Given the data set:
[tex]\lbrace57,53,53,71,73,57,61,58,78,64,54,69,56,58,49,56,53,52,82,62,61,60,71,75,60\rbrace[/tex]• You can find the Mean by adding all the values and dividing the sum by the number of values in the data set:
[tex]Mean=\frac{57+53+53+71+73+57+61+58+78+64+54+69+56+58+49+56+53+52+82+62+61+60+71+75+60}{25}[/tex][tex]Mean\approx61.72[/tex]• By definition the term for the third quartile can be found with this formula:
[tex]\frac{3}{4}(n+1)[/tex]Where "n" is the number of observations.
In this case:
[tex]n=25[/tex]Then:
[tex]\frac{3}{4}(25+1)\approx19.5[/tex]Since it is an integer, you get that the position of the terms is:
[tex]Q_3=\frac{69+71}{2}=70[/tex]Because, when you order the data set, 69 is the 19th value and 71 is the 20th value. Then, the third quartile is the average between them:
[tex]\lbrace49,52,53,53,53,54,56,56,57,57,58,58,60,60,61,61,62,64,69,71,71,73,75,78,82\rbrace[/tex]• By definition:
[tex]IQR=Q_3-Q_1[/tex]And the term position of the first quartile is found with:
[tex]\frac{n+1}{4}[/tex]You get:
[tex]\frac{25+1}{4}=6.5[/tex]Therefore, you can determine that:
[tex]Q_1=\frac{54+56}{2}=55[/tex]Then:
[tex]IQR=70-55=15[/tex]• By definition, the Five-Number Summary is:
- The minimum value:
[tex]Minimum=49[/tex]- The first quartile:
[tex]Q_1=55[/tex]- The median:
[tex]Median=60[/tex]- The third quartile:
[tex]Q_3=70[/tex]- The maximum value:
[tex]Maximum=82[/tex]Hence, the answers are:
• Mean:
[tex]Mean\approx61.72[/tex]• IQR:
[tex]IQR=15[/tex]• Five-Number Summary:
[tex]Minimum=49[/tex][tex]Q_1=55[/tex][tex]Median=60[/tex][tex]Q_3=70[/tex][tex]Maximum=82[/tex]• Third quartile:
[tex]Q_3=70[/tex]if y=3x+4 and y=2x+8, find the value of both x and y.
having that x=4, we get that
[tex]y=2\cdot4+8=16[/tex]Question #10: A pizza restaurant sells a personal square pizza (5 inch side) for $4. What should the cost of a large square pizza (12 inch side) be, so that both pizzas cost the same amount per square inch?
The per square-inch cost of the first kind of pizza is $0.16 to maintain this ratio for 12-inch side pizza the cost must be $23.04.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given,
Cost of first pizza = $4
Area = 5 x 5 = 25 square inch
Per square cost = 4/25 = $0.16
With this ratio,
Cost of 12 inches side = 12 x 12 x 0.16 = $23.04
Hence "The per square-inch cost of the first kind of pizza is $0.16 to maintain this ratio for 12-inch side pizza the cost must be $23.04".
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What is the perimeter of the figure2x + 3 inchesX- 6 inches
Perimeter of the figure = 6x - 6
Explanation:Perimeter = 2(length + width)
length = 2x + 3 inches
width = x- 6 inches
Perimeter = 2(2x + 3 + x- 6)
collect like terms in the bracket:
= 2(2x +x + 3 - 6)
= 2(3x - 3)
Expand the bracket:
Perimeter = 2 × 3x + 2× -3
Perimeter of the figure = 6x - 6
Help with number one a and b is both parts of number one
Design A. The garden is 9 ft by 12 ft.
Design B. The garden is a circle of radius 5 ft
Area of garden A:
[tex]A_A=9\times12=108[/tex]Area of garden B:
[tex]A_B=\pi\left(5\right)^2=25\pi\approx78.54[/tex]The areas are:
Design A = 108 square ft
Design B ≈ 78.54 square ft
Note: The area of garden B can also be expressed in exact form as 25π square ft
The composition of rigid motions T(10,- 27 OT(-24,4, describes the route of a limousine in a city from its starting position. Describe the route in words. Assume that the positive y-axis points north. block(s) north, and then it drives 3 block(s) west and 4 block(s) north. First the limousine drives 2 block(s) east and (Type whole numbers.)
The problem describes two operations of translation on the car. The first operation says that the car translated "10" units on the x-coordinate and "-2" units on the y-coordinate.
When translations are performed on the "x-coordinate" if they are positive, the function is moved to the left and if they are negative the function is moved to the right. When translations are performed on the "y-coordinate" if they are positive the function is moved up and if negative, the function is moved down.
Since the first translation on the x-axis was positive, then the car moved to the left 10 units, which would be "10 blocks" on the west direction. The translation on the y-coordinate was negative, so the function moved down. The car moved "2 blocks" on the south direction.
The second translation is (-24, 4). The translation on the x-axis is negative so the car is moved 24 units to the east direction. The translation on the y-axis is positve so the car is moved 4 units on the north direction.
The final answer is:
First the limousine drives 10 blocks west and 2 blocks south and then it drives 24 blocks east and 4 blocks north.
A builder is buying boxes of nails. She has $187 to spend and each box of nails costs $4. How many boxes of nails can the builder buy?42503746
To find How many boxes of nails can the builder buy divide the total she has into the cost of each box:
Then, she can buy 46 boxes of nailsThe total annual sales for Herman's Hardware Store was $1,246,135 and the total accounts receivable was $41,728. What was the average collection period to the nearestwhole day?12 days14 days18 days24 daysNone of these choices are correct.
The average collection Period formula is
[tex]\text{Average collection period=}\frac{Account\text{ receivable}}{\frac{Annual\text{ sales}}{365}}[/tex][tex]\begin{gathered} \text{Annual sales=\$1,246,135} \\ \text{Account receivable =\$41,728} \end{gathered}[/tex]Substitute the values above in the average collection period
[tex]\begin{gathered} \text{Average collection period =}\frac{41728}{\frac{1246135}{365}} \\ =\frac{41728}{3414.06} \\ =12.222 \\ \approx12days \end{gathered}[/tex]Hence the average collection period to the nearest whole day is 12 days
In which quadrant, or on which axis, does the terminal side of angle (- 100straight pi) lie?
The given angle is
[tex]\theta=-\frac{100}{\pi}[/tex]First, we have to transform this angle into degrees. We know pi=180°, so
[tex]\theta=-\frac{100}{180}=-\frac{50}{90}=-\frac{5}{9}=-0.56[/tex]The given angle is placed on the first quadrant.Assuming that the angle is starting on the positive x-axis.
Over the summer, Audrey had a job and earned $528. She spent $125.70 on a new bike and $85.09 for some new clothes. How much money does Audrey have left?
Step 1: Problem
Over the summer, Audrey had a job and earned $528. She spent $125.70 on a new bike and $85.09 for some new clothes. How much money does Audrey have left?
Step 2: Concept
Word problem on subtraction
Step 3: Method
Audrey total earning = $528
Money spent on new bike = $125.7
Money spent on new clothes = $85.09
Money left = 528 - 125.7 - 85.09
= $317.21
Step 4: Final answer
Audrey money left = $317.21
if 5 pounds of apples cost 5.50,then what is the cost of 1 pound of apples
The cost of 1 pound of apple is 1.10
Here, we want to calculate the cost of 1 pound of apples given the cost of 5 pounds
From the question;
5 pounds = 5.5
1 pound = x
Thus, we have that;
[tex]\begin{gathered} 5\text{ }\times\text{ x = 1 }\times\text{ 5.5} \\ \\ 5x\text{ = 5.5} \\ \\ x\text{ = }\frac{5.5}{5} \\ \\ x\text{ = 1.1} \end{gathered}[/tex]find the correct area
we have that the area of the semicircle is 100,530964915 m^2
[tex]\begin{gathered} A\text{ = }\frac{\pi r^2}{2} \\ =\text{ }\frac{\pi(8m)^2}{2}=\text{ }32\pi m^2 \\ =\text{ }100,530964915m^2 \end{gathered}[/tex]Now we need to find the area of the triangle, we now that the area of the non rectangle triangle is 96 m^2
[tex]\begin{gathered} A\text{ = }\frac{b\cdot h}{2}\text{ = }\frac{16m\cdot\text{ 12m}}{2} \\ =\text{ }\frac{192m^2}{2}=96m^2 \end{gathered}[/tex]So the area of the figure is 196,530964915, the answer is 196.5 m^2.
I need help with this
Ok, so
We have the following expression:
We're going to multiply all terms inside the bracket by "-x", and we obtain:
So, the answer is B.
solve for x[tex] \frac{x + 3}{2} + \frac{2x}{7} = 7[/tex]just need some help with this
Here, we are to calculate for the value of x.
We start by finding the Lowest common multiples of both fractions. The lowest common multiple of both fractions is 14
Now, we can multiply each of the terms in the question by 14. Thus, we have;
14(x + 3)/2 + 14(2x/7) = (7 * 14)
7(x + 3) + 2(2x) = 98
Opening the brackets, we have;
7x + 21 + 4x = 98
Collect like terms;
7x + 4x = 98 - 21
11x = 77
x = 77/11
x = 7
A survey wanted to determine if there was a relationship between the number of joggers who used a local park for exercise and the temperature outside. The data in the table display their findings.Use graphing technology to create a scatter plot of the data.What is the slope of the line of best fit and what does it mean in this context? Is it realistic?
Step 1
In order to find the slope of the line of the best fit, we must graph the points given.
Step 2
From the image above we can conclude that the equation of the line is;
[tex]y=0.410045x-2.8757[/tex]The slope is, therefore;
[tex]0.410045[/tex]The Slope (or Gradient) we call m, represents the change in y-value per unit change in x-value. In the case of this survey, the slope represents the increase in the number of joggers per degree rise in temperature.
From the calculated slope, there are about 0.4 more joggers for every degree rise in temperature. Using whole numbers to represent this, we can multiply the slope by 5:
[tex]0.4\times5=2[/tex]Therefore, there are 2 more joggers for every 5°F increase in temperature.
J is the midpoint of HK, H has coordinates (5,-3), and J has coordinates (7,3). Find the coordinates of K.The coordinates of K are
Answer:
The coordinates of K is;
[tex](9,9)[/tex]Explanation:
We want to find the coordinates of point K.
Given that J is the midpoint of HK and;
H has coordinates (5,-3)
J has coordinates (7,3).
The formula for calculating midpoint is;
[tex]\begin{gathered} x=\frac{x_1+x_2}{2} \\ y=\frac{y_1+y_2}{2} \end{gathered}[/tex]where x1 and x2 are the x coordinates of the endpoints and y1 and y2 are the y coordinates of the endpoints.
To get the coordinates of one of the endpoints, we have;
[tex]\begin{gathered} x_2=2x-x_1 \\ y_2=2y-y_1 \end{gathered}[/tex]substituting the given coordinates of the mid point and endpoint;
[tex]\begin{gathered} x_2=2(7)-5 \\ x_2=14-5 \\ x_2=9 \end{gathered}[/tex][tex]\begin{gathered} y_2=2(3)-(-3) \\ y_2=6+3 \\ y_2=9 \end{gathered}[/tex]Therefore, the coordinates of K is;
[tex](9,9)[/tex]The function h is defined below.xh (x) =2+5x-- 142x- 81Find all values of × that are NOT in the domain of h.If there is more than one value, separate them with commas.
We want to find the value of x that is not in the domain of the function;
[tex]h(x)=\frac{x^2+5x-14}{x^2-81}[/tex]The value of x that will make h undefined is the value that makes the denominator zero.
Therefore;
[tex]\begin{gathered} x^2-81=0 \\ x^2=81 \\ x=\pm9_{} \end{gathered}[/tex]Therefore, the values not in the domain is +9 and -9
what is (x + 5)(2× - 3) = 0 in expanded form??
(x + 5)(2x -3) = 0
2x² - 3x + 10x - 15 = 0
2x² + 7x - 15 = 0
Answer:
2x² + 7x - 15 = 0
question will be in picture
Consider the guven system of equations,
[tex]\begin{gathered} x-y=-1 \\ 2x+y=4 \end{gathered}[/tex]It is asked to find the correct graph which represent the solution of this system.
Logic: Find the solution and see which graph gives the same solution.
Add the equations,
[tex]\begin{gathered} (x-y)+(2x+y)=-1+4 \\ 3x+3 \\ x=1 \end{gathered}[/tex]Substitute this value in the first equation,
[tex]\begin{gathered} 1-y=-1 \\ y=1+1 \\ y=2 \end{gathered}[/tex]Thus, the given system has a unique solution (1,2).
Now, observe that only the graph given in option (c) shows the line intersecting at point (1,2).
Therefore, option (c) is the correct choice.
Simplify each expression using Product to a Power Property a. (9a)^2 b. ( 3x)^2
1) Let's simplify those expressions making use of exponents rules:
[tex](9a)^2=81a^2[/tex]Note that the exponent outside the parenthesis is 'distributed' over each term inside.
2) Similarly for the second expression we can state that:
[tex](3x)^2=9x^2[/tex]how do you dilate with a scale factor of -1/2Coordinates (-2,8)
Multiply the coordinates by the scale factor.
(-2,8) = (-2x-1/2, 8x-1/2) = (1,-4)
Solve for t and graph the solution.|t+ 4| < 2
The solution to the inequality is (-6, -2). The graph of the solution is attached below.
We are given an inequality. The inequality consists of a variable "t" and it also uses the modulus function. A function connects an input with an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input. The inequality is |t + 4| < 2. We can solve the inequality by expanding the modulus operator. The inequality becomes -2 < (t + 4) < 2. Now we will subtract 4 from all the sides in the inequality. The inequality is solved as -6 < t < -2. The interval notation for the solution is (-6, -2). The graph is attached below.
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The lines represented by the equations y = 1/2x-8 and 2y+4x=10
The first equation is in slope-intercept form but the second equation is not. Therefore, our first step is to bring 2y+4x=10 into slope-intercept form.
Subtracting 4x from both sides gives
[tex]2y=10-4x[/tex]finally, dividing both sides by 2 gives
[tex]y=-2x+5[/tex]Now, that we have the equation in slope-intercept form, let us compare their slopes to see how they relate to each other.
The lines are perpendicular if the slope of one line is negative of the reciprocal of the other.
Now, -2 is negative of the reciprocal of 1/2. Meaning if you take the reciprocal 1/2, then multiply it by -1 you will end up with -2.
Since the slope of a negative reciprocal of each other, the lines are perpendicular.
what does ☆ equal if the symbols below represents digits 0-9?
First, let's start from the sixth equation.
Since the parallelogram divided by the circle is equal the parallelogram, it means the circle has a value of 1.
Then, from the 7th equation, the pentagon minus the arrow is equal the pentagon, it means the arrow is equal 0.
From the 8th equation, the two curved arrows summed are equal 10, so the curved arrow is equal 5.
From the 2nd and 4th equations we can find that the triangle is equal 2.
Using the value of the pentagon from the 4th equation in the 3rd one, we have that 3 * moon is equal parallelogram, so the only option is:
moon = 3, pentagon = 6, parallelogram = 9.
From the 1st equation, the square is equal 8.
Finally, from the 5th equation, the arrow with circle is equal 7.
So we have:
pentagon = 6
parallelogram = 9
moon = 3
triangle = 2
arrow = 0
curved arrow = 5
arrow with circle = 7
circle = 1
square = 8
So the star is the missing algarism: 4
Options for all the three boxes are:neither student, Becky and Laura
The parent cosine function is given to be:
[tex]f(x)=\cos (x)[/tex]The graph of this function is shown below:
Laura's Function:
Laura's function is given to be horizontally compressed by a factor of 1/3 and reflected over the x-axis.
The rule for horizontal compression by a factor of 1/a is given to be:
[tex]f(x)\Rightarrow f(\frac{1}{a}\cdot x)[/tex]and the rule for reflection over the x-axis is given to be:
[tex]f(x)\Rightarrow-f(x)[/tex]Therefore, Laura's function will be:
[tex]f(x)=-\cos (3x)[/tex]The graph of the function will be:
Becky's Function:
Becky's function is given to be:
[tex]f\mleft(x\mright)=3\cos \mleft(x-\pi\mright)[/tex]The graph is given to be:
ANSWERS:
BECKY's GRAPH is the FIRST GRAPH
The SECOND GRAPH belongs to NEITHER
LAURA's GRAPH is the THIRD GRAPH
The diameters of ball bearings are distributed normally. The mean diameter is 125 mm and the standard deviation is 3 mm. Find the probability that the diameter of a selected bearing is greater than 127 mm. Round your answer to four decimal places.
Explanation
Given that the mean diameter is 125 mm and the standard deviation is 3 mm. We can find the probability that the diameter of a selected bearing is greater than 127 mm below.
We will first find the z score of the given value.
[tex]z=\frac{x-\mu}{\sigma}=\frac{127-125}{3}=\frac{2}{3}=0.66667[/tex]Using the z score calculator,
[tex]P\left(x>127\right)=0.2525[/tex]Answer: 0.2525
Mrs. Walsh assigned 16 worksheets each month, how many did she assign over 4 montns?
Data Input
Mrs. Walsh assigned 16 worksheets each month
Procedure
To calculate the number of worksheets we need to multiply the number of months by the number of worksheets per month
Total = 16*4 = 64 Worksheets
a tree that is 20 feet tall casts a shadow 30 feet long. a girl standing next to the tree has a shadow 9 feet long. how tall is the girl?
The shadow of the three is proportional to the shadow of the girl, then we can use a rule of three:
if x is the height of the girl: 20 is to 30 is the same as x is to 9
This can be written as:
[tex]\frac{20}{30}=\frac{x}{9}\Longrightarrow x=\frac{9\cdot20}{30}=\text{ 6}[/tex]Answer:
The girl is 6 feet tall
selecting among the numbers 1 through 8 and repeating none of them, fill in the boxes below to make the sum as close as possible to one but not equal to one
We need ti fill in the boxes below, selecting among the numbers 1 through 8 and repeating none of them to make the sum as close as possible to 1 but not equal to 1.
First fraction could be 1/2
Now, the second fraction should be closer to 1/2 to make the sum as close as possible to 1, but not equal to 1.
We know that 3/6 = 1/2
So, 3/7 would be closer to 1/2
Therefore, the boxes could be filled as;
[tex]\frac{1}{2}+\frac{3}{7}[/tex]..
Please help me and explain how to find the result
A family consumes 1.2kg of rice a day
If the family have 30ky of rice
Let the number of days be x
The minimum number of days required for the amount of rice remaining not to be more than 6kg can be expressed below as
[tex]30-1.2x\le6[/tex]Solve for x by collecting like terms
[tex]\begin{gathered} 30-1.2x\le6 \\ 30-6\le1.2x \\ 24\le1.2x \\ 1.2x\ge24 \\ \text{Divide both sides by 1.2} \\ \frac{1.2x}{1.2}\ge\frac{24}{1.2} \\ x\ge20\text{ days} \end{gathered}[/tex]Hence, the minimum number of days required for the amount of rice remaining not to be more than 6kg is 20 days
unsure about this one tried and couldn’t seem to figure it out
Given:
The figure contains the rectangle and half-circle.
The perimeter of the half-circle is,
[tex]\begin{gathered} \text{Half}-\text{circle}=\pi r+d \\ r=\frac{d}{2}=\frac{8}{2}=4 \\ \text{Half}-\text{circle}=\pi(4)+8 \\ =3.14\times4+8 \\ =20.56 \end{gathered}[/tex]The perimeter of the figure is,
[tex]P=10+8+10+20.56=48.56[/tex]Answer: P = 48.56 ft.