if the area of the shaded region shown below is 120 square units, and the height of the line segment above the horizontal axis is 4 units, what is point a?

Answer:

I think that the answers would be

bc : 17.5

ab : 20.1

C : 90 °

A : 60 °

B : 30 °

perimeter : 47.6

area : 87.5

Hope it was helpful .

The Normal model is a good approximation for the sampling distribution.

a) According to the Central Limit Theorem, the theoretical mean and standard deviation for a sample size of 20 should be 0.05 and 0.02, respectively. For a sample size of 100, the theoretical mean and standard deviation should be 0.05 and 0.01, respectively.

b) The observed mean and standard deviation for a sample size of 20 was 0.052 and 0.021, respectively. For a sample size of 100, the observed mean and standard deviation was 0.051 and 0.012, respectively. These values are fairly close to the theoretical values.

c) Looking at the histograms in Exercise 1, I would be comfortable using the Normal model as an approximation for the sampling distribution at a sample size of 100.

d) The Success/Failure Condition states that the sample size should be large enough for the sampling distribution of the sample proportions to be approximately normal. Since I chose a sample size of 100, which satisfied the condition, I can be confident that the Normal model is a good approximation for the sampling distribution.

The sample size of 100 is large enough for the sampling distribution of the sample proportions to be approximately normal, and the observed mean and standard deviation is close to the theoretical values. Therefore, the Normal model is a good approximation for the sampling distribution.

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The sequence after subtracting n² from original sequence is :

132, 650 , 2070, 5112, 10712, 20022 .

A sequence is a collection of real and natural numbers where each term or list of elements is ordered in a specific order and repetitions are permitted.

Let n be the nth term of the sequence.

First term, a₁ = 12

n² = 12² = 144

Second term, a₂ = 26

n² = 26² = 676

Third term, a₃ = 46

n² = 46² =2116

Fourth term, a₄ = 72

n² = 72² = 5184

Fifth term, a₅ = 104

n² = 104² = 10816

Sixth term, a₆ = 142

n² = 142² = 20164

The new n² sequence =  144, 676, 2116 , 5184, 10816, 20164

By subtracting n² from n

We get ,  132, 650 , 2070, 5112, 10712, 20022 .

The new sequence = 132, 650 , 2070, 5112, 10712, 20022 .

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a)  The 10th percentile of pit depths is approximately 784.12 μm.

B)   The pit depth of 780 μm is approximately on the 7.64th percentile.

A) To find the 10th percentile of pit depths, we need to determine the value below which 10% of the pit depths lie.

We can use the standard normal distribution table or a statistical calculator to find the z-score associated with the 10th percentile. The z-score represents the number of standard deviations an observation is from the mean.

Using the standard normal distribution table, the z-score associated with the 10th percentile is approximately -1.28.

To find the corresponding pit depth, we can use the z-score formula:

z = (x - μ) / σ,

where x is the pit depth, μ is the mean, and σ is the standard deviation.

Rearranging the formula to solve for x:

x = z * σ + μ.

Substituting the values:

x = -1.28 * 29 + 822,

x ≈ 784.12.

Therefore, the 10th percentile of pit depths is approximately 784.12 μm.

B) To determine the percentile of a pit depth of 780 μm, we can use the z-score formula again:

z = (x - μ) / σ,

where x is the pit depth, μ is the mean, and σ is the standard deviation.

Substituting the values:

z = (780 - 822) / 29,

z ≈ -1.45.

Using the standard normal distribution table or a statistical calculator, we can find the percentile associated with the z-score of -1.45. The percentile is approximately 7.64%.

Therefore, the pit depth of 780 μm is approximately on the 7.64th percentile.

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Answer:

Rewrite the equation as y−6=35 .

y−6=35

Move all terms not containing y to the right side of the equation.

y=41

Step-by-step explanation:

The standard deviation is relatively small when the data are all concentrated close to the mean, exhibiting little variation or spread.

The standard deviation could be a degree of the changeability or spread of a set of information. It is calculated by finding the square root of the normal of the squared contrasts between each information point and the cruel(mean).

In other words, it tells us how much the information values are scattered around the mean.

When the information is all concentrated near the cruel(mean), it implies that the contrasts between each information point and the cruel are moderately little.

This comes about in a little while of squared contrasts, which in turn leads to a little standard deviation. On the other hand, when the information is more spread out, it implies that the contrasts between each information point and the cruel are bigger.

This comes about in a bigger entirety of squared contrasts, which in turn leads to a bigger standard deviation.

For case, let's consider two sets of information:

Set A and Set B.

Set A:

2, 3, 4, 5, 6

Set B:

1, 3, 5, 7, 9

Both sets have the same cruel(mean) (4.0), but Set A encompasses a littler standard deviation (1.4) than Set B (2.8).

This is because the information values in Set A are all moderately near to the cruel(mean), while the information values in Set B are more spread out.

Subsequently, we will say that the standard deviation is generally small when the information is all concentrated near the mean, showing a small variety or spread.

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(a) Matrix P = [1/2, 7/16; -1/2, 55/16] transforms coordinates between bases B and C. (b) Linear combination: (3, 12, 11) = 4a + 5b + 6c. (c) Representation: [(3, 12, 11)]B.

(a) The matrix P = [1/2, 7/16; -1/2, 55/16] transforms the coordinates of a vector in the basis C to the basis B.

(b) To express the vector (3, 12, 11) as a linear combination of a = (-1, 4, -2), b = (0, 4, 5), and c = (-4, 4, 2), we solve the equation (3, 12, 11) = x * a + y * b + z * c for the unknowns x, y, and z. The solution will be in the form of 4a + 5b + 6c.

(c) To represent the vector (3, 12, 11) in terms of the ordered basis B = {(-1, 4, -2), (0, 4, 5), (-4, 4, 2)}, we express it as a linear combination of the basis vectors. The answer should be in the form [(3, 12, 11)]B.

Please note that the provided matrix P is the correct answer for part (a), and parts (b) and (c) require further calculations based on the given information.

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Step-by-step explanation:

non saprei fome risolvere

The diameter of the circle with the circle equation (x+8)² + (y+4)² = 256 is 32 units

The equation of the circle is given as:

(x+8)² + (y+4)² = 256

As a general rule, a circle equation is represented as:

(x - a)² + (y - b)² = r²

Where r is the radius.

By comparing both equations, we have:

r² = 256

Take the square roots of both sides

r = 16

Multiply by 2 to get the diameter

d = 32

Hence, the diameter of the circle is 32 units

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Answer:

Step-by-step explanation:

8 sqaure feet

The maximum value of the data is given as follows:

75.

A box and whisker plot shows these five metrics from a data-set, listed and explained as follows:

The maximum value on the box plot is the end of the plot, hence it is of 75.

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Recall that a periodic function is a function that repeats itself at regular intervals, and the period is the distance between the repetitions.

Notice that the given graph repeats itself regularly, then it must be periodic.

From the given diagram we get that the period of the given graph is:

Answer: Option C.

Therefore, the apparent nth term of the expression is: aⁿ = 5n² - 3n - 2.

The given sequence is not an arithmetic or geometric sequence. However, we can notice that the sequence of differences between consecutive terms is an arithmetic sequence.

The sequence of differences is: 7, 19, 37, 61,...

To find the nth term of this sequence, we can use the formula for the nth term of an arithmetic sequence:

dn = a1 + (n-1) * d

where dn is the nth term of the sequence of differences, a1 is the first term of the sequence of differences, d is the common difference of the sequence of differences, and n is the index of the term we want to find.

So, we have:

dn = 7 + (n-1) * 12

Simplifying this expression, we get:

dn = 5n - 3

Now, we can use this formula to find the nth term of the original sequence. Let's call the nth term an:

an = an-1 + dn-1

where an-1 is the (n-1)th term of the original sequence and dn-1 is the (n-1)th term of the sequence of differences.

We know that a1 = 2 and d1 = 7, so we can use the above formula to find the next terms:

a2 = a1 + d1 = 2 + 7 = 9

a3 = a2 + d2 = 9 + 19 = 28

a4 = a3 + d3 = 28 + 37 = 65

a5 = a4 + d4 = 65 + 61 = 126

Therefore, the apparent nth term of the sequence is: aⁿ = 5n² - 3n - 2.

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Big O notation is a notation that can be used to compare the complexity of different algorithms. Big O notation describes the upper bound of the algorithm, which means the maximum amount of time it will take for the algorithm to solve a problem of size n.

An algorithm that has a Big O notation of O(n) is considered less complex than an algorithm with a Big O notation of O(n²) when it comes to solving problems of size n.

The QuickSort algorithm is a good example of Big O notation. The worst-case scenario for QuickSort is O(n²), which is not efficient. On the other hand, the best-case scenario for QuickSort is O(n log n), which is considered to be highly efficient.

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Answer:

Short and simple: 625

Answer:

45

Step-by-step explanation:

you can use m a th w ay to help you

To draw a conclusion based on the chi-square test for goodness of fit, we need to compare the calculated test statistic value (6.25) with the critical value from the chi-square distribution for the given significance level and degrees of freedom.

The chi-square test for goodness of fit compares the observed frequencies with the expected frequencies to determine if there is a significant difference between them. The degrees of freedom for this test are equal to the number of categories minus 1.

In this case, we need additional information about the number of categories or options the students had in the taste test (e.g., three brands of cola). Please provide the number of categories or the degrees of freedom so that I can assist you in drawing a conclusion based on the chi-square test statistic.

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Edna should leave at 2:07 PM in order to arrive at Jake's party by 2:30 PM

To determine the time Edna should leave, we need to subtract the travel time from the desired arrival time.

If Edna needs to be at Jake's party at 2:30 PM and it takes her 23 minutes to drive there, she should leave 23 minutes before 2:30 PM.

To calculate the departure time, we subtract 23 minutes from 2:30 PM:

2:30 PM - 23 minutes = 2:07 PM

Therefore, Edna should leave at 2:07 PM in order to arrive at Jake's party by 2:30 PM

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Answer:

Quadratic Trinomial

Step-by-step explanation:

Hello there!

quadratic trinomial equations look like -  \(x^2+bx+c\)

given formula \(n^2-7n+21\) which is in the form of a quadratic trinomial

a quadratic trinomial consist of a constant, a  variable to the power of 2,  and a variable

Reasons why its not the other answer choices:

Linear equations do not have variables with powers therefore we can eliminate answer choice linear trinomial and linear polynomial

\(n^2-7n+21\) is not a quadratic polynomial because a quadratic polynomial consists of a = 0

This is what a quadratic polynomial looks like

\(ax^2+bx+c=0\)

so we can conclude that \(x^2+bx+c\) is an example of a quadratic trinomial

Answer:yes

Step-by-step explanation: why not whatcha need

Step-by-step explanation:

Answer:

1. How many points was each part worth?

 - 12 points

2. How many questions did part A have?

 - 2 questions

3. How many questions did Part B have?

 - 3 questions

Step-by-step explanation:

We can set up our equation like this:

6x = 4y

In the above equation, x is representing the number of true/false questions and y is representing the nymber of multiple choice questions.

Now, the problem tells us that they want the least number of points possible so we know we need to use low numbers.

Since 6 is higher than 4, it's easier to go off of there.

6 x 1 = 6                        4 is too big to go into 6 so we will move on.

6 x 2 = 12                      4 goes into 12 3 times so we can use this.

Now that we've figured this out, we can put it in our equation:

6(2) = 4(3)

In the above equation, we can see that I've put 2 in for x because we multiplied 6 by 2 to get 12. I also put 3 in for y because we multiplied 4 by 3.

Now we can start with the questions:

1. How many points was each part worth?

Each part was worth 12 points because we can multiply 6 by 2 and get 12 or 4 by 3 and get the same thing

2. How many questions did part A have?

Part A had 2 questions because this is what x was when we multiplied by 6

3. How many questions did Part B have?

Part B had 3 questions because this is what y was when we multiplied by 4

Hope this helps!!

Answer:

x=-8, x=0

Step-by-step explanation:

For the sample of soil given a) the porosity is 100.4%; b) the specific yield is 12.2%; c) the specific retention is 14.6%; d) the void ratio is 0.5342; e) the initial moisture content is 2.3%; and f) the initial degree of saturation is 41.97%.

a) The porosity of soil can be defined as the ratio of the void space in the soil to the total volume of the soil.

The total volume of the soil = Initial volume of soil = 100 c.m³

Weight of water added to the soil = 234.6 g – 220 g = 14.6 g

Volume of water added to the soil = 14.6 c.m³

Volume of soil occupied by water = Weight of water added to the soil / Density of water = 14.6 / 1 = 14.6 c.m³

Porosity = Void volume / Total volume of soil

Void volume = Volume of water added to the soil + Volume of voids in the soil

Void volume = 14.6 + (Initial volume of soil – Volume of soil occupied by water) = 14.6 + (100 – 14.6) = 100.4 c.m³

Porosity = 100.4 / 100 = 1.004 or 100.4%

Therefore, the porosity of soil is 100.4%.

b) Specific yield can be defined as the ratio of the volume of water that can be removed from the soil due to the gravitational forces to the total volume of the soil.

Specific yield = Volume of water removed / Total volume of soil

Initially, the weight of the oven dried soil is 220 g. After allowing it to drain by gravity, the weight of soil is 222.4 g. Therefore, the weight of water that can be removed by gravity from the soil = 234.6 g – 222.4 g = 12.2 g

Volume of water that can be removed by gravity from the soil = 12.2 c.m³

Specific yield = 12.2 / 100 = 0.122 or 12.2%

Therefore, the specific yield of soil is 12.2%.

c) Specific retention can be defined as the ratio of the volume of water retained by the soil due to the capillary forces to the total volume of the soil.

Specific retention = Volume of water retained / Total volume of soil

Initially, the weight of the oven dried soil is 220 g. After adding water to the soil, the weight of soil is 234.6 g. Therefore, the weight of water retained by the soil = 234.6 g – 220 g = 14.6 g

Volume of water retained by the soil = 14.6 c.m³

Specific retention = 14.6 / 100 = 0.146 or 14.6%

Therefore, the specific retention of soil is 14.6%.

d) Void ratio can be defined as the ratio of the volume of voids in the soil to the volume of solids in the soil.

Void ratio = Volume of voids / Volume of solids

Initially, the weight of the oven dried soil is 220 g. The density of solids in the soil can be calculated as,

Density of soil solids = Weight of oven dried soil / Volume of solids

Density of soil solids = 220 / (100 – (14.6 / 1)) = 2.384 g/c.m³

Volume of voids in the soil = (Density of soil solids / Density of water) × Volume of water added

Volume of voids in the soil = (2.384 / 1) × 14.6 = 34.8256 c.m³

Volume of solids in the soil = Initial volume of soil – Volume of voids in the soil

Volume of solids in the soil = 100 – 34.8256 = 65.1744 c.m³

Void ratio = Volume of voids / Volume of solids

Void ratio = 34.8256 / 65.1744 = 0.5342

Therefore, the void ratio of soil is 0.5342.

e) Initial moisture content can be defined as the ratio of the weight of water in the soil to the weight of oven dried soil.

Initial moisture content = Weight of water / Weight of oven dried soil

Initial weight of soil = 225.1 g

Weight of oven dried soil = 220 g

Therefore, the weight of water in the soil initially = 225.1 – 220 = 5.1 g

Initial moisture content = 5.1 / 220 = 0.023 or 2.3%

Therefore, the initial moisture content of soil is 2.3%.

f) Initial degree of saturation can be defined as the ratio of the volume of water in the soil to the volume of voids in the soil.

Initial degree of saturation = Volume of water / Volume of voids

Volume of water = Weight of water / Density of water

Volume of water = 14.6 / 1 = 14.6 c.m³

Volume of voids in the soil = 34.8256 c.m³

Initial degree of saturation = 14.6 / 34.8256 = 0.4197 or 41.97%

Therefore, the initial degree of saturation of soil is 41.97%.

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Answer:

2xy(8x + 5)

Step-by-step explanation:

16x²y + 10xy ← factor out 2xy from each term

= 2xy(8x + 5)

The result of the test is that the assumption that the two population variances are equal is rejected at the 5% significance level, since the p-value is less than 0.05.

The first step is to set up the null hypothesis, which is that the population variances are equal for groups with and without a moderator. Then, we can use an F-test to compare the variances of the two groups. We calculate the F-statistic and its associated p-value. If the p-value is less than 0.05, then we reject the null hypothesis that the population variances are equal at the 5% significance level. In this case, the p-value is less than 0.05, so we reject the null hypothesis and conclude that the population variance is higher for groups with a moderator.The calculation of the F-statistic is as follows: F = (σ2_moderator) / (σ2_no moderator) = (24.4^2)/(20.2^2) = 1.49. The associated p-value is calculated using the F-distribution table, and is less than 0.05.

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Answer: The cost of 15 meals at $7.25 per meal is:

15 x $7.25 = $108.75

To find the cost including the 5% sales tax, we need to add 5% of the cost to the cost:

5% of $108.75 = 0.05 x $108.75 = $5.44

So the total cost, including the sales tax, is:

$108.75 + $5.44 = $114.19

Therefore, the coach's total cost for 15 meals, including sales tax, will be $114.19.

The Distance of pluto in AU is 39.2.

The astronomical unit ( AU) is a unit of length, roughly the distance from Earth to the Sun and equal to 150 million kilometres (93 million miles) or 8.3 light minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits the Sun, from a maximum to a minimum and back again once each year.

1 Astronomical unit (AU) is nearly equals to 93,000,000 miles.

Given that formula for converting any distance d in miles to AU is AU =d/93,000,000.

So,

\(Distance\ of \ pluto \ from \ sun = d = 3,647,720,000\\distance \ d \ in \ miles \ to \ AU \ is \ AU =\frac{d}{93000000} \\\\distance \ pluto \ in \ miles \ to \ AU \ is \ AU =\frac{3,647,720,000}{93000000} \\distance \ pluto \ in \ miles \ to \ AU \ is \ AU = 39.2\)

Therefore, distance of pluto from sun is 39.2 AU

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The Distance of pluto in AU is 39.2.

The astronomical unit ( AU) is a unit of length, roughly the distance from Earth to the Sun and equal to 150 million kilometres (93 million miles) or 8.3 light minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits the Sun, from a maximum to a minimum and back again once each year.

1 Astronomical unit (AU) is nearly equals to 93,000,000 miles.

Given that formula for converting any distance d in miles to AU is AU =d/93,000,000.

So,

Distance of pluto from sun in miles = d = 3,647,720,000

distance d in miles to AU is AU =\(\frac{ d}{93,000,000}\)

distance pluto in miles to AU is AU = \(\frac{3,647,720,000 }{93,000,000}\)

distance of pluto in miles to AU is AU =39.2

Therefore, distance of pluto from sun is 39.2 AU

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We are given the relationship:

a. It's required to find a relationship where r is a function of t. To do that, we need to solve the equation for r.

Subtract 4t:

Divide by 7:

b. We use the function found in part a and evaluate it for t=-7:

Thus, f(-7) = 6

c. Solve f(t) = 18

Again, we use the function from part a and solve the equation:

Multiplying by 7:

Subtract 14 and then divide by -4:

t = -28

The possible values for x, y, and z that cause the expression xy' to evaluate to 1 are (1,0,0), (1,0,1), (1,1,0), and (1,1,1).

In Boolean algebra, literals refer to the basic elements or variables that are used to represent binary values, i.e., 0 or 1.

The expression xy' evaluates to 1 if x = 1 and y = 0. To see why, we can substitute these values into the expression: xy' = 10' = 11 = 1.

Therefore, the possible values for x, y, and z that cause the expression xy' to evaluate to 1 are (1,0,0), (1,0,1), (1,1,0), and (1,1,1).

However, xy' is not a minterm for a function with input variables x, y, and z, because there is more than one setting of the input variables that causes the expression xy' to evaluate to 1.

Specifically, both (1,0,0) and (1,1,0) cause xy' to evaluate to 1.

A minterm, as defined, must have exactly one setting of the input variables that causes the minterm to evaluate to 1.

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