What is the median of the data represented by the stem
and leaf plot above?
Hint: Use the key to determine the individual values
MEDIAN middle data value when values are listed least to greatest
A 108.75
B 57
C 309

The values of each number using power 10 is shown below.

1. 79 x 10

= 790

2. 15 x 100

= 1500

3. 22 x 1,000

= 22,000

4. 15 x 1000

= 15,000

5. 83 x 102

= 8,466

6. 23 x 10²

= 2300

7. 72 x 10²

= 7200

8. 4 x 10²

= 400

9. 75 x 10²

= 7500

10. 55 x 10²

= 5500

11. 81 x 10³

= 81,000

12. 3 x 10³

= 3000

13. 85 x 10³

= 85, 000

14. 98 x [tex]10^{-1[/tex]

= 9.8

15. 86 x [tex]10^{-3[/tex]

= 0.086

16. 65 x [tex]10^{-2[/tex]

= 0.65

17. 19 x 10³

= 19,000

18. 3.49 x [tex]10^{9[/tex]

= 349,000,000,000

19. 2.79 x [tex]10^{8[/tex]

= 27,900,000,000

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The correct statements regarding a translation are given as follows:

A : The sides of the image and pre-image are congruent.

G: each point has moved the same number of units.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The side lengths are not changed, hence the image and the pre-image are congruent. The angle measures are also not changed, hence the image and the pre-image are similar, and the shapes also remain constant.

For a translation, the movements have to be:

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The equation of the line in slope - intercept form, given the two points, would be D. y = - 10 / 3 x - 2 / 3.

First, write out the points on the graph to be ( -2, 6 ) and ( 1, - 4 ) .

The slope would be:

=  (change in y) / (change in x)

=  (-4) - 6  / 1 - (-2)

= - 10 / 3

Use a point to find the y - intercept in the form:

y = mx + b

6 = - 10 / 3 ( - 2 ) + b

b = - (2/3)

The equation then is :

y = - 10 / 3 x - 2 / 3

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Answer:

Cylinder problem:

28.26 = 3.14(r^2)(9)

28.26 = 28.26(r^2), so r = 1 cm

Trapezoid problem:

Since we have similar trapezoids, the side lengths of WXYZ are each 5 times the side lengths of ABCD.

60/12 = 5, so b = 5 × 10 = 50 inches

You would need a sample size of at least 138.32 to obtain a 90% confidence interval with a margin of error of plus or minus 3.

To determine whether the credit scores have decreased since 2019, we need to compare the 2019 average credit score of 749 with the lower bound of the 2022 confidence interval of 730.343. Since 730.343 is lower than 749, we can conclude that there is evidence to suggest that the credit scores have decreased since 2019.

Finally, if you want to obtain a 90% confidence interval with a margin of error of plus or minus 3, you can use the formula for the sample size n =

=> (z² x s²) / (E²),

where z is the critical value, s is the estimated standard deviation from a previous study or pilot sample, and E is the desired margin of error.

Since s is unknown in this case, we can use a conservative estimate of 50 for the standard deviation.

Therefore, n = (1.725² x 50²) / (3²) = 138.32.

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Answer:

In the numerator:

2x^2 + 3x - 20 = (2x - 5)(x + 4)

- no asymptotes

- x-intercept is at x = 2.5 (since there is a hole at x = -4)

- y-intercept is at y = -5

The triangle which has hypotenuse GF include the following: C. triangle EFG.

In Mathematics and Geometry, a triangle can be defined as a two-dimensional (2D) geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

In Mathematics and Geometry, a right angle can be defined as a type of angle that is formed in a triangle by the intersection of two (2) straight lines at 90 degrees. This ultimately implies that, a right angled triangle has a measure of 90 degrees.

By critically observing the image (see attachment), we can reasonably infer and logically deduce that triangle EFG has hypotenuse GF because it is opposite the right angle (90 degrees).

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Complete Question:

Which triangle has hypotenuse GF?

triangle AFG

triangle BFG

triangle EFG

triangle DFG

The value of z that divides the standard normal distribution so that half the area is on one side and half is on the other is 0.00.

To understand this better, let's visualize the standard normal distribution. The graph of the standard normal distribution is a bell-shaped curve that is symmetrical around the mean of 0.

When we say that half the area is on one side and half is on the other, we mean that the area under the curve to the left of the z-score is equal to the area under the curve to the right of the z-score.

Since the standard normal distribution is symmetric, this occurs when the z-score is equal to 0.00. At this point, the area to the left of 0.00 is 0.50 (or 50%), and the area to the right of 0.00 is also 0.50 (or 50%).

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The length of each piece of wood is 0.725 feet.

We are given that the Length= 3.5feet

Now,

This is a word problem that can be solved by using algebra and arithmetic.

Part A: Let x be the length of each of the four pieces of wood he cut. Then, according to the problem, we have:

4x + 0.6 = 3.5

This is the equation that could be used to determine the length of each piece of wood.

Part B: We know the equation from part A is correct because it represents the total length of the wood before and after cutting. The left side of the equation is the sum of the lengths of the four pieces of wood and the leftover piece of wood. The right side of the equation is the original length of the wood. Since cutting does not change the total length of the wood, these two sides must be equal.

Part C: To solve the equation from part A, we need to isolate x by using inverse operations. We get:

4x + 0.6 = 3.5 4x = 3.5 - 0.6 (subtract 0.6 from both sides) 4x = 2.9 x = 2.9/4 (divide both sides by 4) x = 0.725

Therefore, by the algebra the answer will be 0.725 feet.

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Option B To find the z-score corresponding to an observation of 470, we use the formula: z = (x - μ) / σ

where x is the observation, μ is the mean, and σ is the standard deviation. Substituting the values given in the question, we get: z = (470 - 570) / 10.1489.

z = -9.84, Therefore, the z-score corresponding to an observation of 470 is -0.97, which is option B.

By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.

A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently. Sal Khan invented it.

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Therefore, the 90% confidence interval for the mean height of the population of female runners is (64.77, 66.83) inches.

A confidence interval is a range of values that provides an estimate of the unknown population parameter with a certain level of confidence. The confidence level represents the percentage of times that the true population parameter will be contained within the interval, based on repeated sampling.

a) Using a t-distribution with 11 degrees of freedom (n-1), and a 90% confidence level, the t-value is 1.796.

The left boundary of the confidence interval is:

65.80 - (1.796 * (1.95 / √(12))) = 64.77 inches (rounded to two decimal places)

b) The right boundary of the confidence interval is:

65.80 + (1.796 * (1.95 / √(12))) = 66.83 inches (rounded to two decimal places)

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If the 2 thirds of the sum of two numbers are 74 and the 3 fifths of their difference 9, the two numbers are 63 and 48.

Let x and y be the two numbers. Then we have two equations based on the given information:

2/3(x+y) = 74 ... (1)

3/5(x-y) = 9 ... (2)

To solve for x and y, we can start by isolating one variable in terms of the other from one of the equations. For example, from equation (1), we have:

x + y = (3/2) * 74

x + y = 111

Next, we can substitute this value of (x + y) into equation (2) and solve for the other variable:

3/5(x - y) = 9

x - y = 15

Now we have two equations with two variables:

x + y = 111

x - y = 15

Solving for x and y by adding the two equations gives:

2x = 126

x = 63

Substituting this value of x into either equation gives:

y = 48

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Complete question is:

The 2 thirds of the sum of two numbers are 74 and the 3 fifths of their difference 9. Find the two numbers.

Histograms are primarily used to demonstrate how often data values fall into certain ranges. So, option 3 is correct.

Histograms are graphical representations of a dataset's distribution, with the data separated into intervals or "bins" and the frequency of values falling into each bin represented as bars.

Histograms can be used to find the trends and the specific information in the data for the help of data analyst. They are especially useful for huge datasets when the distribution of values from a simple list may be difficult to understand. Although histogram could be used for more than two data types and but this is not there natural purpose. Hence option option 3 is correct choice.

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Complete question - A data analyst creates a histogram to share in a presentation. what are histograms used to demonstrate?

1. how two or more values contrast and compare

2. how much each part of something makes up the whole

3. how often data values fall into certain ranges

4. how data has changed over time.

The axis of symmetry for the given object and image is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The object and the image

By definition, the axis of symmetry is any line that divides a shape and its image into symmetrical parts i.e. into identical shapes and sizes

In this case, the axis of symmetry would be a vertical line that divides both triangles in to identical figures

Using the above definition as a guide, we can draw the axis of symmetry for the object and image & then label it AB

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The point that is not a solution of the system of inequalities is (3, 1).

A point is a solution of the system of inequalities only if it lies in the shaded region (the green one) or in top of the solid line (this would be the line with negative slope).

Then from the given points the ones that are solutions are:

(1, 3) (it lies on the shaded region)

(1, 4) (it lies in the shaded region)

(0, 5) (it lies in the shaded region)

Then the anser is the remaining one (3, 1), that is not a solution.

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An employee receives a 2% rise once every year. If an employee's starting salary is $61,900.00, salary after seven years will be $71,103.64.

We will calculate the salary for each year till 7th year.

Salary after 1 year = Original salary × (100 + raise)/100

= 61,900 × (100+2)/100
= 61,900 × 102/100

= $63,138

Salary after second year = salary after first year × 1.02

= 63,138 × 1.02

= $ 64,400.76

Salary after third year = salary after second year × 1.02

= 64,400.76 × 1.02

= $ 65,688.78

Salary after fourth year = salary after third year × 1.02

= 65,688.78 × 1.02

= $ 67,002.55

Salary after fifth year = salary after fourth year × 1.02

= $ 67,002.55 × 1.02

= $ 68,342.60

Salary after sixth year = salary after fifth year × 1.02

= $ 68,342.60 × 1.02

= $ 69,709.45

Salary after seventh year = salary after sixth year × 1.02

= $ 69,709.45 × 1.02

= $ 71,103.64

So, the final salary after seven years after all the increments will be $ 71,103.64

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13 is the y-intercept, which is the initial number of space.

6 is the slope, which means the number of spaces is increasing by 6.

x represent number of rolls.

40 the minimum number of spaces required to win the game.

The fewest number of rolls it would take Li to win the game is 0.054 rolls.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided about Li's current situation, we have the following inequality:

13 ÷ 6x ≥ 40

13/6x ≥ 40

13 ≥ 240x

x ≤ 0.054

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The calculated probability that the job is offered to a man is 0.455

From the question, we have the following parameters that can be used in our computation:

There are 5 men and 6 women interviewed for a job.

This means that

Men = 5

Women = 6

The probability that the job is offered to a man is

P = men/Total

So, we ave

P = 5/11

Evaluate

P = 0.455

Hence, the probability is 0.455

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There are 210 ways we can give 4 different prizes to any 4 of 10 people if no person receives more than 1 prize.

To calculate the number of ways we can do this, we can use the formula for combinations. The formula for the number of ways to choose r objects from a set of n objects is:

ⁿCₓ = n! / x!(n-x)!

where n! represents the factorial of n, which is the product of all positive integers up to n.

5! = 5 x 4 x 3 x 2 x 1 = 120.

In this problem, we want to choose 4 people from a set of 10, so we can use the formula:

¹⁰C₄ = 10! / 4!(10-4)!

Simplifying this expression, we get:

¹⁰C₄ = (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1)

¹⁰C₄ = 210

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The area formed by the water pattern of a sprinkler that can spray out 14 feet in any direction is about 615.44 square feet.

Explain the term area.

Area is the measure of the size of a two-dimensional surface or region, usually measured in square units. It is the amount of space enclosed by a flat shape or the surface of an object. The area of a shape can be calculated using formulas based on its dimensions and geometry.

According to the given information

The formula for calculating the area of a circle is A = πr² where A is the area and r is the radius of the circle. In this case, r = 14 feet and π = 3.14 so A = 3.14 x (14)² = 615.44 square feet

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Answer:

Angle A° is less than 90°

Angle B° is less than 90°

Step-by-step explanation:

Angle A° = Angle B° = 45°

The ratio of y to x is not constant for each pair of values, we cannot conclude that the relationship between x and y is proportional.

Define constant?

A constant is a fixed value or quantity that does not change in a particular context or situation.

The tables you provided appear to show a proportional relationship between x and y. Specifically, the ratio of y to x is constant for each pair of values. We can confirm this by computing the ratios:

For the first table:

Ratio of y to x for the pair (2,6): 6/2 = 3

Ratio of y to x for the pair (3,9): 9/3 = 3

Ratio of y to x for the pair (4,12): 12/4 = 3

Since the ratio of y to x is constant for each pair of values, we can conclude that the relationship between x and y is proportional.

Similarly, for the second table:

The ratio of y to x for the pair (2, 1): 1/2 = 0.5

The ratio of y to x for the pair (4, 8): 8/4 = 2

The ratio of y to x for the pair (12, 16): 16/12 = 4/3

Hence, the ratio of y to x is not constant for each pair of values, we cannot conclude that the relationship between x and y is proportional.

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The complete question is in the attached image.

The area and perimeter of the shape are 370mm² and 90mm respectively.

Perimeter is the distance around the outside of a shape. Area measures the space inside a shape.

Perimeter is the addition of the sides of the shape.

Therefore, the perimeter of the shape = 15+15+30+30 = 30+60 = 90mm

The area of the shape = area of the whole shape - area of the cut out

area of the whole shape = l×w

= 30×15 = 450mm²

area of the cut out =l×w

8× 10 = 80mm²

area of the shape = 450-80

= 370mm²

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Answer:

  y = -6x +3

Step-by-step explanation:

You want the slope-intercept equation matching the given graph.

The line on the graph crosses the y-axis at the marked point (0, 3). Another point is marked at (1, -3), which is 1 unit right and 6 units down.

The first point tells you the y-intercept (b) is +3.

The second point tells you the slope (m) is rise/run = -6/1 = -6.

Then the point-slope equation is ...

  y = mx + b

  y = -6x +3

<95141404393>

In statistics, a series of random events in which the probability of a given event is determined only by its predecessors is known as a "chain". This concept is attributed to the Russian mathematician Andrey Markov, and such chains are commonly referred to as Markov chains.

Markov chains have important applications in many areas of science and engineering, including physics, economics, genetics, and computer science. They are used to model a wide range of phenomena, including the behavior of financial markets, the spread of diseases, the performance of computer networks, and the evolution of populations.The basic idea behind a Markov chain is that the future state of the system depends only on the current state, and not on any previous states. The probability of transitioning from one state to another is determined by a transition matrix, which specifies the probabilities of moving from one state to another in a single time step.

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Integrating and evaluating the function gives f(x) = 1/12x⁴ - 2/3x³ + 3/2x² - 5x and f(2) = -8

From the question, we have the following parameters that can be used in our computation:

∫ 1/3x³ - 2x² + 3x - 5 dx

The rule of integration is

x^n = x^(n + 1)/(n + 1)

using the above as a guide, we have the following:

∫ 1/3x³ - 2x² + 3x - 5 dx = 1/12x⁴ - 2/3x³ + 3/2x² - 5x

So, we have

f(x) = 1/12x⁴ - 2/3x³ + 3/2x² - 5x

Next, we are to calculate f(2)

This means that x = 2

So, we have

f(2) = 1/12(2)⁴ - 2/3(2)³ + 3/2(2)² - 5(2)

Evaluate

f(2) = -8

Hence, the value of f(2) is -8

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Answer:

Step-by-step explanation:

The diameter of each bead is 1.5 millimeters, which means the radius of each bead is 0.75 millimeters (since radius = diameter/2).

The volume of a sphere is given by the formula V = (4/3)πr^3.

Substituting the radius of each bead into the formula, we get:

V = (4/3)π(0.75)^3 ≈ 1.7671 cubic millimeters

To find the total volume of the 360 beads used to create the border of the picture frame, we can simply multiply the volume of one bead by the total number of beads:

Total volume = 360 × 1.7671 ≈ 635.76 cubic millimeters

Therefore, the approximate total volume of the beads that form the border of the picture frame is about 635.76 cubic millimeters.

Answer:

6x^2+16x+8

Step-by-step explanation:

it is handwritten in the photo

the width of the reproduced piece is 2.78 inches.

Now, we first need to find the original area of the painting.

Since, The original area is,

= 29 inches x 25 inches

= 725 square inches

Now. we know that the reproduction has 1/9 of the original area, which means that the area of the reproduction is:

= 725 square inches / 9

= 80.56 square inches

Hence, for the width of the reproduced piece, we need to find the width of a rectangle whose area is 80.56 square inches, given that the height is 29 inches which remains constant in the reproduction.

Hence, We can use the formula for the area of a rectangle,

Area = length x width

In this case, we know the area is, 80.56 square inches)

and the length is, 29 inches

Thus, we can solve for the width:

80.56 square inches = 29 inches x width

width = 2.78 inches

Thus, the width of the reproduced piece is 2.78 inches.

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Answer:

C

Step-by-step explanation:

7.3<7.4<72.14<91.34<723.99