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What geometric shape may describe a quadrilateral that has exactly two pairs of parallel sides and
no right angles?

By using the concept of testing of hypothesis, the null and alternative hypothesis is given by

\(H_0 :p_i = \frac{1}{5}\)

\(H_a : p_i \neq \frac{1}{5}\) for atleast one day

What is testing of hypothesis?

Suppose there is a hypothesis and there is a data at hand. Testing of Hypothesis determines whether a particular hypothesis is supported by the data at hand.

The null and alternative hypothesis can be written are as follows-

Null hypothesis: \(H_0\) : There is no difference in the number of swimmers from day to day.

Alternative hypothesis: \(H_a\) : There is a difference in the number of swimmers from day to day.

\(H_0 :p_i = \frac{1}{5}\)

\(H_a : p_i \neq \frac{1}{5}\) for atleast one day

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Complete Question

The manager of the city pool has scheduled extra lifeguards to be on staff for Saturdays. However, he suspects that Fridays may be more popular than the other weekdays as well. If so, he will hire extra lifeguards for Fridays, too. In order to test his theory that the daily number of swimmers varies on weekdays, he records the number of swimmers each day for the first week of summer. Test the manager’s theory at the 0.10 level of significance.

Swimmers at the City Pool

Monday Tuesday Wednesday Thursday Friday

Number 46 68 43 51 70

Step 1 of 4 :

State the null and alternative hypotheses in terms of the expected proportion for each day. Enter your answer as a fraction or a decimal rounded to six decimal places, if necessary.

H0: pi=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

Ha: There is a difference in the number of swimmers from day to day.

Therefore, the sum of the first 1234 terms of this sequence is 1234.

To find the sum of the first 1234 terms of the sequence consisting of 1's separated by blocks of 2's with n 2's in the nth block, we need to determine the number of blocks and the number of 1's in each block.

Let's examine the pattern of the sequence:

Block 1: 2's

= 1's

= 1 (1 2)

Block 2: 2's

= 2's

= 22 (1 22 1)

Block 3: 2's

= 3's

= 222 (1 222 1)

Block 4: 2's

= 4's

= 2222 (1 2222 1)

...

We observe that the number of 2's in each block is equal to the number of the block itself. So, in the nth block, there are n 2's.

Now, let's calculate the number of blocks required to reach the 1234th term:

To find the number of blocks, we need to determine the maximum block number before the 1234th term. We can calculate this by finding the sum of the series 1 + 2 + 3 + ... + n until the sum is greater than or equal to 1234.

The formula for the sum of the series 1 + 2 + 3 + ... + n is given by: S = (n/2)(n+1).

Let's solve this equation:

(n/2)(n+1) = 1234

\(n^2 + n - 2468 = 0\)

Using the quadratic formula:

n = (-1 + √(1 + 4*2468)) / 2

n ≈ 61.76

Since n must be a whole number, we take the ceiling of n, which gives us 62.

Therefore, there are 62 blocks in the sequence.

Next, let's calculate the number of 1's in each block:

In the nth block, there are n 2's. Since each 2 is separated by a 1, there are n + 1 terms in each block.

So, the number of 1's in each block is (n + 1) - n = 1.

Since there is always one 1 between two consecutive blocks, the total number of 1's in the sequence is equal to the number of blocks, which is 62.

Finally, let's calculate the sum of the first 1234 terms:

Each block has n + 1 terms, which gives us (n + 1) + (n + 1) + ... + (n + 1) (62 times).

Sum of (n + 1) repeated 62 times = 62(n + 1)

= 62 * 2

= 124.

In addition to the blocks, we have 1234 - 62 = 1172 remaining terms, which are all 1's.

So, the sum of the first 1234 terms is 62 + 1172 = 1234.

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If the horizontal distance between Tyler and the kite is 600 feet then the kite is 80 ft above the ground.

Pythagoras's Theorem is a fundamental result in Euclidean geometry that states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. This can be mathematically represented as:

\(c^2 = a^2 + b^2\)

Where c is the length of the hypotenuse, and a and b are the lengths of the legs of the triangle.

The theorem is named after the ancient Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof, although it is often argued that the theorem may have been known to the Babylonians and Indians over a thousand years earlier.

Pythagoras's theorem is widely used in mathematics and physics, especially in trigonometry and in the study of triangles and their properties, and it's also used to find the distance between two points in a two-dimensional space, for example, in cartesian coordinates.

Hypotenuse2 = Perpendicular2 + Base2

c2 = a2 + b2  

We apply the Pythagorean Theorem to determine the kite's height, h

the problem can solve if the kite is 60feet

\(h^2 = 100^2 - 60^2\\h^2 = 10000 - 360\\h^2 = 6,400\\h=\sqrt{6400} \\h=80\)

h =80 ft (we take the positive solution since the height can not be negative number)

The kite is 80 ft above the ground.

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According to the question we have  the 99% UCB on the mean time of the race is 223.

The formula for finding the upper confidence bound (UCB) is UCB = Mean + (Zα/2)(σ/√n), where Mean is the sample mean, Zα/2 is the z-score for the desired level of confidence, σ is the population standard deviation (which is not given, so we'll use the sample standard deviation instead), and n is the sample size.

We are given the sample of times as follows:137, 143, 153, 162, 168, 176, 190, 192, 196, 203, 218, 223, 236, 243, 252, 269, 271, 276, 283, 287.

We'll need to calculate the sample mean and standard deviation before we can find the UCB. Using a calculator, we get: mean ≈ 207.65s ≈ 48.41 Next, we'll use a table or calculator to find the z-score for a 99% confidence interval, which is Zα/2 = 2.576.

Now we can plug in the values we know to get the UCB:UCB = mean + (Zα/2)(σ/√n)UCB ≈ 207.65 + (2.576)(48.41/√20)UCB ≈ 223.02 .Therefore, the 99% UCB on the mean time of the race is 223.

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Answer: Graph A shows the correct probability distribution.

Step-by-step explanation:

The probability of the spinner landing on "A" is 1/2. Similarly, the probability of the spinner landing on "B" is 3/8. Therefore, the probability of the spinner landing on "C" is 1-1/2-3/8=1/8. So:

probability of landing on "A" is 1/2 = 0.5,

probability of landing on "B" is 3/8 = 0.375, and

probability of landing on "C" is 1/8 = 0.125.

Thus the correct probability distribution should be answer choice \(\boxed{\text{A}}.\)

The actual park had been designed to be 100 feet long,  the length of the park depicted in the blueprint is 5 inches.

Given details on the question are as follows:

As John is an architect used a scale factor

1 inch = 20 feet to design a site plan

The actual park has been designed to be 100 feet long.

The basic formula to find the scale factor of a figure is expressed as, Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape...(1)

let the length of the park decided in the blueprint be x.

The length of the park as depicted in blue print

Dimensions of the new shape  = x

Dimensions of the original shape. =100

putting value in equation number 1

1 / 20 = x/100

x= 100/20

x= 5 inch

The actual park had been designed to be 100 feet long,  the length of the park depicted in the blueprint is 5 inches

An inch is a unit of length in the British imperial and the United States customary systems of measurement. It is equal to 1/36 yard or 1/12 of a foot.

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Answer:

i think it B

Step-by-step explanation:

The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

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Write an example from daily life that uses rational numbers .

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Answer:

3/4 = 16/x. Step-by-step explanation: Set up the original ratio: 3:4 (a.k.a. 3/4 or 3 to 4) Because 16 correlates to red paint and 3 correlates to red paint the will be in the same location (as the numerator or denominator).. Also, the amount of blue paint is unknown so that is x.4 also represents blue paint, so 4 and x will also be on the same level (as the numerator of denominator).

Step-by-step explanation:

In the given question both the options D and E are necessary for the Central Limit Theorem to hold.

The Central Limit Theorem (CLT) is a fundamental concept in statistics that describes the behavior of sample means when the sample size is large. According to the CLT, the distribution of sample means approaches a normal distribution regardless of the shape of the original population distribution, given certain conditions.

Option A states that each individual measurement must be normally distributed. This is not a necessary condition for the CLT to hold. The original population distribution does not have to be normal; it can be any distribution shape.

Option B states that each individual measurement must be identically distributed. This is not a necessary condition for the CLT to hold. The measurements can have different distributions, as long as they satisfy the other conditions.

Option C states that each individual measurement must be independent of every other measurement. This is a necessary condition for the CLT to hold. The independence of measurements ensures that each observation contributes to the overall sample mean independently, without being influenced by other observations.

Therefore, options D and E are the correct choices. Both the independence of measurements (option C) and a sufficient sample size (option B) are necessary conditions for the Central Limit Theorem to hold.

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Answer:

1/2

Step-by-step explanation:

- find the least common denominatir for the two. (12)

-multiply 4 and 3

-multiply 6 and 2

- Add 1 and 5

-Keep the denominator.

-simplify if needed

Answer:

Step-by-step explanation:

answer 1 1/12 hours

Answer: Ummm   Thanks :D

Step-by-step explanation:

The midpoint of the segment with endpoints (9, 7, 3) and (5, 3, 2) is (7, 5, 2.5).

To find the distance between two points in three-dimensional space, we can use the formula:

Distance = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}\)

Let's calculate the distance between the points (9, 7, 3) and (5, 3, 2):

Distance = \(\sqrt{(5 - 9)^2 + (3 - 7)^2 + (2 - 3)^2}\)

= (\(\sqrt{(-4)^2 + (-4)^2 + (-1)^2}\)

= \(\sqrt{(16 + 16 + 1)}\)

= \(\sqrt{33}\)

≈ 5.7 (rounded to the nearest tenth)

Therefore, the distance between the points (9, 7, 3) and (5, 3, 2) is approximately 5.7.

To find the midpoint of the segment with these endpoints, we can use the midpoint formula:

Midpoint = \((x_1 + x_2) / 2, (y_1 + y_2) / 2, (z_1 + z_2) / 2)\)

Let's calculate the midpoint:

Midpoint = ((9 + 5) / 2, (7 + 3) / 2, (3 + 2) / 2)

= (14 / 2, 10 / 2, 5 / 2)

= (7, 5, 2.5)

Therefore, the midpoint of the segment with endpoints (9, 7, 3) and (5, 3, 2) is (7, 5, 2.5).

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Answer:

Step-by-step explanation:

Since Z is midpoint of SR and Y is midpoint of QR, so as per triangle midpoint theorem ZY is parallel to SQ and measures half of its value:

Correct answer choice is B

Answer:

the answer is B.12 ......

Answer: 36 squared < 26/4

Step-by-step explanation:

simplified 36 squared is 6 and 26/4 is 6.5

hope this helps

stay safe and stay awesome :)

Answer : The fifth term in the sequence is -2.

Step-by-step explanation :

As we are given that the expression to calculate the \(n^{th}\) term.

The expression is as follows:

\(a_n=2(-1)^n\)

where,

n is the number of term

Given:

n = 5

Now putting the value of n in the above expression, we get:

\(a_n=2(-1)^n\)

\(a_5=2(-1)^5\)

\(a_5=2\times (-1)\)

\(a_5=-2\)

Therefore, the fifth term in the sequence is -2.

Answer:

A. c ║d, Converse of the Corresponding Angles Postulate

Step-by-step explanation:

Line B (including numbers 1-8) can be ignored in the diagram.

When 2 angles are located on one side of the transversal (line a) and are also located below on the same side of one of the parallel lines (below lines c and d) they are called corresponding angles.

Hope that makes sense.

Aluminum's density is 2700 kg per cubic meter.

The number of molecules per unit volume is called density. The SI unit is kilograms per meter cube. The density is a scalar quantity. More density means more molecules present in a unit volume. Then the density is given as,

Density = Mass / Volume

A chunk of metal weighs 9.45 grams. 3.5 cubic centimeters is the volume.

Then the density of the aluminum is given as,

D = 9.45 / 3.5

D = 2.7 grams per cubic cm

D = 2700 kilograms per cubic meter

Aluminum's density is 2700 kg per cubic meter.

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The possible Values of x are x = 0 and x = 8/5.

To find the value of x in the given geometric progression, we need to determine the common ratio between consecutive terms.

Let the first term of the geometric progression be a, and let the common ratio be r. Then, we can write the second term as ar, the fourth term as ar^3, and the sixth term as ar^5.

Given that the second term is 2x - 4, the fourth term is 13x + 4, and the sixth term is 122x - 4, we can set up the following equations:

ar = 2x - 4    (equation 1)

ar^3 = 13x + 4    (equation 2)

ar^5 = 122x - 4    (equation 3)

To solve these equations, we can divide equation 2 by equation 1, and equation 3 by equation 2:

(ar^3) / (ar) = (13x + 4) / (2x - 4)

(ar^5) / (ar^3) = (122x - 4) / (13x + 4)

Simplifying these equations, we get:

r^2 = (13x + 4) / (2x - 4)    (equation 4)

r^2 = (122x - 4) / (13x + 4)    (equation 5)

Since the common ratio r is the same in both equations, we can equate the right sides of equations 4 and 5:

(13x + 4) / (2x - 4) = (122x - 4) / (13x + 4)

To solve this equation for x, we can cross-multiply and simplify:

(13x + 4)(13x + 4) = (2x - 4)(122x - 4)

169x^2 + 104x + 16 = 244x^2 - 16x - 1

Simplifying further, we get:

75x^2 - 120x = 0

15x(5x - 8) = 0

This equation is satisfied when either 15x = 0 or 5x - 8 = 0.

If 15x = 0, then x = 0.

If 5x - 8 = 0, then x = 8/5.

Therefore, the possible values of x are x = 0 and x = 8/5.

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The value of x in the given geometric progression is 2.

In a geometric progression, the ratio between each consecutive pair of terms is the same. Therefore, we can identify that the common ratio in our case is equal to the ratio (13x+4) / (2x-4). We can also find the ratio between the second term and the third term, which is (122x-4) / (13x+4). Since both these ratios must be the same, we can set them equal to each other and solve for x.

So, we end up with the equation: (13x + 4) / (2x - 4) = (122x - 4) / (13x + 4), simplifying this equation would give us x = 2.

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Answer:

C. Their slopes are equal.

Step-by-step explanation:

Given : If two lines are parallel.

To find  : which statement must be true.

Solution : We have given that If two lines are parallel.

We know that two parallel line have same slope

By rise over run :

Therefore, C. Their slopes are equal

Step-by-step explanation:

Answer:

Their slope is equal

Step-by-step explanation:

Their equal because they'll both be the same length, and I got it right

Tom drives 243 miles in 3 hours.

What is speed?

So, to find how many miles Tom can drive in 3 hours:

Tom drives 81/2 miles every 1/30 hour.

81/2 miles = 40.5 miles

1/30 hours = 30 minutes

So, in 30 minutes Tom drives 40.5 miles.

Then, in 1 hour Tom will drive 40.5 + 40.5 = 81 miles.

Miles Tom will drive in 3 hours = 81 × 3 = 243 miles.

Therefore, Tom drives 243 miles in 3 hours.

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Answer:

the correct answer is B. 2 & 4

Answer:

2 and 4

Step-by-step explanation:

This is because adjacent angles are next to each other.

Answer:

1. x=6 y=7

hope that helps!

Answer:

Yes

Step-by-step explanation:

7/21 -> Divide both sides by 7 which gets you 1/3

Answer:

i would say yes

my work :

so i did 21 times 1 which is 21.

Tben i did 3 times 7 which is also 21.

So in conclusion i would say yes but i can't guarantee that

Based on the given information and performing a one-sample t-test, the conclusion is that if the population mean (μ) is greater than 30.8294 km per litre, we reject the null hypothesis.

Given:

Sample mean (x') = 30 km per litre

Sample standard deviation (s) = 3.5 km per litre

Sample size (n) = 50

Significance level (α) = 0.05 (5%)

Null hypothesis \((H_0)\): The mean petrol consumption of the new car is equal to or higher than that of the existing car.

Alternative hypothesis \((H_1)\): The mean petrol consumption of the new car is lower than that of the existing car.

We'll calculate the test statistic (t-value) and compare it with the critical t-value.

The formula for the t-value is:

t = (x' - μ) / (s / √n)

where μ is the population mean (mean petrol consumption of the existing car).

First, we need to calculate the critical t-value from the t-distribution table. Since we have a significance level of 0.05 and (50 - 1) degrees of freedom, the critical t-value for a one-tailed test is approximately -1.677.

Now, let's calculate the t-value:

t = (30 - μ) / (3.5 / √50)

To reject the null hypothesis, the t-value should be less than the critical t-value.

Simplifying the equation:

t = (30 - μ) / (0.495)

To find the critical value, we compare it with the calculated t-value:

-1.677 > (30 - μ) / (0.495)

Multiplying both sides of the inequality by 0.495:

-0.8294 > 30 - μ

Rearranging the inequality:

μ > 30 + 0.8294

μ > 30.8294

Therefore, if the population mean (μ) is greater than 30.8294 km per litre, we reject the null hypothesis in favor of the alternative hypothesis, concluding that the mean petrol consumption of the new car is lower than that of the existing car.

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A large t-statistic indicates a greater difference between the sample means and provides stronger evidence for a significant difference between the populations.

The t-statistic is a measure of the difference between two sample means relative to the variability within the samples. When the population means are different, the difference between the sample means will tend to be larger, which will result in a larger numerator in the t-statistic formula. The larger the difference between the sample means, the greater the evidence for a difference between the populations. In contrast, if the population means are similar, the difference between the sample means will be smaller, resulting in a smaller numerator and a weaker test of significance.

The denominator of the t-statistic formula is the standard error of the mean, which measures the variability of sample means around the population mean. If the sample size is large enough, the standard error of the mean will be small, resulting in a smaller denominator and a larger t-statistic. Therefore, when the population means are different, a larger t-statistic would be expected due to a combination of a larger numerator and a smaller denominator.

In summary, If the population means are different, a large t-statistic would be expected.

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