A person Rents a canoe for 4 Hours and paid a total of $36. of Renting a canoe costs am initial fee of the $2 Plus an additional amount for each hour the canoe is rented,which graph represents the total cost,y, in dollars of renting a canoe for x hours

Answer:

Possible

Step-by-step explanation:

The rule for triangle side lengths is that the two shortest sides must add up to the longest side so it is possible because

3+7 = 10

Two short sides = The longest side

Answer:

possible

Step-by-step explanation:

3+7= 10

The constant term would be the sum of A and B, and the polynomial fraction would be C/(x + 6)(2x + 3).  The remaining fraction in constant  is a separate partial fraction with a specific denominator.

The given fraction is 6x² - x - 127 / [(x - 5)(x + 4)] + (x - 5)(x + 4) / (2x² + 13x + 18). To express it as a constant plus a polynomial fraction, we first factor the denominators. We have (x - 5)(x + 4) and 2x² + 13x + 18, which can be factored as (x + 6)(2x + 3).

Next, we decompose the given fraction into partial fractions. We express the fraction as a sum of simpler fractions with specific denominators. Let's assume the decomposed form is A/(x - 5) + B/(x + 4) + C/(x + 6)(2x + 3).

To determine the values of A, B, and C, we can use various methods such as equating numerators, finding common denominators, and comparing coefficients. Solving the resulting equations will provide us with the values of A, B, and C.

Once we have the values of A, B, and C, we can rewrite the original fraction as a constant plus a polynomial fraction. The constant term would be the sum of A and B, and the polynomial fraction would be C/(x + 6)(2x + 3).

In conclusion, by factoring the denominators and decomposing the given fraction into partial fractions, we can express it as a constant plus a polynomial fraction. The constant term is the sum of two specific partial fractions, and the remaining fraction is a separate partial fraction with a specific denominator.

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The smallest possible product of these four numbers is 59.0625

The equation is given as:

a + b + c + d = 12

The numbers are consecutive numbers.

So, we have:

a + a + 1 + a + 2 + a + 3 = 12

Evaluate the like terms

4a = 6

Divide by 4

a = 1.5

The smallest possible product of these four numbers is represented as:

Product = a * (a + 1) * (a + 2) * (a + 3)

This gives

Product = 1.5 * (1.5 + 1) * (1.5 + 2) * (1.5 + 3)

Evaluate

Product = 59.0625

Hence, the smallest possible product of these four numbers is 59.0625

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The annuity that should be worth after 6 years is $63,900.

Given that,

Now the following formula should be used:

\(Amount = Present\ value \times \frac{(1+ rate)^{(n)} - 1} {rate}\\\\= \$4,500 \times \frac{(1+0.03)^{12} - 1}{0.03}\\\\= \$4,500 \times \frac{0.4257}{0.03}\\\\= \$4,500 \times 14.1920\\\\= \$63,864\\\\= \$63,900\)

Therefore we can conclude that the annuity that should be worth after 6 years is $63,900.

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Answer: 63900

Step-by-step explanation: Use the savings annuity formula

PN=d((1+r/k)N k−1)r/k

to calculate the value of P6. The question states that r=0.06, d=$4,500, k=2 compounding periods per year, and N=6 years. Substitute these values into the formula results in

P6=$4,500 ((1+0.06/2)6⋅2−1)/(0.06/2).

Simplifying, we have P6=$4,500 ((1.03)12−1)/(0.03). Therefore P6=$63,864.13. Our final answer is 63900.

The answer for the system is, (2, 5)

y= 5, x= 2

Answer:

D. 4

Explanation:

Linear relationship refers to relationships which give straight lines when graphed. All the segments, except segment 4, show straight-line, linear relationships.

As section 4 is curved, it show nonlinear relationship.

Answer:

see image

Step-by-step explanation:

see image

\(\qquad \textit{Centroid of a Triangle} \\\\ \left(\cfrac{x_1+x_2+x_3}{3}~~,\cfrac{y_1+y_2+y_3}{3}~~ \right)\quad \begin{cases} X(\stackrel{x_1}{6},\stackrel{y_1}{0})\\ Y(\stackrel{x_2}{2},\stackrel{y_2}{8})\\ Z(\stackrel{x_3}{-2},\stackrel{y_3}{-2}) \end{cases} \\\\\\ \left( \cfrac{6+2-2}{3}~~,~~\cfrac{0+8-2}{3} \right)\implies \left(\cfrac{6}{3}~~,~~ \cfrac{6}{3} \right)\implies \text{\LARGE (2~~,~~2)}\)

To argue why the liberal arts are so important in education and leisure, one must discuss its Greek origin and how it is received today.

The term "liberal arts" comes from the Latin word "liberalis," which means free. It was used in the Middle Ages to refer to topics that should be studied by free people. Liberal arts refers to courses of study that provide a general education rather than specialized training. It encompasses a wide range of topics, including literature, philosophy, history, language, art, and science.The liberal arts curriculum is based on the idea that a broad education is necessary for individuals to become productive members of society. In ancient Greece, education was focused on developing the mind, body, and spirit.  

The study of the liberal arts is necessary to create well-rounded individuals who can contribute to society in meaningful ways. While the importance of the liberal arts has been debated, it is clear that they are more important now than ever before. The study of the liberal arts is necessary to develop the skills that are required in a rapidly advancing technological world.

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The likelihood that the mean sample will deviate by 1.8 watts from the population mean is 0.7498.

What are the values for the median and mean?

By adding up the numbers and dividing the total by the number of numbers in the list, the arithmetic mean can be calculated. This is typically referred to as an average. The middle value in a list that is ranked from least to greatest is called the median.

P(382.2<x<385.8)

Z-score is calculated as z=(x-)/Z.

However, since n=41, /n 100/41=15.6174, so when x=382.2, z=(-1.8)/15.6174, z=-0.1152, and P(z-0.1152)=0.1251, respectively.

P(z0.1152)=0.8749 for x=385.8; consequently, P(113.7x120.3)=0.8749-0.1251 = 0.7498.

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Answer:

A

Step-by-step explanation:

The searched angle is a circumference angle that insists on the arc whose angle is 134 degrees. So its measure is half of it

134 : 2 = 67 degrees

Answer:

y = x - 3

Step-by-step explanation:

Answer:

Y= x-3

Step-by-step explanation:

The distance from our y values is -1.

The distance from our x values is -1.

Rise/ Run = Y/X

-1/-1 = 1 or 1/1

You would rise 1 and run 1!

You can use this strategy if you're using graph paper to eventually get the y intercept which is -3.

Hope this helps! :)

The probability that Mark will score either in a two-point shot or in a three-point shot is 61.5%.

P(A) = Probability of scoring in a two-point shot = 30%

P(B) = Probability of scoring in a three-point shot = 45%

P(neither) = Probability of scoring in neither shot = 25%

P(A and B) = P(A) * P(B)

Let's calculate P(A or B) using the given probabilities:

P(A or B) = P(A) + P(B) - P(A and B)

= P(A) + P(B) - (P(A) * P(B))

Substituting the values:

P(A or B) = 0.30 + 0.45 - (0.30 * 0.45)

= 0.30 + 0.45 - 0.135

= 0.615

Therefore, the probability that Mark will score either in a two-point shot or in a three-point shot is 61.5%.

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Answer: Heyaa!

The Answer is 2x+2

Step-by-step explanation:

Simplify the expression.

hopefully this helps you !

- Matthew ~

answer is in the attachment hope it helps you ^_^

=======================================================

Explanation:

The inscribed angle 20 degrees doubles to 2*20 = 40 which is the measure of the central angle, and the arc in which the inscribed angle subtends (or cuts off). This is due to the aptly named inscribed angle theorem.

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

A slightly longer alternative path would be to do this:

The triangle with interior angles 20 and c is isosceles. Note how the missing angle up top is one of the congruent base angles, so the missing angle is 20 degrees. That means angle c is...

20+20+c = 180

40+c = 180

c = 180-40

c = 140

Then angle b is supplementary to this

b+c = 180

b+140 = 180

b = 180-140

b = 40

This path leads to the same answer. It's slightly longer, but it's a path you can take if you aren't familiar with the inscribed angle theorem.

In fact, this line of thinking is effectively how the inscribed angle theorem is proved as shown in the diagram below.

The pdf of the kth order statistic X(k) can be found using the formula: f(k)(x) = n!/[ (k-1)! (n-k)! ] * [ F(x) ]^(k-1) * [ 1-F(x) ]^(n-k) * f(x) where F(x) is the cdf of the uniform distribution on [0,8] and f(x) is the pdf of the uniform distribution, which is 1/8 for x in [0,8]. The expected value of X is 4.

Using this formula, we can find the pdf of X(k) for any k between 1 and n.

For the expected value of X, we can use the formula:

E[X] = ∫₀⁸ x * f(x) dx

Since X is uniformly distributed on [0,8], the pdf f(x) is constant over this interval, equal to 1/8. Therefore, we have:

E[X] = ∫₀⁸ x * (1/8) dx = 1/16 * x^2 |_₀⁸ = 4

So the expected value of X is 4.

Regarding the hint given, it seems to be unrelated to the problem at hand and does not provide any additional information for solving it.

Let X1, X2, ..., Xn denote independent and uniformly distributed random variables on the interval [0, 8]. To find the pdf of the kth order statistic, X(k), where k is an integer between 1 to n, we can use the following formula:

pdf of X(k) = (n! / [(k-1)! * (n-k)!]) * (x^(k-1) * (8-x)^(n-k)) / (8^n)

For the expected value E[X(k)], we can use the provided hint:

∫(x * pdf of X(k)) dx from 0 to 8 = ∫[x * (n! / [(k-1)! * (n-k)!]) * (x^(k-1) * (8-x)^(n-k)) / (8^n)] dx from 0 to 8

The hint suggests that the integral can be simplified using a gamma function Γ(a+) with unknown parameters a and β:

∫(x^4-4 * (1 - x)^β-1) dx = Γ(a)(β)

To find E[X(k)], solve the integral with the appropriate parameters for a and β.

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The correct option is the first one:

The theoretical probability, P(gold), is 25%, and the experimental probability is 27.5%.

The experimental probability is equal to the quotient between the number of times that a gold block was taken and the total number of trials, so it is:

E = 11/40 = 0.275

Multiply this by 100% to get the percentage:

0.275*100% = 27.5%

For the theoretical probability, take the quotient between the number of gold blocks and the total number:

T = 10/40 = 0.25

And multiply it by 100%

100%*0.25 = 25%

Then the correct option is The theoretical probability, P(gold), is 25%, and the experimental probability is 27.5%.

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Given that the brand of light bulb you use at home has an average life of 900 hours and a manufacturer claims that its new brand of bulbs, which cost the same as the brand you are using, has an average life of more than 900 hours.

Suppose 64 bulbs were tested based on the fact that 36 out of the 64 bulbs had life of more than 900 hours. Let us check if the new brand of bulbs should be purchased or not. Since the population standard deviation is unknown, we will use the t-test.

The null and alternative hypotheses are given as follows:H0: The average life of the new brand of bulbs is less than or equal to 900 hours (μ ≤ 900)Ha:

The average life of the new brand of bulbs is greater than 900 hours (μ > 900)The conclusion can be drawn using the p-value or the critical value approach. Using the critical value approach, with a significance level of 0.05 and degrees of freedom (df) of n-1 = 63, the critical value for one-tailed test is t=1.67. Let's calculate the test statistic using the formula:

t=(x¯-μ)/(s/√n)t=(x¯−μ)/(s/n
where
x¯ is the sample mean = (36/64) × 100% = 56.25%
μ is the hypothesized population mean = 900 hours
s is the sample standard deviation = 80 hours
n is the sample size = 64

t=(56.25-900)/(80/√64)

= -15.79
The calculated t-statistic is -15.79.

Since -15.79 < -1.67, we can reject the null hypothesis and conclude that the average life of the new brand of bulbs is greater than 900 hours.

Therefore, it would be wise to purchase the new brand of bulbs.The conclusion drawn above is more efficient than the one we previously made.

As the sample mean is found to be 920 hours, which is 20 hours more than the claimed life, the new brand of bulbs is more reliable and should be preferred for use. The sample mean is the unbiased estimator of the population mean.

The hypothesis test shows that the new brand of bulbs has an average life of more than 900 hours. As a result, it is recommended to use the new brand of bulbs. With a sample size of 64 bulbs, the average life of the new brand of bulbs was calculated to be 920 hours with a standard deviation of 80 hours. Therefore, the sample mean of 920 hours is more efficient than the previously stated sample size of 36 out of 64 bulbs having a life of more than 900 hours.

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Given:

The ellipse has center (2,2), focus (2,0), and vertex (2,5).

The equation of elllipse is given as,

a is the distance between vertex and center.

c is distance between focus and center.

It gives,

So, the equation of the ellipse is,

Answer: option b)

D

Step-by-step explanation:

he took 32 out then put it right back in

Answer:

D

Step-by-step explanation:

when you add 32 you get 224 but then when you add 32 you get 256 back.

The probability of rolling a 1 with this loaded die is 1/9.

Let's first assign probabilities to the possible outcomes of rolling the die:

There are 3 even numbers (2, 4, and 6) and 3 odd numbers (1, 3, and 5) on a standard six-sided die.

Since rolling an even number is twice as likely as rolling an odd number, we can assign probabilities as follows:
P(2) = P(4) = P(6) = 2x
P(1) = P(3) = P(5) = x
Now, we need to remember that the total probability of all outcomes must add up to 1:
P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = x + 2x + x + 2x + x + 2x = 9x
Since the total probability is 1, we can write the equation:
9x = 1.

Now, we can solve for x:
x = 1/9
Since we want the probability of rolling a 1, we just use the value of x:
P(1) = x = 1/9.

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Answer:

Step-by-step explanation:

all three angles must equal 180 bc theyre on a straight line

so add 76 + 63 to get 139

then subtract that from 180

180 - 139 = 41

so x = 41

hope this helps <3

Answer:

41

Step-by-step explanation:

Answer:

Step-by-step explanation:

Its D

Answer:

Two imaginary solutions.

Step-by-step explanation:

In order to simplify the equation, we square root both sides. As the argument (value in the root) is negative, and we know that the square root function's domain is only positive numbers, we would have two imaginary solutions.

This would be positive/negative \(3i\sqrt{5}\).

Another way to visualize this is by looking at the parabola's graph. Through algebraic manipulation, we know that the parabola is z^2 + 45. This parabola never crosses the x-axis. Therefore there are two solutions that are imaginary.

I hope this helps!

The exact values of a and b are \(5\) and \(5\sqrt{3}\)  respectively. Thus, option A is correct.

A right-angled triangle's sine function is defined as the ratio of the opposite side's length to the hypotenuse's length.

Sin α= Opposite/ Hypotenuse

In trigonometry, the cos is defined as the ratio of the length of the adjacent side to that of the longest side i.e. the hypotenuse

cos α = Adjacent Side/Hypotenuse

In ΔACB,

AB is the hypotenuse, AB=10

Sin 30=BC/AB

\(1/2 = a/10\)

Multiply both sides by 10:

\(a = 10 \times (1/2) = 5\)

Therefore, the value of a is 5.

Cos 30=AC/AB

\(\sqrt3/2 = b/10\)

Multiply both sides by 10:

\(b = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt3\)

Therefore, the value of b is 5√3.

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The exact value of a and b is 5 and \(5\sqrt{3}\) which means option a is correct.

The triangle is a right-angle triangle.

The hypotenuse is given = 10

By applying the trigonometric ratios we can find the value of a and b.

Apply sine formulae to find value a.

\(sin30 = \frac{opposite side of the angle 30}{hypotenuse} \\sin30 = \frac{a}{10} \\\frac{1}{2} = \frac{a}{10} \\2a = 10\\a = 5\)

Apply cosine formulae to find value b.

\(cos30 = \frac{adjacent side of the angle 30}{hypotenuse} \\cos30 = \frac{b}{10} \\\frac{\sqrt{3} }{2} = \frac{a}{10} \\2a = 10 *\sqrt{3} \\a = 5\sqrt{3}\)

Therefore the values of a and b are 5 and \(5\sqrt{3}\)

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Answer: the volume of the rubber ball when the radius equals five-sevenths feet.

Step-by-step explanation: On Edge!!!!!

The money in his bank account after the deposit is $12.09.

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PART 1:

To find the mean of the sampling distribution of sample means, we use the formula:

Mean of sampling distribution = μ

In this case, the given mean (μ) is 80. Therefore, the mean of the sampling distribution of sample means is also 80.

PART 2:

To find the standard deviation of the sampling distribution of sample means, we use the formula:

Standard deviation of sampling distribution = σ / √n

In this case, the given standard deviation (σ) is 9 and the sample size (n) is 25. Plugging these values into the formula:

Standard deviation of sampling distribution = 9 / √25

Calculating the square root and simplifying:

Standard deviation of sampling distribution = 9 / 5

Rounding to one decimal place, the standard deviation of the sampling distribution of sample means is approximately 1.8.

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PART 1: Find The Mean Of The Sampling Distribution Of Sample Means Using The Given Information. Round To One Decimal Place, If Necessary. Μ=80 And Σ=20; N=64 PART 2: Find The Standard Deviation Of The Sampling Distribution Of Sample Means Using The Given Information. Round To One Decimal Place, If Necessary. Μ=50 And Σ=9; N=25

PART 1: Find the mean of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary.

μ=80 and σ=20; n=64

PART 2:

Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary.

μ=50 and σ=9; n=25