A sample of n sludge specimens is selected and the pH
of each one is determined. The one-sample t test will
then be used to see if there is compelling evidence for
concluding that true average pH is less than 7.0. What
conclusion is appropriate in each of the following
situations?
a. n = 6, t = 22.3, a = .05
b. n = 15, t = 23.1, a = .01
c. n = 12, t = 21.3, a = .05
d. n = 6, t = .7, a = .05
e. n = 6, x = 6.68, s/\sqrt{n}= .0820

Answer:

Step-by-step explanation:

Part A: Based on the given graph, we can observe that as the temperature of the city increases, the number of people at the swimming pool generally tends to increase as well. This suggests a positive correlation between temperature and the pool's population. In other words, when it gets hotter, more people are likely to visit the swimming pool. The relationship is not strictly linear, but it shows a general trend of increasing pool population with increasing temperature.

Part B: To determine the line of best fit, we can calculate the approximate slope and y-intercept using the given data points. Let's select two points from the data, such as (2.5, 1) and (12, 12):

Slope (m) = (change in y) / (change in x)

= (12 - 1) / (12 - 2.5)

= 11 / 9.5

≈ 1.16

To find the y-intercept (b), we can choose one of the points and substitute the values into the slope-intercept form (y = mx + b). Let's use the point (2.5, 1):

1 = 1.16 * 2.5 + b

1 = 2.9 + b

b ≈ -1.9

Therefore, the approximate slope of the line of best fit is 1.16, and the approximate y-intercept is -1.9.

to factor we must recognize the elements in common

the r exist on both terms, so we can divide by r on each term to factor

The diameter of the cups used for a slushy stand uses dome shaped lids is 4 inches.

A slushy stand uses dome shaped lids

Lids resemble the shape of a hemisphere

Volume of lid as 16/3 pi cubic inches

Therefore, volume of hemisphere is 16/3 pi cubic inches as lid resemble shape of hemisphere,

Volume of hemisphere is 2/3πr³

V =  2/3πr³

16/3π = 2/3πr³

8 = r³

r = 2

So the radius of the lids is 2

Diameter  = 2r

d = 2x2

D = 4 inches.

Therefore, the diameter of the cups used of lids is 4 inches.

The area that a hemisphere takes up is referred to as its volume. The volume of a thing determines how much space it takes up. A hemisphere is a half-sphere in three dimensions, such as bowls, headphones, an igloo, domes in buildings, etc.

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Given the values that we have here for the large sizes and the family size of cereal the one that has the lowest price per ounce is that of the Large size at $0.21 per ounce

For the family size

We would first have to divide 5.34 by 24

= 5.34 / 24

= 0.22 per dollar

For the large size we have

15 ounces for $3.14

= 3.14 / 15

= 0.21 dollars

Hence we can see that the size of the cereal that is the lowest price per ounce is given as Large size at $0.21 per ounce

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9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Starting 3 feet from the motion detector, you will be at the point (0, 3) on the graph.

A normal walking speed is about 3 mph, or about 4.4 feet per second. So, walking slowly may be something less than 2 feet per second. In the attached graph, we show a walking speed of about 4 feet in 10 seconds, a really slow speed. Since you're walking away, the distance is increasing with time.

Answer:

D. (2,2) and (8,2)

Step-by-step explanation:

Distance (d) = √(8 - 2)2 + (2 - 2)2

= √(6)2 + (0)2

= √36

= 6

Answer:

option D

Step-by-step explanation:

(-9, 1) and (3, 1) these points are 12 units apart

- looking at change in x value

- 9 to 0 is 9

- 3 to 0 is 3

- visual representation below

(6, 2) and (6, 10) these points are 8 units apart

- looking at change in y value

 2 + x = 10

-2 + 2 + x = 10 - 2

 x = 8

- visual representation below

(-7, 8) and (-3, 8) these points are 4 units apart

- looking at change in x value

-7 + x = -3

+7 - 7 + x = -3 + 7

x = 4

- visual representation below

(2, 2) and (8, 2) these points are 6 units apart

- looking at change in x value

 2 + x = 8

- 2 + 2 + x = 8 - 2

x = 6

- visual representation below

Answer:

1) 3(d+5e)

2) 20a

Step-by-step explanation:

The ratio of A to B is approximately 0.7826, the ratio of B to A is approximately 1.2778, and A is approximately 78.26% of B.

a. The ratio of A to B can be found by dividing the value of A (1.8 million) by the value of B (2.3 million):

A/B = 1.8 million / 2.3 million = 0.7826

Therefore, the ratio of A to B is approximately 0.7826.

b. The ratio of B to A can be found by dividing the value of B (2.3 million) by the value of A (1.8 million):

B/A = 2.3 million / 1.8 million = 1.2778

Therefore, the ratio of B to A is approximately 1.2778.

c. To complete the sentence "A is percent of B," we need to find the percentage that A represents in relation to B. We can calculate this by dividing A by B and multiplying by 100:

(A/B) * 100 = (1.8 million / 2.3 million) * 100 = 78.26%

Therefore, A is approximately 78.26% of B.

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Answer:

3,14

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

This is a reflection transformation because the shape of the polygon is identical, but flipped over the vertical line of reflection.

A polygon is a two-dimensional shape that consists of a closed line made up of a series of straight-line segments. The number of sides a polygon has determines its name. Common names for polygon shapes include triangle, square, pentagon, hexagon, and octagon. Polygons are used in everyday life, such as in architecture, engineering, and design. They are also used in mathematics, where they are studied for their properties and formulas. Polygons can be regular or irregular, convex or concave, and each has its own unique characteristics.

The coordinates of the vertices of the original shape are reflected across this line to obtain the coordinates of the vertices of the new shape. This type of transformation is also known as a line reflection.

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Based on the image provided, it appears that the polygon was reflected across a line of symmetry to produce the image shown. Therefore, the correct answer is A. Reflection.

what is a polygon?

A polygon is a two-dimensional geometric shape that is made up of straight lines connecting a sequence of points, which are called vertices. A polygon is a closed shape, meaning that the last vertex is connected to the first vertex to form a complete boundary.

A reflection is a transformation that involves "flipping" an object across a line of symmetry. In the image provided, the polygon appears to have been reflected across a vertical line of symmetry, which means that each point on one side of the line is reflected across the line to a corresponding point on the other side. The result is a mirror image of the original polygon.

A rotation, on the other hand, involves rotating an object around a fixed point. A dilation involves scaling an object up or down, while maintaining its shape. A translation involves moving an object without changing its size or shape.

In this case, we can eliminate rotation, dilation, and translation as options because the image of the polygon is not rotated, scaled up or down, or moved without changing its shape. Instead, it is flipped across a line of symmetry, which is characteristic of a reflection.

Therefore, based on the image provided, it appears that the polygon was reflected across a line of symmetry to produce the image shown. Therefore, the correct answer is A. Reflection.

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The interest on the loan is $1200.

Given,

In the question:

You get a loan from the loan star bank to help pay for your home.

and, if you borrowed $12,000 at 10% for one year.

To find the interest on the loan.

Now, According to the question;

Based on the given conditions:
Formulate:

Borrowed= $12,000

At 10% for one year

12000 x 10%

Convert percentage into decimal

12000 x 0.1

calculate the product or quotient:

= 1200

Hence, The interest on the loan is $1200.

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well, if she bought 3 lamps at 40 bucks a pop, that's 120 bucks, but she paid 129.90, so the extra 9.90 is the tax.

now if we take the 120 as the 100%, what is 9.90 off of it in percentage?

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 120 & 100\\ 9.90& x \end{array} \implies \cfrac{120}{9.90}=\cfrac{100}{x}\implies \cfrac{120}{9.9}=\cfrac{100}{x} \\\\\\ 120x=990\implies x=\cfrac{990}{120}\implies x=8.25\)

Step-by-step explanation:

I think this the answer hope it helps

Answer:

See Below.

Step-by-step explanation:

Remember that:

Where c is the longest side, and a and b are the two remaining sides.

\(4^2\text{ is }\textbf{ less than (or $<$) } 3^2+3^2\)

\(\text{Therefore, }\Delta JKL \text{ is }\textbf{an acute triangle.}\)

(16 is less than 9 + 9 or 18.)

\(5^2\text{ is } \textbf{equal to (or $=$) } 3^2+4^2\)

\(\text{Applying the same method, $\Delta ABC$ is }\textbf{ a right triangle.}\)

(25 is equal to 9 + 16 = 25.)

Answer:

less then

acute

equal to

right

Step-by-step explanation:

The point of concurrency that is determined by the three altitudes of any triangle is called orthocenter.

In geometry, an orthocenter is the intersection of the altitudes of a triangle. An altitude of a triangle is a line through a vertex of the triangle, perpendicular to the opposite side.

In other words, if you were to draw three lines from the vertices of a triangle down to the opposite sides, and these lines were all perpendicular to their respective sides, the point at which all three lines intersect would be the orthocenter of the triangle.

The orthocenter is one of the four points of concurrency that can be determined in a triangle, along with the circumcenter, the centroid, and the incenter. The circumcenter is the center of the circumcircle of the triangle, the centroid is the center of the triangle's mass, and the incenter is the center of the circle inscribed in the triangle.

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Answer: 1. 10^3

One thousand

2. 10^5

One Hundred Thousand.

3.10000  4.2000  5. 60000

6. 7

70

700

7000

70000

7.12

120

1200

12000

120000

8.  9 × 1

9 × 10

9 × 100

9 × 1000

9 × 10000

9. value= 20

Step-by-step explanation:

There are 36 possible outcomes when rolling a pair of dice, as each die can land on any number from 1 to 6, and the total of the two dice is the sum of their individual values.

To calculate the probability of getting a sum of 8, we need to count the number of outcomes that add up to 8. There are five possible outcomes: (2,6), (3,5), (4,4), (5,3), and (6,2). Each of these outcomes has a probability of 1/36, so the probability of rolling a sum of 8 is:

P(sum of 8) = 5/36

To calculate the probability of getting at least one 5, we need to count the number of outcomes that include at least one 5. There are 11 possible outcomes: (1,5), (2,5), (3,5), (4,5), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), and (6,5). Each of these outcomes has a probability of 1/36, so the probability of rolling at least one 5 is:

P(at least one 5) = 11/36

To calculate the probability of getting either a sum of 8 or at least one 5, we need to add the probabilities of these two events and subtract the probability of both events happening at the same time (i.e., rolling two fives). There is only one outcome that gives two fives, so its probability is 1/36. Therefore, the probability of getting either a sum of 8 or at least one 5 is:

P(sum of 8 or at least one 5) = P(sum of 8) + P(at least one 5) - P(rolling two fives)

= 5/36 + 11/36 - 1/36

= 15/36

= 5/12

So the probability of getting either a sum of 8 or at least one 5 when rolling a pair of dice is 5/12 or approximately 0.417.

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Answer:

Abiola stayed at work for 8 hours and 40 minutes.

Step-by-step explanation:

Abiola wasted 20 minutes waiting for her friend, so she actually left for work at 7:50 am (7:30 am + 20 minutes).

She arrived at work at 8:20 am, so she spent 30 minutes (8:20 am - 7:50 am) traveling to work.

Abiola worked from 8:20 am to 4:00 pm, which is a total of 7 hours and 40 minutes (4:00 pm - 8:20 am).

She then stayed at work for an additional 1 hour to watch African Magic, so in total, she was at work for 8 hours and 40 minutes (7 hours and 40 minutes of work + 1 hour of watching African Magic).

Therefore, Abiola stayed at work for 8 hours and 40 minutes.

The missing part of the equation is \(-7.0\times10^4 s^2kg⋅m^2 / 1000000.\)

To fill in the missing part of the equation, let's analyze the given information and the desired conversion. The equation is:

\((-7.0\times 10^4 s^2g⋅m^2)\cdot \pi = ? s^2kg\cdot m^2\)

In this equation, we have a quantity expressed in\(s^2g\cdot m^2\) units on the left-hand side. To convert it to \(s^2kg\cdot m^2\) units, we need to multiply it by a conversion factor.

To perform the conversion, we can use the fact that 1 kg is equal to 1000 g. Therefore, the conversion factor we need is:

1 kg / 1000 g

To ensure that the units cancel out correctly, we need to square this conversion factor because we have \(s^2g\cdot m^2\) on the left-hand side. So the missing part of the equation is:

\((-7.0\times 10^4 s^2g\cdot m^2)\cdot \pi = (-7.0\times 10^4 s^2g\cdot m^2)\cdot (1 kg / 1000 g)^2\)

Simplifying this expression, we get:

\((-7.0\times10^4 s^2g\cdot m^2)\cdot \pi = -7.0 \times10^4 s^2kg\cdot m^2 / 1000000\)

Therefore, the missing part of the equation is \(-7.0 \times 10^4 s^2kg\cdot m^2 / 1000000.\)

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\(distance = | \frac{2 - ( - 1)}{ \sqrt{ { (\frac{ - 1}{4} )}^{2} + {( - 1)}^{2} }} | \\ = \frac{1 2\sqrt{17} }{17} \\ = 2.9\)

Jane would take 5 hours painting the window so both of them could end up charging the same amount

An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.

Let y represent the total charge for working x hours.

Suzie has quoted a flat rate of $250 for the job. For Suzie:

y = 250

Jane's quote is $40 per hour, plus $50 to cover the cost of materials. For Jane:

y = 40x + 50

For the two to charge the same amount:

250 = 40x + 50

40x = 200

x = 5 hours

Jane would spend 5 hours painting the window.

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From hypothesis testing, the test statistic value for two samples is 0.30. The p-value = 0.766> 0.05, null can't reject the null hypothesis. So, there is no evidence to support claim that a difference in population mean percentage increases for corporate revenue and CEO salary. So, option(A) is right one.

For comparing means of two population where population variance are unknown, then our hypothesis is \(H_0 :μ_1−μ_2 =ξ_0 \)

\(H_1 :μ_1−μ_2 ≠ξ_0\)

The test statistic for the given hypothesis is \(T= \frac{ (\bar x_{1} − \bar x_2) - ξ_0}{ \sqrt{\frac{ s²_1}{n_1} + \frac{ s²_2}{n_2}}}\)

\( s_ i = ∑_{j=1}^{n_i}\frac{ x_{ij} - \bar x_i}{ n_i - 1} \\ \)

Now, there are america's top chief executive officers. Let's consider A denotes be the CEO's annual percentage salary increase and B denote be the annual company percentage increase in revenue, in that same company. To test the different of population mean percentage increase in corporate revenue \((μ_B)\) and the population mean percentage increase in CEO salary \((μ_A)\). We need the hypothesis as : For A sample, \(n_1 = 8\)

sample mean \(\bar x_1 = \sum_{j = 1}^{n_1} x_{ij} = 16.13 \\ \)

Standard deviations, \(sd_1 = \sqrt{ \sum_{j = 1}^{8} \frac{ x_{1j} - \bar x_1}{n_1 - 1} } \\ \)

= 9.46

Similarly for B, \(n_2 = 8\)

sample mean \(\bar x_2 = \sum_{j = 1}^{n_2} x_{ij} = 17.28 \\ \)

standard deviations, \(sd_2 = \sqrt{ \sum_{j = 1}^{8} \frac{ x_{1j} - \bar x_2}{n_2- 1} } \\ \)

=11.8

d = \(\bar x_1 - \bar x_2 = 1.67\)

Therefore the test statistic :

\(T= \frac{ 1.67 - 0}{ \sqrt{\frac{ 9.41²}{8} + \frac{11.8² }{8}}}\)

= 0.30

degree of freedom, df = 8 + 8 - 2 = 14

Level of significance= 0.05

The above test statistic follows t-distribution with, so the critical value for t = 0.30 and degree of freedom 14 is equals to 0.766 > 0.05.

Based on obtained answers, we will fail to reject the null hypothesis because p-value is greater than the level of significance then we can says that the data is not statistically significant at level 0.05. Hence, we conclude that there is no enough evidence at the 5% level of significance to the claim that a difference in population mean percentage increases for corporate revenue and CEO salary.

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Complete question:

are america's top chief executive officers (ceos) really worth all that money? one way to answer this question is to look at row b, the annual company percentage increase in revenue, versus row a, the ceo's annual percentage salary increase in that same company. suppose a random sample of companies yielded the following data: b: percent increase for company 4 20 24 18 6 4 21 37 a: percent increase for ceo 17 14 21 14 -4 19 15 30 do these data indicate that the population mean percentage increase in corporate revenue (row b) is different from the population mean percentage increase in ceo salary? Use a 5% level of significance. Solve the problem using the critical region method of testing. (Let

d=B−A. Round your answers to three decimal places.)

test statistic = _____

critical value =

A: Fail to reject the null hypothesis, there is insufficient evidence to claim a difference in population mean percentage increases for corporate revenue and CEO salary.

B. Fail to reject the null hypothesis, there is sufficient evidence to claim a difference in population mean percentage increases for corporate revenue and CEO salary.

C. Reject the null hypothesis, there is insufficient evidence to claim a difference in population mean percentage increases for corporate revenue and CEO salary.

D. Reject the null hypothesis, there is sufficient evidence to claim a difference in population mean percentage increases for corporate revenue and CEO salary.

The centroid of an octant of a solid sphere is located at the point (r/3, r/3, r/3), where r is the radius of the sphere.

An octant is one-eighth of a solid sphere, so it is formed by cutting the sphere into eight equal parts along the x, y, and z axes. The centroid of a solid is the point at which the mass of the solid is evenly distributed, and for an octant of a sphere, this point is located at (r/3, r/3, r/3).

This can be determined by using the formula for the centroid of a solid, which is the average of the x, y, and z coordinates of all the points in the solid. For an octant of a sphere, the x, y, and z coordinates all range from 0 to r, so the average of these coordinates is r/3.

In conclusion, the point representing the centroid is (r/3, r/3, r/3).

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The simplified solution to the equation 1 = √(3) tan(2θ) where 0 < θ < π/2 is θ = π/12.

To find the solution, we start by isolating the tangent term by dividing both sides of the equation by √(3). This gives us tan(2θ) = 1/√(3). We know that for 0 < θ < π/2, the tangent function is positive, and we are looking for the value of θ that satisfies this condition.

Using the inverse tangent function, we take the arctan of both sides to find the angle whose tangent is 1/√(3). The exact simplified solution is θ = π/12.

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Explanation:- When they had asked, Round 468986 to the nearest thousand, You should know that :-

Th H T O

4 6 8 9 8 6

So, Here In Thousand place we have 8.

Then see the all numbers after 8 That is :-

8986

So 8986 is nearest to 9000

Therefore, answer will be 469000.

the answer is 469000 hope it help's

Answer:

X=30 Y=60 Z=90

Step-by-step explanation:

When you dilate the triangle the angles don’t change and they are similar triangles so you just follow the order QRS the X would have the same angle as the Q, Y would have the same angle as R and Z would have the same angle as S.

expected value of defected lamps =1.5

Probability of 5 defected lamps= 0.166

probability less than five defected lamps=0.995

Given, the probability that a lamp is defective is 0.05. A random sample of 30 lamps is tested.

(a) The number of defective lamps expected in the sample is found by calculating the expected value of the number of defective lamps in a sample. The expected value of the number of defective lamps in a sample is E(X) = np = 30 × 0.05 = 1.5 defective lamps.    

(b) The probability that there are exactly five defective lamps in the sample is found using the probability mass function (PMF) of the binomial distribution. The PMF is P(X = k) = C(n, k) × p^k × (1 - p)^(n - k)

where C(n, k) is the number of ways to choose k items from a set of n items, p is the probability of success, and n is the number of trials.

P(X = 5) = C(30, 5) × 0.05^5 × (1 - 0.05)^(30 - 5) = 0.166.

(c) The probability that there are fewer than five defective lamps in the sample is found using the cumulative distribution function (CDF) of the binomial distribution. The CDF is

P(X ≤ k) = Σ P(X = i) where Σ is the sum from i = 0 to i = k.

P(X ≤ 4) = Σ P(X = i) = 0.995.

The expected value of the number of defective lamps in a sample is E(X) = np = 30 × 0.05 = 1.5 defective lamps.

The probability that there are exactly five defective lamps in the sample is P(X = 5) = C(30, 5) × 0.05^5 × (1 - 0.05)^(30 - 5) = 0.166.

The probability that there are fewer than five defective lamps in the sample is P(X ≤ 4) = 0.995.

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The solution of the compound inequality is 4 ≤ x ≤ 6.

The solution of the compound inequality is calculated as follows;

The given inequality equation;

2 + x ≤ 3x – 6 ≤ 12

Break down the compound inequality into two equations as;

2 + x ≤ 3x – 6

add 6 to both sides of the equation;

2 + 6 + x ≤ 3x

8 + x ≤ 3x

Subtract x from both sides of the equation;

8 ≤ 2x

4 ≤ x

Another solution of the inequality is determined as;

3x – 6 ≤ 12

3x ≤ 12 + 6

3x ≤ 18

x ≤ 18/3

x ≤ 6

The solution = 4 ≤ x ≤ 6

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The complete question is below:

Which best describes the solution set of the compound inequality below?

2 + x ≤ 3x – 6 ≤ 12

a: 4 ≤ x ≤ 9

b: 4 ≤ x ≤ 6

c: –2 ≤ x ≤ 2

d: –2 ≤ x ≤ 3

A data set's attributes are enumerated through descriptive statistics. You can use inferential statistics to test a hypothesis or determine whether your data can be applied to a larger population.

Descriptive statistics concentrate on describing the features of a dataset that are readily evident (a population or sample). In contrast, inferential statistics concentrate on drawing conclusions or generalisations from a sample of data in a larger dataset.

The information from a research sample is described and condensed using descriptive statistics. We can draw conclusions about the larger population from which we drew our sample using inferential statistics.

The area of statistics known as descriptive statistics is focused on providing a description of the population being studied. A type of statistics known as inferential statistics concentrates on inferring information about the population from sample analysis and observation.

Hence we get the required answer.

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