The box plot shows the times for sprinters on a track team.

A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 41, 43, 49.5, 56, and 58 are all marked by the box plot. The graph is titled Sprinters' Run Times, and the line is labeled Time in Seconds.

Which value does 50% of the data lie above, and what is it called?

58, the median
56, the upper quartile
43, the lower quartile
49.5, the median

45 and 27.6 degrees are the two complementary angles.

The various angles or measurements include:

Angles that are complementary are those whose sum is 90 degrees. If the smaller angle has a measure of x, then the complementary angle's measure is 90 - x.

The issue shows that the greater angle (x + 17.4) is 17.4 degrees larger than the corresponding angle's measurement (90 - x). To find x, we can construct the following equation:

x + 17.4 = 90 - x + 17.4

When we simplify and find x, we obtain:

2x = 55.2

x = 27.6

The greater angle's measure is x + 17.4 = 45 degrees, while the smaller angle's measure is x = 27.6 degrees.

The two complementary angles are 27.6 and 45 degrees as a result.

To know more about Complementary Angle visit:

https://brainly.com/question/5708372

#SPJ1

If the shortest leg of the small triangle is 4 in and the hypotenuse is 12 in and the shortest leg of the large triangle 8 in, then the length of the hypotenuse of the large triangle is 24 inches.

We know that two triangles are proportional if their corresponding sides are in proportion to each other. That is, the ratio of the lengths of the corresponding sides is the same for both triangles.

Let's denote the length of the hypotenuse of the large triangle by "h". We can set up a proportion using the given information:

shortest leg of small triangle / hypotenuse of small triangle = shortest leg of large triangle / hypotenuse of large triangle

Plugging in the values we get:

4/12 = 8/h

Simplifying the equation we get:

h = (12*8)/4 = 24

To explain the solution, we used the fact that similar triangles have proportional sides. We then used the given information about the lengths of the sides of the small and large triangles to set up a proportion and solve for the unknown length of the hypotenuse of the large triangle.

The key to this problem was recognizing the relationship between similar triangles and using that relationship to set up and solve a proportion.

To learn more about triangle click on,

https://brainly.com/question/8425335

#SPJ4

Note that the Upper limit and the lower limit of the Proportion Interval are given as follows:

Upper limit-  27%

Lower limit - 19%

The proportion interval, also known as the confidence interval, can be calculated using the point estimate of the proportion and the margin of error.

The lower limit of the proportion interval is calculated by subtracting the margin of error from the point estimate, and the upper limit is calculated by adding the margin of error to the point estimate.

Lower limit = point estimate - margin of error

Upper limit = point estimate + margin of error

In this case, the point estimate is 23% and the margin of error is ±4%.

Lower limit = 23% - 4% = 19%

Upper limit = 23% + 4% = 27%

Therefore, the proportion interval is [19%, 27%], which means that we can be 90% confident that the true proportion of the population lies within this range.

Learn more about Proportion Interval:
https://brainly.com/question/15873157
#SPJ1

You have to  spend $26,500 over the course of the first year with rent and equipment.

To calculate how much money you will spend over the course of the first year with rent and equipment, you need to add the cost of rent to the cost of equipment.

In a hypothetical scenario, Let's assume that the cost of rent for the first year is $1,500 per month.

To calculate the total cost of rent for the first year, you can multiply the monthly rent by the number of months in a year:

$1,500/month x 12 months = $18,000

So the total cost of rent for the first year is $18,000.

To calculate the total cost of equipment, you can take the average cost of the equipment (i.e., the midpoint of the given range) and assume that you will spend that amount:

($7,000 + $10,000) / 2 = $8,500

So the total cost of equipment is $8,500.

To calculate the total cost of rent and equipment for the first year, you can add the two costs together:

$18,000 + $8,500 = $26,500

Therefore, you will spend $26,500 over the course of the first year with rent and equipment.

Learn more about equipment cost from

https://brainly.com/question/29359843

#SPJ1

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The coordinates of points where the two lines intersect, is the solution of the equations/lines, that is (6, 64)

Answer: -3, 0

Step-by-step explanation:

If a line segment with endpoints (0,−3) and (0,−7) is rotated 90° clockwise, an endpoint of this rotated segment is (-3, 0) and (-7, 0).

In Mathematics and Geometry, a rotation is a type of transformation that moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

By applying either a rotation of 90° clockwise or a rotation of 270° counterclockwise to the coordinate of this line segment with endpoints (0,−3) and (0,−7), the coordinate of its image;

(x, y)                            →            (y, -x)

Point (0,−3)          →     Point (-3, 0)

Point (0, -7)          →     Point (-7, 0)

Read more on rotation here: brainly.com/question/28854313

#SPJ2

According to the given function net change and average rate of change between the given values of the variable.

A. 2

B. 2/a

A rate of change's integral is taken into account by the net change theorem. According to this, a quantity's new value equals its initial value plus the integral of its rate of change whenever it changes. There are two methods to formulate the equation. The second is more widely known and is just the definite integral.

The (definite) integral of a function's derivative, in other words, represents the overall change in a function. In specifically, the integral of velocity is the net distance travelled (final position minus initial position). The integral of acceleration is the difference between the final velocity and the starting velocity.

g(x) =2/x

x = 1

x = a

A.

g(x) =2/x

g(1) =2/x

g(1) =2

B.

g(x) =2/x

g(a) =2/x

g(a) =2/a

To know more about net change  visit:

https://brainly.com/question/30299107

#SPJ1

Opposite sides JK and ML are equal and parallel (with slopes of -1/5 and 1/5, respectively), and opposite sides KL and MJ are equal and parallel (with slopes of 7/3 or 7). /3) We can conclude that JKLM is a parallelogram. 

To determine if JKLM is a parallelogram, we need to check if its opposite sides are parallel and equal in length.

First, we can find the lengths of the sides using the distance formula:

JK = [tex]\sqrt{(1 - (-4))^2 + (3 - 2)^2} = \sqrt{25} = 5[/tex]

KL = [tex]\sqrt{(-4 - (-1))^2 + (2 - (-5))^2} = \sqrt{58}[/tex]

LM = [tex]\sqrt{(-1 - 4)^2 + (-5 - (-4))^2} = \sqrt{26}[/tex]

MJ = [tex]\sqrt{(4 - 1)^2 + (-4 - 3)^2} = \sqrt{50}[/tex]

Next, we can find the slopes of the sides using the slope formula:

Slope of JK = (2 - 3)/(-4 - 1) = -1/5

Slope of KL = (-5 - 2)/(-1 - (-4)) = 7/3

Slope of LM = (-4 - (-5))/(4 - (-1)) = 1/5

Slope of MJ = (3 - (-4))/(1 - 4) = 7/3

Since opposite sides, JK and ML have the same length and are parallel (they have slopes of -1/5 and 1/5, respectively), and opposite sides KL and MJ have the same length and are parallel (they have slopes of 7/3 and 7/3, respectively), we can conclude that JKLM is a parallelogram.

To learn more about parallelogram visit:

https://brainly.com/question/1563728

#SPJ1

According to the information, the graph would be as shown in the attached image (4 * 1/3 = 1 1/3)

According to the information we must take into account that a complete hexagon represents an integer. So one third of the hexagon would be the rhomboid. So, to graph this equation, we must replace the values with the corresponding figures.

In this case we must multiply the rhomboid by four, the rhomboid represents 1 of 3 elements that make up a hexagon. Therefore, if we have 4 rhomboids, we would have a hexagon and a rhomboid.

Note: This question is incomplete. Here is the complete information:

Image attached

Learn more about hexagons in: https://brainly.com/question/3295271

#SPJ1

The first quartile of the data set represented by the box plot shown in the figure is 20 option 'C' is correct.

What is the first quartile of the data set?

The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order. The upper quartile, or third quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order.

Since we have given a box and whisker plot.

As we know about the box and whisker method that :

Left most part of the box represents the first quartile and the rightmost part of the box represents the third quartile.

And the middle value is for median

so, we can conclude that

First quartile = 20

Third quartile = 40

Median = 25

Hence, the first quartile of the data set represented by the box plot shown in the figure is 20 option 'C' is correct.

To learn more about the first quartile of the data set visit:

https://brainly.com/question/28168026

#SPJ1

The total weight of the bottles the truck carries is 6020 ounces.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

Example:

2 + 1x + 4y = 7 is an expression.

3 + 3x + 3 = 7 is an expression.

We have,

Number of bottles the truck carries = 430

One bottle weight = 14 ounces

Now,

The total weight of the bottles.

= Number of bottles x Weight of one bottle

= 430 x 14

= 6020 ounces

Thus,

The total weight of the bottles the truck carries is 6020 ounces.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ9

The value of the limit of the rational function evaluated x = - 5 is equal to - 6.

In this problem we find the limit of rational function evaluated at a given value. According to the statement, there is apparently a discontinuity at x = 5. The expression can be simplified by algebra properties:

[tex]\lim_{x \to - 5} \frac{x^{2} + 4 \cdot x - 5}{x + 5}[/tex]

[tex]\lim_{x \to -5} \frac{(x + 5)\cdot (x - 1)}{(x + 5)}[/tex]

[tex]\lim_{x \to - 5} (x - 1)[/tex]

Then, we can complete the table by means of the following expression:

f(x) = x - 1

x = - 5.01

f(- 5.01) = - 5.01 - 1

f(- 5.01) = - 6.01

x = - 5.001

f(- 5.001) = - 5.001 - 1

f(- 5.001) = - 6.001

x = - 5.0001

f(- 5.0001) = - 5.0001 - 1

f(- 5.0001) = - 6.0001

x = - 5

f(- 5) = - 5 - 1

f(- 5) = - 6

x = - 4.9999

f(- 4.9999) = - 4.9999 - 1

f(- 4.9999) = - 5.9999

x = - 4.999

f(- 4.999) = - 4.999 - 1

f(- 4.999) = - 5.999

x = - 4.99

f(- 4.99) = - 4.99 - 1

f(- 4.99) = - 5.99

To learn more on limits: https://brainly.com/question/20512128

#SPJ1

Answer: The equation of the line passing through the points (1, -1, 2) and (0, 2, -3) is:       y = 3x - 4.

Step-by-step explanation:

To find the equation of a line passing through two points, we can use the point-slope form of a line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where m is the slope of the line, (x1, y1) is a point on the line, and (x, y) are the coordinates of any other point on the line.

Step 1: Find the slope of the line (m)

The slope of the line can be found using the two points:

m = (y2 - y1) / (x2 - x1)

Plug in the values of x1, x2, y1, and y2 from the two given points:

m = (2 - (-1)) / (0 - 1) = 3

Step 2: Write the equation using the point-slope form

Use the point-slope form and the slope from step 1, and one of the given points:

y - (-1) = 3(x - 1)

Step 3: Simplify the equation

y + 1 = 3x - 3

Step 4: Solve for y

y = 3x - 4

So, the equation of the line passing through the points (1, -1, 2) and (0, 2, -3) is y = 3x - 4.

The following is deduced from the equation f(x)=(x - 1)^3 + 5

Horizontal shift: 1 left

Vertical shift: 5 down

Vertical stretch factor: 1

Vertical compression factor: 1

Axis of reflection: -x + 6

Domain: all real numbers

Range: all real numbers

Inflection Point: (1, 5)

The vertical stretch factor is a term used in mathematics to describe the transformation that changes the height of a graph while leaving the horizontal axis unchanged. In other words, it's a factor by which the y-values of a function are multiplied to produce a new, stretched or compressed version of the original graph.

The stretch factor is usually represented by the symbol "k". For example, if the equation of a function is y = f(x), then the equation of its vertically stretched image would be y = k * f(x). A positive value of k stretches the graph upward, while a negative value of k compresses the graph downward. If k > 1, the graph is stretched vertically; if 0 < k < 1, the graph is compressed vertically; if k = 1, the graph remains unchanged.

Learn more about vertical stretch factor:

https://brainly.com/question/28353408

#SPJ1

The y-coordinate of point P is 16/3, which rounded to two decimal places is approximately 5.33.

First, we need to find the coordinates of point P. Since point P partitions the directed segment AB in the part-to-part ratio of 2:4, we can use the following formula to find its coordinates:

P = (4A + 2B) / 6

Substituting the coordinates of A and B, we get:

P = (4(5,7) + 2(1,-6)) / 6

P = (20,28) + (2,-12) / 6

P = (22,16) / 6

P = (11/3, 16/3)

y-value = 5.33

learn more on segment theorem here;

https://brainly.com/question/19509993

#SPJ1

The given differential equation:

y''' − 2y'' + y' = 2 − 24ex + 40e5x,

y(0) = 1/2, y'(0) = 5/2, y''(0) = −11/2

Therefore, the next solution is 13/2

Differential Equation:

In mathematics, a differential equation is an equation relating one or more unknown functions to their derivatives. In applications, functions usually represent physical quantities, derivatives represent rates of change, and differential equations define the relationship between them. These relationships are common.

Now,

Given differential equation is

y''' - 2y'' +y' = 2- 24eˣ +40e⁵ˣ                 ------------ (1)

Auxiliary equation is m³ - 2m² +2m = 0

Now,

   m(m² - 2m +2) = 0

⇒ m(m-1)² = 0

Therefore, m = 0,1,1

Therefore,

[tex]y_{c} = c_{1}+ c_{2} e^{x} + c_{2}x e^{x}[/tex]

Now, we have to find the particular solution by method of undetermined coefficient.

   [tex]y'_{y} = a + b(x^{2} e^{x} +2xe^{x} ) +5ce^{x}[/tex]

⇒ [tex]y''_{p} = a + bx^{2} e^{x} +2bxe^{x} +5ce^{x}[/tex]

⇒ [tex]y''_{p} = b(x^{2} e^{x} +2xe^{x}) + 2b(ex^{x}+ e^{x} +25ce^{x}[/tex]

⇒ [tex]y'''_{p} = bx^{2} e^{x} +6bxe^{x} +6be^{x} +125ce^{5x}[/tex]

Putting these values in differential equation (1), we get:

y'''(0) = 13/2

Complete Question:

Solve the given initial-value problem. y''' ? 2y'' + y' = 2 ? 24ex + 40e5x, y(0) = 1 2 , y'(0) = 5/ 2 , y''(0) = ? 13/ 2

Learn more about Differential Equation:

https://brainly.com/question/16663279

#SPJ4

7 nickels is 7/5, thus 7 nickels to 47 dime is 1.4 dime to 47 dime.

When both terms are multiplied by their biggest common factor, 1.4 dime, the ratio can be simplified to its simplest form: 47 dimes = 14: 470

The ratio of quantity, amount, or size of two or more items is known as proportion. It is the indicated quotient of two mathematical expressions.

"1 to 2" is the way to write the ratio 1: 2. Accordingly, of the total of 3, there is one component that is worth 1 and another part that is worth 2. Changing a part-to-part ratio to a fraction To get the whole, add the ratio terms. The denominator should be this.

To know more about Ratio visit:

https://brainly.com/question/29343644

#SPJ1

In reference to the given focus and directrix, the standard form of the equation of the parabola is (x - 3)² = 12y.

The standard form of the equation of a parabola with a horizontal axis of symmetry and a focus at (p, q) is:

(x - p)² = 4c(y - q)

where, c is the distance from the focus to the vertex.

In this case, the focus is at (3,0), which means that p = 3 and q = 0. The directrix is at x = -3, which means that the vertex is at the midpoint between the focus and the directrix, which is (0,0). The distance from the vertex to the focus (or from the vertex to the directrix) is c = 3.

Substituting these values into the standard form equation, we get:

(x - 3)² = 4(3)(y - 0)

Simplifying, we get:

(x - 3)² = 12y

So the standard form of the equation of the parabola is (x - 3)² = 12y.

To know more about the equation of the parabola, visit: https://brainly.com/question/11911877

#SPJ1

Answer:

29 feet by 40 feet to get a viable dimension for the goats pen

The total amount of interest that Alvin paid over the course, guven the value of the student loan and the interest rate is $ 6, 185

To find the interest paid, you need to find the total amount that Alvin paid in the 10 years that he was paying.

To do this, you first need to find the monthly payments. This will be an annuity as the amount will be the same throughout the student loan payment period.

The amount would be :

Student loan value = Amount x Present value interest factor of annuity, 120 periods, 4. 4 % / 12

The periods are :

= 10 years x 12 months

= 120 months

The amount is:

26, 000 = Amount x 96.939576551857

Amount = 26, 000 / 96.939576551857

Amount = $ 268. 21

The total paid over the 10 years is :

= 268. 21 x 120 months

= $ 32, 184. 9972

The interest is :

= 32, 184. 9972 - 26, 000 loan amount

= $ 6, 185

Find out more on interest at https://brainly.com/question/11686424

#SPJ1

Answer:

The fraction 14/16 is greater than 7/8.

Step-by-step explanation:

A sorting algorithm is defined as an algorithm that sorts the elements of a list. The most commonly used sequences are numerical sequence and lexicographical sequence, ascending or descending.

A sorting algorithm is used to reorder an array or list of elements according to an element comparison operator. Comparison operators are used to define a new order of elements in that data structure. Consider example, The above list of characters is sorted in ascending order by their value. That is, characters with lower values are placed before characters with higher values. It is important in real life because it supports the development of the scientific concept that things can be owned and organized into distinct groups (e.g. creatures, cars, weather types, etc.). We will now discuss some real-world examples of using sorting algorithms.

1) Your phone's contact list is sorted. This means that your data is organized in this way so you can easily access the contacts you want from your phone. That is, "I ordered."

2) Paper sorting : Imagine a teacher sorting students' work alphabetically by student name. This type of operation is similar to the functionality of sorting algorithms such as bucket sort. Sorting is more efficient process.

3) Traffic lights : Traffic lights are a good example of how algorithms are used in the real world around us. Next time you get stuck in a car at a red light, think about the algorithm that traffic lights run." Most traffic lights don't automatically switch between green, yellow, and red. This algorithm is a well-established turn-by-turn algorithm that directs traffic correctly. It's in order (it may not seem that way when you're sitting at a red light).

To learn more about sorting algorithm, refer:

https://brainly.com/question/14698104

#SPJ4

Answer:

Step-by-step explanation:

We can use algebra to solve for the unknown number. Let's call the number "x".

The equation can be written as:

9 + x * (-7) = -19

Expanding the product on the left side:

9 + -7x = -19

Subtracting 9 from both sides:

-7x = -28

Dividing both sides by -7:

x = 4

So the number x is 4.

ΔXVZ and ΔXWY are similar by SAS property of similarity.

We have,

ΔXVZ and ΔXWY

XW/WV = XY/YZ

15/20 = 27/36

3/4 = 3/4

The ratio of two pairs of corresponding sides is equal. ______(1)

And,

m∠XWY = m∠XVZ = 90

The included angle of the two triangles is equal. ________(2)

Now,

From (1) and (2),

ΔXVZ and ΔXWY are similar.

By SAS property of similarity.

Thus,

ΔXVZ and ΔXWY are similar by SAS property of similarity.

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ4

The measure of the remaining sides of a quadrilateral will be 4.8 cm, 3.6 cm, and 6.4 cm.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

The sides of the quadrilateral measure 12cm, 9cm, 16cm, and 20cm. The longest sides of a similar quadrilateral measure 8cm. Then the scale factor is given as,

SF = 8 / 20

SF = 0.40

Then the other sides of the quadrilateral are given as,

⇒ 0.40 x 12

⇒ 4.8 cm

⇒ 0.40 x 9

⇒ 3.6 cm

⇒ 0.40 x 16

⇒ 6.4 cm

The measure of the remaining sides of a quadrilateral will be 4.8 cm, 3.6 cm, and 6.4 cm.

More about the dilation link is given below.

https://brainly.com/question/2856466

#SPJ1

Answer:

[tex]\frac{-1}{5}[/tex] [tex]y^{2}[/tex] - [tex]\frac{1}{2}[/tex] y + [tex]\sqrt{2}[/tex]

Step-by-step explanation:

Answer:

[tex]-\frac{y^3}{10} +\frac{y^2}{5} -\frac{y}{4} -\sqrt{2}[/tex]

Step-by-step explanation:

Answer: (a) -6x²y

Step-by-step explanation:

[tex]\frac{-18x^{3}y^{2} }{3x^{2} y}[/tex]
X to the power of 2 should be cancelled from the top and bottom, which leads to:
[tex]\frac{-18xy^{2} }{3y}[/tex]
Then Y to the power of 1 should be cancelled from top and bottom (since it can go into both), which leads to:

[tex]\frac{-18xy}{3}[/tex]
Then find the highest common factor (which is 3), and cancel it out from the top and bottom, which leads to:
[tex]\frac{-6xy}{1}[/tex]
which equals to
-6x²y (a)

Answer:

84

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

We can first convert 96 into a fraction.

Now that we know this, we can solve for the number of shrubs. If we know that at least [tex]\frac{7}{8}[/tex] of the shrubs should survive, we can use an equation that looks like this:

Solving the equation:

Therefore, the minimum number of shrubs that should survive is 84.

Answer: x ≅ 11.2

Step-by-step explanation:

We can set up two equations:

Let y = measure of <BAD = measure of <CAD

then:

sin y = x/23

sin y = (20-x)/18

Since both of these are sin y, we can set them equal to each other:

x/23 = (20-x)/18

.: 18x = 460 - 23x

41x = 460

.: x ≅ 11.2

Answer:

x = 11.2

--------------------

Use angle bisector theorem. It states that:

Apply this to the given triangle:

Cross-multiply and solve for x:

The least possible total number of cookies are 21.

A total is a whole or complete amount, and "to total" is to add numbers or to destroy something. In math, you total numbers by adding them: the result is the total.

Given that, Bailey is making festive cookie bags. She tried to split all her cookies evenly by putting 15 per bag, but the last bag had only 14 cookies.

Here, 15+14=29

29 is our first number. Bailey cannot evenly split the cookies into each bag with that amount of cookies, so we must move on to the next number.

Now, 10+9+2=21

21 can be divided 3 times by 7. Now we know the least amount of cookies total, is 21.

Therefore, the total number of cookies are 21.

Learn more about the total here:

https://brainly.com/question/15842940.

#SPJ9