commission = 0.10 × p550,000 = P55,000

The agent will receive P55,000 in commission.

_____

Check

The amount of commission cannot be more than the value of the sale. It is generally a small fraction of the sale value. Here, it is 1/10.

Answer:

D

Step-by-step explanation:

The area of the region that lies above the x-axis, below the curve \(x=t^2+7t+8\), y=e^-t with 0≤t≤1 is approximately 2.1185 square units.

To find the area of the region bounded by the x-axis and the curve, we need to integrate the curve between the limits of t=0 and t=1.

∫₀¹ \(e^-t dt = [-e] ^{-t}\)from 0 to 1 = 1 - 1/e

So, the equation of the curve intersects the x-axis when y=0. To find the x-coordinate of the intersection point, we set y=0 in the equation of the curve:

\(0=e^-t\)

t=0

Thus, the intersection point is (8,0). We also need to find the value of t for which the curve is at its lowest point. To find the minimum point of the curve, we take the derivative of the equation of the curve and set it equal to zero.

y' = \(-e^{-t(2t+7)}\)

0 = \(-e^{-t(2t+7)}\)

t = -7/2

Since t is bounded by 0 and 1, the minimum point of the curve lies within the given range of t. Therefore, the area of the region bounded by the x-axis and the curve is given by the definite integral:

∫₀¹\((t^2+7t+8) e^{-t} dt\)

This integral can be evaluated using integration by parts. After integrating, differentiating, and simplifying, we get:

∫₀¹\((t^2+7t+8) e^{-t} dt\)  = 2.1185 (rounded to four decimal places).

Therefore, the area of the region that lies above the x-axis, below the curve\(x=t^2+7t+8\), \(y=e^-t\) with 0≤t≤1 is approximately 2.1185 square units.

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The scalar line integral ∫ c (3x y) ds, where c is the line segment from (−1,3) to (4,2) is equal to 78√26/5

To evaluate the scalar line integral ∫ c (3x y) ds, where c is the line segment from (−1,3) to (4,2), we first need to parameterize the curve c.

Let t be the parameter such that

x = -1 + 5t,

y = 3 - t,

for 0 ≤ t ≤ 1.

The length of the curve c is given by the integral ∫ c ds, which can be calculated using the formula ∫ a to b \(√(dx/dt)^2 + (dy/dt)^2\) dt. Plugging in the values from the parameterization, we get

\(∫ c ds = ∫ 0 to 1 √(5^2 + (-1)^2) dt = ∫ 0 to 1 √26 dt = √26.\)

Using the parameterization, we can now write the integral as

\(∫ c (3x y) ds = ∫ 0 to 1 (3(-1+5t)(3-t)) √(5^2 + (-1)^2) dt = 78√26/5.\)

Therefore, the scalar line integral ∫ c (3x y) ds, where c is the line segment from (−1,3) to (4,2) is equal to 78√26/5.

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The scalar line integral ∫ c (3x y) ds, where c is the line segment from (−1,3) to (4,2), is approximately equal to

22.229.

We can do this by letting x = t and y = 3 - t/2, where -1 ≤ t ≤ 4.

Then, we can find ds/dt using the formula \(ds/dt = \sqrt{(dx/dt^2 + dy/dt^2)}\), which simplifies to

\(ds/dt = \sqrt{(1 + 1/4) } = \sqrt{(5)/2} .\)

Next, we can substitute x and y in terms of t into the integrand and simplify to get:

\(3x y = 3t(3 - t/2) = 9t - (3/2)t^2\)

Now, we can evaluate the integral by integrating with respect to t from -1 to 4:

\(\int c (3x y) ds = ∫ from -1 to 4 (9t - (3/2)t^2) (\sqrt{(5)/2)}  dt\)

\(= (\sqrt{(5)/2)}  [ (9t^2/2) - (3/8)t^3 ] evaluated from -1 to 4\)

\(= (\sqrt{(5)/2)}  [ (81/2) - (243/8) - (-27/8) + (3/8) ]\)

\(= \sqrt{(5)/2)}  [ (189/8) ]\)

= 22.229
Therefore, the scalar line integral ∫ c (3x y) ds, where c is the line segment from (−1,3) to (4,2), is approximately equal to

22.229.

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The correct answer is (c) I and II only.

Given that the linear mapping U preserves lengths and orthogonality, we can determine the correct equalities.

I. (Ux) · (Uy) = x · y

This equality is true because preserving orthogonality means that the dot product of Ux and Uy is equal to the dot product of x and y.

II. (Ux) · (Uy) = x · y

This equality is also true because preserving lengths means that the dot product of Ux and Uy is equal to the dot product of x and y.

III. (Ux) · (Uy) = 0 · x · y = 0

This equality is not necessarily true. It states that the dot product of Ux and Uy is always zero, which is not necessarily the case. The preservation of lengths and orthogonality does not guarantee that the dot product will always be zero.

Therefore, the correct answer is (c) I and II only.

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Answer:

57 for the third side

Step-by-step explanation:

a = √(c² - b²)

To find the radius of convergence, R, of the series

Σ (n!)^(k+4)/((k+4)n)! x^n

we can use the ratio test. The ratio test states that if

lim |a_(n+1)/a_n| = L as n approaches infinity,

then the series converges if L < 1 and diverges if L > 1.

Applying the ratio test to our series, we have:

|((n+1)!)^(k+4)/((k+4)(n+1))! x^(n+1)| / |(n!)^(k+4)/((k+4)n)! x^n|

Simplifying this expression, we get:

|n+1| |x| / (k+4)(n+1)

As n approaches infinity, the term |n+1| / (n+1) simplifies to 1, and the expression becomes:

|x| / (k+4)

For the series to converge, we need |x| / (k+4) < 1. This implies that the radius of convergence, R, is given by:

R = k + 4

Therefore, the radius of convergence, R, for the given series is k + 4.

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The constant of proportionality for Tables 1,2,3,4,5 and 6 are 7, 3, 0.25, 14, 5/12 and 7/30 respectively

What is constant of proportionality?

The constant of proportionality is the constant value of the ratio between two proportional quantities.

In this case, the constant of proportionality (k) is the ratio of y and x

i.e. k = y/x

To complete the table:

Note:  k = y/x, y = kx and x = y/k

Table1:

x | 3  |  7   |  8  |  10 |

y | 21 | 49 | 56 | 70 |

constant of proportionality = 21/3 = 7

Table 2:

x |  4 | 24 | 15 |  3 |

y | 12 | 8  | 45 |  9 |

constant of proportionality = 24/8 = 3

Table 3:

x | 12 | 36 | 8 | 48 |

y |  3 |  9   | 2 | 12 |

constant of proportionality = 12/48 = 0.25

Table 4:

x |  7  |  11    | 5   | 2 |

y | 98 | 154 | 70 | 28 |

constant of proportionality = 70/5 = 14

Table 5:

x | 24 | 12 | 36 | 108 |

y | 10  | 5  | 15  | 45   |

constant of proportionality = 5/12

Table 6:

x | 60 |  1     | 0  | 30 |

y | 14  | 7/30 | 0  |  7  |

constant of proportionality = 7/30

Therefore, the corresponding values of the constant of proportionality for Tables 1, 2, 3, 4, 5 and 6 are 7, 3, 0.25, 14, 5/12 and 7/30

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Heterozygous refers to a pair of alleles in which one is dominant and one is recessive. As you can see, all genotypes for possible offspring in the Punnett square are heterozygous. This means the probability of the parents having a child that is heterozygous is 100 percent likely.

Answer: 100%

If the probability that a household owns a pet is 0.55 then the probability that all households will have pets is equal to 0.0503.

Given that the probability that a household owns a pet is 0.55 and there are 5 houses on a block.

We are required to calculate the probability that all the five households will have pets.

Probability is basicallly the chance of happening an event among all the events possible. It cannot be negative.

Binomial probability distribution is basically the probability calculations but in different combinations.

In this we have to calculate the probability that all the houses will have the pets then the probability that all five households will have pets is equal to \(5C_{5}(0.55)^{5} (1-0.55)^{0}\)

=1(0.0503)\((0.45)^{0}\)

=1*0.0503*1

=0.0503

Hence the probability that all the five households will have pets is equal to 0.0503.

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the answer would be 4 purple to 3 green

4:3