The table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10. The second column, Height in inches, has the entries, 8, 12, 16, 20, 24. The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool? The height of the water increases 2 inches per minute. The height of the water decreases 2 inches per minute. The height of the water was 2 inches before any water was added. The height of the water will be 2 inches when th

In this stem and leaf plot, the median of the data is 6.15 and the range is 8.3.

To find the median and range of the data from the stem and leaf plot, we need to first arrange the data in ascending order.

Arranging the data in ascending order:

1.3, 1.5, 3.2, 3.6, 3.9, 5.4, 5.7, 5.7, 5.8, 5.8, 6.0, 6.3, 6.3, 6.3, 7.4, 7.4, 7.5, 7.6, 8.0, 8.1, 8.1, 8.4, 9.5, 9.6

The median is the middle value of the data set. Since there are 24 values, the median is the average of the 12th and 13th values, which are 6.0 and 6.3. Therefore, the median is (6.0 + 6.3) / 2 = 6.15.

The range is the difference between the largest and smallest values in the data set. The largest value is 9.6 and the smallest value is 1.3. Therefore, the range is 9.6 - 1.3 = 8.3.

Thus, the median of the data is 6.15 and the range is 8.3.

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A and B have the same elements, the measure of AUB will be equal to the measure of B.

To show that if m*(A) = 0, then m*(AUB) = m*(B), we need to prove the following:
1. If m*(A) = 0, then A is a null set.
2. If A is a null set, then AUB = B.
3. If AUB = B, then m*(AUB) = m*(B).
Let's break down each step:
1. If m*(A) = 0, then A is a null set:
  - By definition, a null set has a measure of 0.
  - Since m*(A) = 0, it implies that A has no elements or its measure is 0.
  - Therefore, A is a null set.
2. If A is a null set, then AUB = B:
  - Since A is a null set, it means that it has no elements or its measure is 0.
  - In set theory, the union of a null set (A) with any set (B) results in B.
  - Therefore, AUB = B.
3. If AUB = B, then m*(AUB) = m*(B):
  - Since AUB = B, it implies that both sets have the same elements.
  - The measure of a set is defined as the sum of the measures of its individual elements.
  - Since A and B have the same elements, the measure of AUB will be equal to the measure of B.
  - Therefore, m*(AUB) = m*(B).
By proving these three steps, we have shown that if m*(A) = 0, then m*(AUB) = m*(B).

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Answer:

13 in

Step-by-step explanation:

because that is the longest side length

A. Quadrant I

B. Quadrant I

C. Quadrant II

D. Quadrant III

The 95% confidence interval for the mean weight of bags of that specific brand of candies is approximately 2.4461 ounces to 2.5539 ounces.

To construct a 95% confidence interval for the mean weight of the bags of that specific brand of candies, we can use the following formula:

Confidence Interval = Sample Mean ± (Critical Value)× (Standard Deviation / √Sample Size)

First, let's calculate the critical value. Since the population distribution is assumed to be normal and the sample size is small (n = 16), we can use a t-distribution instead of a z-distribution.

The critical value can be obtained from the t-distribution table or using statistical software. For a 95% confidence level with 15 degrees of freedom (n - 1 = 16 - 1 = 15), the critical value is approximately 2.131.

Now, we can plug in the given values into the formula:

Sample Mean = 2.5 ounces (given)

Standard Deviation = 0.1 ounces (known)

Sample Size (n) = 16 (given)

Critical Value = 2.131 (from t-distribution)

Confidence Interval = 2.5 ± (2.131)× (0.1 / √16)

Calculating the standard error (Standard Deviation / √Sample Size):

Standard Error = 0.1 / √16 = 0.1 / 4 = 0.025

Confidence Interval = 2.5 ± (2.131) × (0.025)

Calculating the bounds of the confidence interval:

Lower Bound = 2.5 - (2.131) ×(0.025)

Upper Bound = 2.5 + (2.131)×(0.025)

Lower Bound ≈ 2.5 - 0.0539 ≈ 2.4461 ounces

Upper Bound ≈ 2.5 + 0.0539 ≈ 2.5539 ounces

Therefore, the 95% confidence interval for the mean weight of bags of that specific brand of candies is approximately 2.4461 ounces to 2.5539 ounces.

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The given Fahrenheit temperatures evaluated to their Celsius equivalents are: 68°F = 20°C, 32°F = 0°C, 23°F = -5°C, -4°F = -20°C, and -40°F = -40°C.

The expression C = 5/9(F - 32) is used to convert temperatures in degrees Fahrenheit to degrees Celsius. To evaluate the expression for a given Fahrenheit temperature, we simply substitute the value of F into the formula and perform the necessary calculations.

For example, when F = 68, we substitute the value of F into the formula and simplify as follows:

C = 5/9 (68 - 32)

C = 5/9 * 36

C = 20

Here are the evaluations of the given Fahrenheit temperatures in degrees Celsius using the formula C = 5/9(F - 32):

F= 68: C = 5/9(68-32) = 20

F= 32: C = 5/9(32-32) = 0

F= 23: C = 5/9(23-32) = -5

F= -4: C = 5/9(-4-32) = -20

F= -40: C = 5/9(-40-32) = -40

Matching the correct Celsius temperatures to their respective Fahrenheit temperatures:

F= 68: C = 20

F= 32: C = 0

F= 23: C = -5

F= -4: C = -20

F= -40: C = -40

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Given a temperature F in degrees Fahrenheit, the expression C = 5/9(F - 32) gives the temperature in degrees Celsius. Evaluate the following Expressions and Match the correct answer to each the degrees listed.

1. F= 68  

2. F= 32

3. F = 23

4. F = -4

5. F = -40

Answer:

81

Step-by-step explanation:

Find out the percentage of people who had mispriced item.

3/50 = 0.06

6% of people had mispriced items.

Find 6% of 1,350.

81

81 people would have mispriced items.

Answer:

81

Step-by-step explanation:

I did this by doing 1,350 ÷ 50, which gave me 27. I then did 27 times 3, the average amount of people with a mispriced item per 50 people, which gave me 81 as a result. And with that, I can conclude that you would expect there to be 81 people per day who have a mispriced item.

Answer:

Step-by-step explanation

Two angles of a triangle are in the ratio of 2:3 if the third angle is 50 degree find the other two angles

the sum of the interior angles in a triangle is 180°

so

180 - 50 = 130°

130 : 5 = 26° (unit)

26 * 2 = 52°

26 * 3 = 78°

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check

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The answer is good

4. We start with the base case of \(5^0 = 1\) and recursively generate the next element in the set by multiplying the previous element by \(5\).

5. if a divides \(b\) and \(b\) divides \(a\), either a equals \(b\) or \(a\) equals negative \(b\).

4. The recursive definition of the set of positive integer powers of 5 can be expressed as follows:

Base case: \(5^0 = 1\) is in the set.

Recursive step: If n is in the set, then \(5^(n+1)\) is also in the set.

Using this definition, we start with the base case of \(5^0 = 1\)and recursively generate the next element in the set by multiplying the previous element by \(5\).

5. To prove that if a divides \(b\) and \(b\)divides \(a\), then a equals \(b\) or \(a\) equals negative \(b\), we can use the definition of divisibility.

Assume that \(a\) divides \(b\), denoted as \(a | b\) , and \(b\) divides \(a\), denoted as \(b | a.\)

By definition, if a divides b, there exists an integer k such that b = ak.

Similarly, if \(b\) divides \(a\), there exists an integer m such that \(a = bm.\)

Substituting the expression for\(b\) in terms of \(a\), we have \(bm = ak.\)

Dividing both sides by b (since b is nonzero), we get m = a/b.

Since \(m\) is an integer, \(a/b\) must be an integer, which means \(a\) is divisible by \(b\).

If \(a/b\)  is an integer, it implies that \(b/a\)is also an integer, which means \(b\) is divisible by \(a\).

Therefore, if \(a\) divides \(b\) and \(b\) divides \(a\), it follows that \(a/b\) and \(b/a\) are both integers.

If \(a/b = m\) and \(b/a = k\), then we have \(a = bm\) and\(b = ak.\)

\(If m = k = 1, then $a = b.\)

\(If m = k = -1, then a = -b.\)

Therefore, if \(a\) divides \(b\) and \(b\) divides \(a\), either \(a\) equals \(b\) or \(a\) equals negative \(b\).

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The largest angle is E = 205°.

To find the measure of the largest angle:

The sum of interior angles of a polygon is:

Where n is the number of sides.

Here n = 5, as pentagon has 5 sides.

Let, C = D = x

Then, E = 2x + 15 (15 more than twice C)

We can express the sum of the 5 angles as:

Simplify the left side by collecting like terms:

Subtract 160 from both sides:

Divide both sides by 4:

The 5 interior angles of the pentagon are:

The largest angle is E = 205°.

Therefore, the largest angle is E = 205°.

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Answer:

200 in all

Step-by-step explanation:

We can see that the statement is not always true for any vectors u and v in V3.

The statement is not always true.

The cross product of vectors u and v in V3 is a vector that is orthogonal to both u and v. That is,

u x v ⊥ u and u x v ⊥ v

However, this does not necessarily mean that (u x v) * u = 0 for all u and v in V3.

For example, let u = <1, 0, 0> and v = <0, 1, 0>. Then,

u x v = <0, 0, 1>

(u x v) * u = <0, 0, 1> * <1, 0, 0> = 0

So in this case, the statement is true. However, consider the vectors u = <1, 1, 0> and v = <0, 1, 1>. Then,

u x v = <1, -1, 1>

(u x v) * u = <1, -1, 1> * <1, 1, 0> = 0

So in this case, the statement is also true. However, if we take the vector u = <1, 0, 0> and v = <0, 0, 1>, then

u x v = <0, 1, 0>

(u x v) * u = <0, 1, 0> * <1, 0, 0> = 0

So in this case, the statement is true as well.

However, if we take the vector u = <1, 1, 1> and v = <0, 1, 0>, then

u x v = <1, 0, 1>

(u x v) * u = <1, 0, 1> * <1, 1, 1> = 2

So in this case, the statement is not true.

Therefore, we can see that the statement is not always true for any vectors u and v in V3.

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According to the empirical rule, approximately 95% of the data falls within two standard deviations of the mean. Therefore, the approximate percentage of daily phone calls numbering between 35 and 75 is 95%.

We have been given that the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 55 and a standard deviation of 10.

We are asked to find out the approximate percentage of daily phone calls numbering between 35 and 75 using the empirical rule.

The empirical rule is used to describe how many of the observations fall within a certain distance of the mean in a normal distribution of data.

The empirical rule states that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean.

To use the empirical rule, we first need to find the z-scores for the values of 35 and 75. We can use the formula

z = (x - μ) / σ,

where x is the value we want to find the z-score for, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

For x = 35, we have

z = (35 - 55) / 10 = -2, and

for x = 75, we have

z = (75 - 55) / 10 = 2.

So, the values of 35 and 75 are 2 standard deviations away from the mean. According to the empirical rule, approximately 95% of the data falls within two standard deviations of the mean.

Therefore, the approximate percentage of daily phone calls numbering between 35 and 75 is 95%.

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Answer:

0.25 is the probability

Step-by-step explanation:

If there are 13 diamonds in a deck of 52 cards, dividing 13 by 52 will get you 0.25. This is the probability of getting a diamond from the deck of 52 cards.

Graphing one period of the function will involve plotting points and connecting them smoothly. However, without a specific interval provided, it is not possible to accurately determine the values of x and y to plot the graph.

a. To determine the height of the arch, we need additional information such as the specific arch or its dimensions. Without specific details, it is not possible to provide a precise answer regarding the height of the arch.

b. For the function y = -½cos(3x + 7), we can identify the amplitude, period, and phase shift:

Amplitude: The amplitude of a cosine function is the absolute value of the coefficient in front of the cosine term. In this case, the amplitude is ½.

Period: The period of a cosine function is calculated by dividing 2π by the coefficient of x. Here, the coefficient of x is 3, so the period is 2π/3.

Phase Shift: The phase shift is determined by isolating the argument of the cosine function (3x + 7) and solving for x when it equals 0. In this case, 3x + 7 = 0 gives x = -7/3. Therefore, the phase shift is -7/3 units to the left.

Graphing one period of the function will involve plotting points and connecting them smoothly. However, without a specific interval provided, it is not possible to accurately determine the values of x and y to plot the graph.

c. Regarding the request to graph each pair of functions, it seems that the instructions for this part of the question are incomplete. Please provide the specific pairs of functions you would like to graph, along with any additional details, so that I can assist you further.

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Answer:

Modal average is the number that appears the most

Modal average: 3

1+2+3+4+5=15

15/3=    Mean: 3

Step-by-step explanation:

add all the bedrooms and divide that sum by the number of numbers added. That's the mean.

Hope this helps.

A) 4 is the mode of the table

B)

1+2+3+4+5=15

15/5=3

To solve algebraic equations, we must combine like terms and perform inverse operations on both sides of the equal sign to isolate the variable.

Inverse operations help us cancel values out.

\(- 4 a - 2 a = - 18\)

⇒ First, combine like terms:

\(- 6a = - 18\)

⇒ a is being multiplied by -6. To isolate a, divide both sides by -6:

\(\dfrac{- 6a}{-6} = \dfrac{- 18}{-6}\\\\a=3\)

a = 3

Answer:

a=3

Step-by-step explanation:

-4a-2a=-18

-6a= -18

Divide both sides by -6

-6a/-6=-18/-6

a=3

To solve the given equations and verify the provided results, let's work through the calculations step by step.

Given:

y₀ + g = 1.9243    ---(1)

y₁ + y = 1.9540    ---(2)

We need to show that:

y₂ + g = 1.9823    ---(3)

y₃ + y = 1.9956    ---(4)

3/4 = 0.9999557    ---(5)

Step 1: Subtract equation (2) from equation (1):

(y₀ + g) - (y₁ + y) = 1.9243 - 1.9540

Simplifying, we get:

y₀ - y₁ + g - y = -0.0297    ---(6)

Step 2: Multiply equation (6) by 2:

2(y₀ - y₁) + 2(g - y) = -0.0594

Simplifying, we get:

2y₀ - 2y₁ + 2g - 2y = -0.0594    ---(7)

Step 3: Add equation (2) to equation (7):

(2y₀ - 2y₁ + 2g - 2y) + (y₁ + y) = -0.0594 + 1.9540

Simplifying, we get:

2y₀ - y₁ + 2g - y = 1.8946    ---(8)

Step 4: Substitute the given value of y₀ + g in equation (8):

2(1.9243) - y₁ + 2g - y = 1.8946

Simplifying, we get:

3.8486 - y₁ + 2g - y = 1.8946    ---(9)

Step 5: Rearrange equation (9) to solve for g:

g = (1.8946 - 3.8486 + y₁ + y) / 2

Simplifying, we get:

g = (-0.9540 + y₁ + y) / 2    ---(10)

Step 6: Substitute the value of g from equation (10) into equation (3):

y₂ + g = 1.9823

y₂ + (-0.9540 + y₁ + y) / 2 = 1.9823

Simplifying, we get:

2y₂ - 0.9540 + y₁ + y = 3.9646    ---(11)

Step 7: Subtract equation (2) from equation (11):

(2y₂ - 0.9540 + y₁ + y) - (y₁ + y) = 3.9646 - 1.9540

Simplifying, we get:

2y₂ - 0.9540 = 2.0106    ---(12)

Step 8: Solve equation (12) for y₂:

2y₂ = 2.0106 + 0.9540

2y₂ = 2.9646

y₂ = 1.4823    ---(13)

Step 9: Substitute the value of y₂ from equation (13) into equation (4):

y₃ + y = 1.9956

y₃ + 1.4823 = 1.9956

Simplifying, we get:

y₃ = 0.5133    ---(14)

Step 10: Verify equation (5):

3/4 = 0.75, which is not equal to

0.9999557.

Therefore, the provided result in equation (5) is incorrect.

In conclusion:

Using the given equations, we have found:

y₂ + g = 1.9823 (equation 3)

y₃ + y = 1.9956 (equation 4)

However, the value provided in equation (5) is not accurate.

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Answer:

\(\frac{-1}{3}\)

Step-by-step explanation:

Look at the red slope triangle that is drawn. If you start at the point on the left, you go down 1 unit and then to the right 3 units.  This would be represented by -1/3.  Down would be negative and going right would be positive.  The slope is the rise over the run.

Helping in the name of Jesus.

Answer:

t = 2

Step-by-step explanation:

   ΔGFI is isosceles triangle. GF = FI.

         ∠FGJ = ∠FIJ

        ∠FGJ = 27°

In ΔGFJ,

  In Rhombus diagonals bisect each other at 90°.

           ∠GJF = 90°

 27° + 90°+ ∠GFJ = 180 {Angle sum property of triangle}

        117 + 2t +59 = 180

               2t + 176 = 180

                         2t = 180 - 176

                         2t = 4

                           t = 4 ÷ 2

                             \(\sf \boxed{\bf t = 2}\)

The correct option is C. Connect every intersection of an arc and the circle with a segment.

When constructing an inscribed regular hexagon, the steps come after six arcs are created on the circle is connect every intersection of an arc and the circle with a segment.

A hexagon is a two-dimensional geometric shapes shape with six sides that have the same or different length dimensions. A hexagonal flooring, pencil cross-section, honeycomb, and other real time of the hexagon shape include.

Some key features related to regular hexagon are-

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It is the location of the center of an equal distance point traced from the center. A circle's radius is the distance among its center and its circumference.

When building an engraved regular hexagon.

Following the creation of six arcs on the circle, the following steps will be taken.

A segment should be connected to every intersection of an arc and a circle.

The correct question is -

When constructing an inscribed regular hexagon, what steps come after six arcs are created on the circle?

A. Connect every other intersection of an arc and the circle with a segment. B. Connect the intersections of the diameters and the circle with a segment.

C. Connect every intersection of an arc and the circle with a segment.

D. Connect the midpoint of the radius to the endpoint of the diameter.

Answer: (C) Connect every intersection of an arc and the circle with a segment.

Step-by-step explanation: butter

Answer:

a) -1/3 b) 3 c) y=3x-10

Step-by-step explanation:

Answer:

A=1

B=6

C=5

Step-by-step explanation:

0=ax²+bx+c

0= 1x²+6x+5

There is no number in front of x², so you know the coefficient is 1.

The coefficient in front of the x is 6.

The remaining number is 5.

Answer:

The answer is -9 if you are solving the formula of y = mx + b

And if you are finding the slope and y- intersect of the graph then your answer is:

slope: 2/5 or 0.4

y-intercept: -7

Step-by-step explanation:

Answer:

Step 3

Step-by-step explanation:

The exponents haven't been solved right.

For powers when multiple you add them together

Answer:

2

Step-by-step explanation:

parallel lines have same slope.

y = 2x + 5

y = mx + b

m is the slope

b is y-intercept

The minimum score required for recruitment is 669

The normal distribution is expressed as

z = (x - µ)/σ

Where

x = SAT Mathematics scores.

µ = mean score

σ = standard deviation

From the question, we have

µ = 518

σ = 113

The probability value for the top 9% would be (1 - 9/100) = (1 - 0.09) = 0.91

the z score corresponding to the probability value is 1.34

1.34 = (x - 518)/113

1.34 × 113 = x - 518

151.42 = x - 518

x = 151.42 + 518

x = 669 to the nearest whole number.

Probability:

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

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