5. a gardener is mowing a 20 by 40 yard rectangular pasture using a diagonal pattern. he mows from one corner of the pasture to the corner diagonally opposite. what is the length of this pass with the mower? give your answer in simplified form. recall from the pythagorean theorem that, for a right triangle, the square of the length of the diagonal is equal to the sum of the squares of the lengths of the sides

The sequence A_n is defined as (-1)^n divided by 8 times the square root of n. It alternates between positive and negative values and decreases as n increases.

The sequence A_n is given by the formula A_n = (-1)^n / (8 √n). Let's break down the formula to understand its properties.

First, (-1)^n alternates between 1 and -1 as n increases. When n is even, (-1)^n equals 1, and when n is odd, (-1)^n equals -1. This alternation leads to the sequence alternating between positive and negative values.

Second, the denominator 8 √n represents the square root of n multiplied by 8. As n increases, the denominator also increases, resulting in smaller values for A_n.

Combining these properties, the sequence A_n alternates between positive and negative values while decreasing in magnitude as n increases. As n approaches infinity, the sequence approaches zero, but it never reaches zero since it alternates between positive and negative values.

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Answer: experiment

Step-by-step explanation:

A course of perception that has an unsure result is alluded to as an experiment.

The study of mathematical objects by computing in order to discover their properties and patterns is known as experimental mathematics. It has been described as "that mathematical theory that concerns itself ultimately with both the convention and transmission of insights within the mathematical neighborhood through the use of experimental investigation of conjectures and also more irregular beliefs and just a careful analysis of the information acquired in this endeavor (in either the Galilean, Baconian, Aristotelian or Kantian sense).

The nineteenth century saw the reemergence of experimental mathematical concepts as a distinct field of study as the range of calculations that could be performed was greatly expanded by the development of the electronic computer, which could perform calculations at speeds and with levels of precision that were unimaginable to earlier generations of mathematicians.

A course of perception that has an unsure result is alluded to as an experiment.

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Answer:

A. 70

Step-by-step explanation:

a triangle has a sum of 180 degrees so you have to add 75 and 35 and you will get 110 and then you subtract 110 for 180 and you get 70

Answer: 5.6 miles per hour

Step-by-step explanation:

Answer:

is it trigonometry...?

Answer:

Step-by-step explanation:

Answer: 60.80

Step-by-step explanation:

you saved 19.20

The correct answer is  9.591, 34.170. (option-d)

To find the critical \(x^2\) values for a sample of size 21 and a 95% confidence level, we need to use a chi-square distribution table with 20 degrees of freedom (df = n-1, where n is the sample size).

From the table, we can find the values of chi-square that correspond to a 95% level of confidence. The critical values are the chi-square values that include 95% of the area under the curve, with 2.5% in each tail.

According to the chi-square distribution table, the critical \(x^2\) values for a 95% confidence level with 20 degrees of freedom are 9.591 and 34.170.

Answer A, B, and C are incorrect, as they do not match the critical values for a 95% confidence level with 20 degrees of freedom. It's important to note that the critical values for chi-square increase as the degrees of freedom increase, so it's crucial to use the correct degrees of freedom when looking up these values in a distribution table.(option-d)

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The final grade you will have using a mixture word problem is 85%.

The mixture word method or mixture word problem is a method in mathematics to solve the problem when creating a mixture of two or more different things. This method will solve the problem of determining the quantity of mixture result.

In the question, we will mix two grades. So,

= (current grade * current worth grade) + (final exam grade * final exam worth grade)

= (85% * (100%-10%)) + (85% * 10%)

= 76.5% + 8.5%

= 85%

Thus, your final grade doesn't change if you get 85% on a final exam.

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Answer:

Step-by-step explanation:

Right Triangle Similarity

Acute Angle Similarity

If one of the acute angles of a right triangle is congruent to an acute angle of another right triangle, then by Angle-Angle Similarity the triangles are similar.

In the figure, ∠M≅∠Y , since both are right angles, and ∠N≅∠Z .

So, ΔLMN∼ΔXYZ .

Leg-Leg Similarity

If the lengths of the corresponding legs of two right triangles are proportional, then by Side-Angle-Side Similarity the triangles are similar.

In the figure,  ABPQ=BCQR .

So, ΔABC∼ΔPQR .

Hypotenuse-Leg Similarity

If the lengths of the hypotenuse and a leg of a right triangle are proportional to the corresponding parts of another right triangle, then the triangles are similar. (You can prove this by using the Pythagorean Theorem to show that the third pair of sides is also proportional.)

In the figure, DFST=DESR .

So, ΔDEF∼ΔSRT .

Taking Leg-Leg Similarity and Hypotenus-Leg Similarity together, we can say that if any two sides of a right triangle are proportional to the corresponding sides of another right triangle, then the triangles are similar.

a. A formula relating total catering cost for a wedding to the number of guests expected is C = 25n + 120

b. The complete table will be

Number of guests| 20   40     60    80    100

Catering cost ($)   |620 1120 1620 2120 2620

c. The graph shown below

d. The cost of catering for a wedding with 110 expected guests is  $3120.

e. If you can only afford to spend $2000 for the wedding feast you can invite a maximum of 75 guests (including yourself and family)

(a) Let n be the number of guests expected, and let C be the total catering cost. Then the formula relating total catering cost for a wedding to the number of guests expected is:

C = 25n + 120

(b) Using the formula from part (a), we can complete the table of values as follows:

Number of guests 20 40 60 80 100

Catering cost ($) 620 1120 1620 2120 2620

(d) Using the trend line, we can estimate the cost of catering for a wedding with 110 expected guests to be approximately $3120.

(e) Setting the catering cost equal to $2000 and solving for n, we get:

25n + 120 = 2000

25n = 1880

n = 75.2

Therefore, you can invite a maximum of 75 guests (including yourself and family) if you can only afford to spend $2000 for the wedding feast.

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To see the graph of y = 2x−5 with the points (5/2,0) and (0,−5)

Now, According to the question:

y = 2x - 5 is a line. Determine the two points that this line intersects with the axes then connect these points to graph it.

y = 2x - 5

Take y = 0

then, solve for the abscissa

y = 2x - 5

0 = 2x - 5

2x = 5

x = 5/2

We now have the point (5/2 , 0)

Take x = 0

then, solve for the ordinate

y = 2x - 5

y = 0 -5

y = -5

We now have the point (0 , -5)

We now simply draw a line passing thru the two points (5/2 , 0) and

(0 ,-5)

Kindly see the graph of y = 2x−5 with the points (5/2,0) and (0,−5)

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Answer: d

Step-by-step explanation:

The 75 degree angle and angle d are same-side interior angles, meaning that if they were supplementary, the lines would be parallel by the converse of the same-side interior angles theorem.

g(h(0)):

answer: g[h(0)]=3

(a) There are 512 subsets of a.

(b) 126 subsets of a contain exactly 5 elements.

(a) To find the number of subsets of a, we can use the formula \(2^n\), where n is the number of elements in the set. In this case, n = 9. So, the number of subsets of a is \(2^9\) = 512. This is because each element in the set can either be included or excluded from a subset, giving us a total of 2 choices for each element. Multiplying these choices for all 9 elements gives us the total number of possible subsets.
(b) To find the number of subsets of a that contain exactly 5 elements, we need to choose 5 elements out of the 9 available elements. This can be done using the combination formula, which is n choose k = n! / (k!(n-k)!), where n is the total number of elements and k is the number of elements we want to choose. So, in this case, the number of subsets of a that contain exactly 5 elements is 9 choose 5, which is 9! / (5!(9-5)!) = 126.

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The probability that the number's units digit will be less than 5 is 0.5 that it is equal to 1/2.

Probability is a branch of mathematics concerned with numerical descriptions of how likely an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

There are 10 possible digits, 0, 1, 2, ... 9 that make up the 5-digit number made up of integral values.

There are 5 digits that are less than 5 which are 0, 1, 2, 3, and 4 so the probability will be found by taking only those nubers which have unit's place less than 5,

By probability formula , Probability= no. of favourable outcomes/total no. of outcomes

So probability will be found that will be equal to 5/10, or 1/2

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By using the simulated results and the law of large numbers, we can estimate that the probability of answering exactly 15 questions correct on a 30-question exam with a 35% chance of getting each question correct is approximately 7.2%.

Based on the simulated results, we can estimate the probability of answering exactly 15 questions correct on a 30-question exam with a 35% chance of getting each question correct. To do this, we first need to look at the histogram or table of the simulated results to see how many of the 1000 exams scored 15.

If we look at the histogram or table, we can see that there were 72 out of 1000 exams that scored exactly 15. This means that the proportion of exams that scored 15 is 72/1000 or 0.072.

Using the law of large numbers, we can estimate that this proportion is the same as the probability of answering exactly 15 questions correctly on a 30-question exam with a 35% chance of getting each question correct. Therefore, the estimated probability of answering exactly 15 questions correct is 0.072 or 7.2%.

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Answer:

u = 92 degrees

v = 44 degrees

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer/how I got this answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

Answer:

U=92 i am not sure about V sorry

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

(2/3)×5

(2/3)×(5/1)

multiply numerator by numerator, denominator by denominator, and you get

10/3 or 3 and 1/3.

Answer:

5

Step-by-step explanation:

q = 6

r = 19

4q^2

= 4 x q^2

= 4 x 6^2

= 4 x 6 x 6

= 144

qr

= q x r

= 6 x 19

= 114

qr + 25

= 114 + 25

= 139

4q^2 - ( qr + 25 )

= 144 - 139

= 5

Probability is a measure of the likelihood of an event occurring.

A. To find how many foreclosures to expect, we can use the expected value formula: E(X) = np, where X is the number of foreclosures, n is the number of loans, and p is the foreclosure rate. Substituting the given values, we have E(X) = (300)(1/136) ≈ 2.21. Therefore, we can expect about 2 foreclosures last month.

B. To find the probability of exactly two foreclosures, we can use the Poisson distribution with parameter λ = E(X) = 2.21. The probability mass function of the Poisson distribution is given by P(X = k) = (e^(-λ) * λ^k) / k!, where k is the number of foreclosures. Substituting k = 2 and λ = 2.21, we have P(X = 2) = (e^(-2.21) * 2.21^2) / 2! ≈ 0.244. Therefore, the probability of exactly two foreclosures is about 0.244.

C. To find the probability of at least one foreclosure, we can use the complement rule: P(X ≥ 1) = 1 - P(X = 0). Since the foreclosure rate is one out of every 136 loans, the probability of not having a foreclosure in a single loan is (135/136). Therefore, the probability of not having a foreclosure in 300 loans is (135/136)^300 ≈ 0.427. Substituting this value into the complement rule, we have P(X ≥ 1) = 1 - 0.427 ≈ 0.573. Therefore, the probability of at least one foreclosure is about 0.573.

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Answer:

9/2 or 4.5

Step-by-step explanation:

3/4x=6

4x=6x3

x=18/4

x=9/2 or 4.5

The average angular velocity during the dive is 10.78 rad/sec.

Given,

displacement of the diver = 10.4m

as the diver falls freely then the acceleration will be g=9.8 \(m/s^2\)

To find average angular velocity during dive use formula,

\(\omega=\frac{\theta}{t}\)

where, θ=angular displacement and t= time taken to reach water

the diver makes 2.5 revolutions, here 1 revolution is 2π radians then total angular displacement is

θ=2.5* 2π=15.7 radian

To find time taken, use formula \(s=ut+\frac{1}{2}gt^2\)

here u=initial velocity=0

s=displacement of diver=10.4m

\(10.4=0+\frac{1}{2}9.8t^2\\\\10.4=4.9t^2\\\\2.122=t^2\\\\t=1.456 s\)

angular velocity, \(\omega=\frac{15.7}{1.456}=10.78\ rad/sec\)

Thus, the average angular velocity during the dive is 10.78 rad/sec.

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The percent error in Jessica's calculation is 4.17%.

To calculate the percent error in Jessica's calculation, we can use the formula:

Percent Error = (|Measured Value - Actual Value| / Actual Value) * 100

Given that Jessica's measured value was 125 seconds and the actual value was 120 seconds, we can substitute these values into the formula:

Percent Error = (|125 - 120| / 120) * 100

Simplifying further:

Percent Error = (5 / 120) * 100

Percent Error = 0.0417 * 100

Percent Error = 4.17%

This means that Jessica's recorded time of 125 seconds differs from the actual time of 120 seconds by approximately 4.17% in relative terms. The positive sign indicates that Jessica's recorded time was greater than the actual time.

Percent error is a way to quantify the discrepancy between a measured value and the true value. It provides a measure of the accuracy of a measurement or calculation, allowing us to understand the degree of error or deviation involved.

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Answer:

answer is d

Step-by-step explanation:

if u do the math the nearest u can get is 0.80x30=24

The time required for the two stocks of Jones Corporation and Overton Company to be nearly equal in value, is 30 months.

A stock is the portion of ownership of a firm, corporation etc which gives the security of asset of the property.

Stock for the Jones Corporation starts with a value of $39.63 and gains $0.30 in value per month.

Stock for the Overton Company starts with a value of $24.45 and gains $0.80 in value per month.

Let after the x month's these two stocks nearly equal in value.

\(39.63+0.30\times x=24.45 +0.80 \times x\)

Solve it further,

\(0.80 \times x-0.30\times x=39.63-24.45 \\0.50 \times x=15.18\\x=\dfrac{15.81}{0.50}\\x=30.36\)

Hence, the time required for the two stocks of Jones Corporation and Overton Company to be nearly equal in value, is 30 months.

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Answer:

48

Step-by-step explanation:

91+41+?=180

91+41=132

180-132=48

The distribution for X is a negative binomial distribution, denoted as nb(x;6, 188​), with parameters r = 6 (number of successes), p = 8/18 (probability of success in each trial).

To compute the probabilities:

P(X = 2): nb(2;6, 8/18)

P(X ≤ 2): nb(0;6, 8/18) + nb(1;6, 8/18) + nb(2;6, 8/18)

P(X ≥ 2): 1 - P(X < 2) = 1 - P(X ≤ 1)

To calculate the mean value and standard deviation of X:

Mean (μ) = r * (1 - p) / p

Standard Deviation (σ) = sqrt(r * (1 - p) / (p^2))

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Answer:

1 1/4 or 5/4

Step-by-step explanation:

one is simplified just in case

Answer:

1/1024

Step-by-step explanation:

If you want the steps, just ask and ill give them in comments :)

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