Based on the calculations, the interquartile range of a data set is equal to 53.
In order to determine the statistical measures or the five-number summary, we would arrange the data set in an ascending order:
6,8,9, 30, 30, 36, 38, 54, 64, 70, 75, 81, 93
Based on the data set, the first quartile can be calculated as follows;
First quartile = [(n + 1)/4]th term
First quartile = (13 + 1)/4
First quartile = 3.5th term
First quartile = (30+9)/2
First quartile = 19.5.
For the third quartile, we have:
Third quartile = [3(n + 1)/4]th term
Third quartile = 3 × 3.5th term
Third quartile = 10.5th term
Third quartile = (75+70)/2
Third quartile = 72.5
Mathematically, the interquartile range of a data set is the difference between third quartile (Q₃) and the first quartile:
Interquartile range of data set = Third quartile - First quartile
Interquartile range of data set = 72.5 - 19.5
Interquartile range of data set = 53.
The value of x that satisfies the equation 4/3=x+10/15
For this case we must find the value of "x" that meets the following equation:
[tex]\frac {4} {3} = x + \frac {10} {15}[/tex]
We subtract [tex]\frac {10} {15}[/tex] on both sides of the equation:
[tex]\frac {4} {3} - \frac {10} {15} = x\\\frac {15 * 4-3 * 10} {3 * 15} = x\\\frac {60-30} {45} = x\\- \frac {30} {45} = x[/tex]
We simplify:
[tex]x =\frac {6} {9}=\frac{2}{3}[/tex]
Finally, [tex]x =\frac {2} {3}[/tex]
Answer:
[tex]x =\frac {2} {3}[/tex]
Jamal bought 2 pounds of red apples and 3.2 pounds of green apples from a grocery store, where both kinds of apples are $1.65 a pound. How much did Jamal spend on apples? PLEASE HELP :(
In this question, we're trying to find out how much Jamal spent on apples.
We know that he bought 2 pounds of red apples and 3.2 pounds of green apples.
We also know that each pound of apples, no matter what kind it is, are $1.65 a pound.
In order to find the total cost of these apples, we would need to multiply the amount of pounds he has to the cost per pound.
Solve:
2 · 1.65 = 3.30
3.2 · 1.65 = 5.28
Add those numbers together:
5.28 + 3.30 = 8.58
This means that Jamal spent $8.58 on apples.
Answer:
$8.58
Answer:
$8.58
Step-by-step explanation: this ok?
The hexagon is made from a rectangle and two identical triangles.
13 cm
5 cm
12 cm
Work out the area of the hexagon.
Answer:
The area of the hexagon is 108 cm².
Step-by-step explanation:
Consider the below figure attached with this question.
From the below figure we get
Length of rectangle = 12 cm
width of rectangle = 5 cm
It is given both triangles are identical.
Base of each triangle = 12cm
Height of each triangle = (13-5)/2 = 4 cm
Area of rectangle is
[tex]Area=length\times width=12\times 5=60[/tex]
Area of rectangle is
[tex]Area=\frac{1}{2}\times base\times height[/tex]
[tex]Area=\frac{1}{2}\times 12\times 4=24[/tex]
Area of one triangle 24 cm². So, area of both triangle is
[tex]2\times 24=48[/tex]
Area of hexagon = Area of rectangle + Area of both triangles
= [tex]60+48[/tex]
= [tex]108[/tex]
Therefore, the area of the hexagon is 108 cm².
By finding the areas of the rectangle and the two triangles separately and adding them together, we determine that the area of the hexagon is 125 cm².
Explanation:To find out the area of the hexagon, you would need to find the areas of the rectangle and the triangles separately, and then add them together. The rectangle's area can be calculated easily using the formula for the area of a rectangle: Length x Breadth.
Assuming the rectangular part length to be 13cm and breadth to be 5cm, area of rectangle = 13cm x 5cm = 65cm².
The two triangles appear to be right triangles. You can use the formula for the area of a right triangle: 0.5 x Base x Height.
Assuming the base and height of the triangles to be 12cm and 5 cm, therefore the area of one triangle is 0.5 x 12cm x 5cm = 30cm². Since there are two of these triangles, their combined area = 2 x 30cm² = 60cm².
Finally, combining the areas of the rectangle and triangles equals the area of the hexagon: 65cm² + 60 cm² = 125 cm².
The area of the hexagon is
125 cm²
.
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Solve equation for X by graphing -2x-3=3^x+2
A.x=-2.75
B.x=-2
C.x=-1.75
D.x=-2.5
Answer:
Option D. x=-2.5
Step-by-step explanation:
we have
[tex]-2x-3=3^x+2[/tex]
I can divide the expression above in a system of two equations
[tex]y=-2x-3[/tex] ----> equation A
[tex]y=3^x+2[/tex] ----> equation B
Solve by graphing
The solution is equal to the x-coordinate of the intersection point both graphs
using a graphing tool
The intersection point is ( -2.5,2.1)
see the attached figure
therefore
The solution is x=-2.5
Answer:
D) -2.5
Step-by-step explanation:
g(x) = (x + 2)2 what is its graph
Answer: The graph is a parabola facing up ,
Step-by-step explanation:
Since the coefficient of [tex]x^{2}[/tex] is positive , then the graph is a parabola facing up.
The minimum point is at x = -2 ( using the formula for calculate vertex , x = [tex]\frac{-b}{2a}[/tex] )
And the y - intercept = 4
standard form Ax+By=C
x-3y=-6
Explanation:
The equation is already in standard form.
A is 1. The number 1 is often unwritten.
B is -3. The negative or positive sign is included with the equation.
C is -6. (If using this for the quadratic formula, c is actually 6 because the equation should equate to 0).
I don’t understand this help please
Answer:
9
Step-by-step explanation:
The first simplification we can make is to replace 6^0 with 1.
The first rules of exponents we can apply are ...
(a·b)^c = a^c·b^c . . . . . . similar to the distributive property
(a^b)^c = a^(b·c)
This reduces your expression to ...
[tex](2^8\cdot 3^{-5})^{-2}\cdot\left(\dfrac{3^{-2}}{2^3}\right)^4\cdot 2^{28}=2^{8(-2)}\cdot 3^{-5(-2)}\cdot\dfrac{3^{-2(4)}}{2^{3(4)}}\cdot 2^{28}\\\\=2^{-16}\cdot 3^{10}\cdot\dfrac{3^{-8}}{2^{12}}\cdot 2^{28}[/tex]
Now we can apply another two rules of exponents:
(a^b)(a^c) = a^(b+c)
1/a^b = a^-b
Using these, we have ...
[tex]=2^{-16-12+28}\cdot 3^{10-8}\\\\=2^0\cdot 3^2\\\\=1\cdot 9=9[/tex]
The value of the expression is 9.
Answer question (picture below) and show work please
Answer:
[tex]A(x)=7x^2-2x+10[/tex]
Step-by-step explanation:
Long Division
The polynomial long division implies the sequential division of each term of the dividend polynomial by the terms of the divisor polynomial. The procedure is a well-know sequence of steps from which there are two outputs: the quotient and the remainder.
We have two mathematical models, one for the total number of visitors who went to a theme park:
[tex]F(x)=126x^3+279x^2+90x+450[/tex]
The other for the number of shows played at the theme park in the same period
[tex]G(x)=18x+45[/tex]
Where x is the number of days since October 1. We are required to find the expression for the average number of visitors per show. It comes by dividing F(x) by G(x). We must perform a long division as shown below.
The average number of visitors per show is
[tex]A(x)=7x^2-2x+10[/tex]
For example, day 5
[tex]A(5)=7\ 5^2-2(5)+10=175[/tex]
There were 175 visitors per show (on average)
Which equation is y = 2x2 – 8x + 9 rewritten in vertex form?
A. y = 2(x – 2)2 + 9
B. y = 2(x – 2)2 + 5
C. y = 2(x – 2)2 + 1
D. y = 2(x – 2)2 + 17
Answer:
C
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square
Given
y = 2x² - 8x + 9
The coefficient of the x² term must be 1, so factor out 2 from 2x² - 8x
y = 2(x² - 4x) + 9
To complete the square
add/ subtract ( half the coefficient of the x- term)² to x² - 4x
y = 2(x² + (- 2)x + 4 - 4) + 9
= 2(x - 2)² - 8 + 9
= 2(x - 2)² + 1 → C
The given quadratic equation y = 2x^2 - 8x + 9 can be rewritten into vertex form by completing the square, resulting in y = 2(x - 2)^2 + 5.
Explanation:The given equation y = 2x2 - 8x + 9 can be rewritten in vertex form by completing the square for the -8x term. The vertex form of a quadratic equation is y = a(x - h)2 + k, where (h,k) is the vertex of the parabola.
First, we need to divide the coefficient of the x term, which is -8, by 2 to get -4. Then, we square this result to get 16.
This should be inserted into the equation to complete the square, however, we must also take it out again in order to not change the equation. The new equation will be y = 2(x2 - 4x + 16) - 2*16 + 9 = 2(x - 2)2 + 5.
The correct answer then is B. y = 2(x - 2)2 + 5
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Which pair of triangles MUST be similar?
a.) Triangles 1 and 2 they each have a 40 degree angle.
b.) Triangle 7 has a 40 degree angle and a 35 degree angle. Triangle 8 has a 40 degree angle and a 105 degree angle.
c.) Triangle 5 has a 25 degree angle and a 75 degree angle. Triangle 6 has a 25 degree angle and a 70 degree angle.
Answer:
b.) Triangle 7 has a 40 degree angle and a 35 degree angle. Triangle 8 has a 40 degree angle and a 105 degree angle.
Step-by-step explanation:
b.) triangle 7's 3 angles: 40° , 35° and 180° - 40° - 35° = 105°
triangle 8: 40° , 105° and 180° - 40° - 105° = 35°
they have all 3 corresponding angles congruent, triangle and triangle 8 is similar (AAA)
Answer:
b.) Triangles 7 and 8 are similar.
Step-by-step explanation:
If triangles have the same angle measurements, they are similar
If we have two angles, we can find the third by using the equation 180 (total of all angles in any triangle) - angle 1 -angle 2 = angle 3.
Let's set up this value with values from triangle 7.
180-40-35=angle 3
105=angle 3
Thus, the angle measurements of triangle 7 are 35, 40, anf 105.
Let's set up the same equation with value for triangle 8.
180-40-105=angle 3
35=angle 3
Thus, the angle measurements of triangle 8 are 35, 40, anf 105, the same as those of triangle 7, meaning the two triangles are similar.
What is the area of a trapezoid with height 14xy^2 cm, a base with length 3x^2 cm, and another base length 7x^2 cm?
Answer:
[tex]\therefore \textrm{Area of Trapezoid }= 70x^{3}y^{2}\ cm^{2}[/tex]
Step-by-step explanation:
Given:
Shape is of Trapezoid
Height = 14xy² cm
Length 1 = 3x² cm ( one Parallel side)
Length 2 = 7x² cm ( other Parallel side)
To Find:
Area of Trapezoid = ?
Solution:
We know that
[tex]\textrm{Area of Trapezoid }= 0.5(length\ 1+length\ 2)Height[/tex]
substituting the given values we get
[tex]\textrm{Area of Trapezoid }= 0.5\times(3x^{2}+7x^{2})\times 14xy^{2}[/tex]
[tex]\textrm{Area of Trapezoid }= (10x^{2})7xy^{2}[/tex]..((x^{a}x^{b}=x^{(a+b)})
[tex]\therefore \textrm{Area of Trapezoid }= 70x^{3}y^{2}\ cm^{2}[/tex]
through(-4,3), slope=-2/3
Answer:
y = -2/3 x + 1/3
Step-by-step explanation:
Use the slope-intercept linear formula: y = mx + b
x and y represent point on the line
m is the slope
b is the y-intercept
The equation of the line requires "m" and "b". We already have "m".
Substitute point (-4, 3) and slope -2/3 into the formula. x=-4; y=3; m=-2/3. Find b by isolating the variable.
y = mx + b
3 = (-2/3)(-4) + b Simplify
3 = 8/3 + b Subtract 8/3 from both sides
b = 1/3
Put b = 1/3 into the formula.
y = -2/3 x + 1/3
7w/4+3=9w/10+6
I really need help on this
Answer:
w=3 9\17
Step-by-step explanation:
Jennie's car gets 32.4 miles per gallon on the highway. If her car's fuel tank holds 12.7 gallons, how far can she drive on one tank of gas?
Multiply the miles per gallon by the total gallons:
32.4 x 12.7 = 411.48 total miles.
Answer:
411.48
Step-by-step explanation:
411.48
Giulia is playing a game with 6 cards: 4 kings, 1 queen, and 1 jack. She draws 1 card out of the stack of cards, replaces it, and then draws another card.
What is the probability that she will draw a king and then a jack, P(king, then jack)?
Answer: 1/9
Step-by-step explanation:
Total number of cards = 6
Probability = required outcome/ all possible outcome
number of kings=4
number of jack=1
Probability of drawing a king = 4/6
probability of drawing a jack = 1/6
Probability of drawing a king and then a jack is p(king and jack) = p(king) × p(jack) = 4/6 × 1/6 = 4/36
= 1/9
Answer:
1/9
thats all
Step-by-step explanation:
The perimeter of a rectangle with a length of 10 cm is 32 cm.
What is the width of the rectangle?
A. 6 cm
B. 10 cm
C. 12 cm
Answer:
32=2(10+x)
32=20+2x
2x=12
x=6
therefore breadth is 6 cm
area=l×b
10×6=60
Step-by-step explanation:
Roots of -2x^2 -6x+5=0
For this case we have the following quadratic equation:
[tex]-2x ^ 2 -6x + 5 = 0[/tex]
Where:
[tex]a = -2\\b = -6\\c = 5[/tex]
The roots will be given by the following formula:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
Substituting the values we have:
[tex]x = \frac {- (- 6) \pm \sqrt {(- 6) ^ 2-4 (-2) (5)}} {2 (-2)}\\x = \frac {6 \pm \sqrt {36 + 40}} {- 4}\\x = \frac {6 \pm \sqrt {76}} {- 4}\\x = \frac {6 \pm \sqrt {2 ^ 2 * 19}} {- 4}\\x = \frac {6 \pm2 \sqrt {19}} {- 4}\\x = \frac {3 \pm \sqrt {19}} {- 2}[/tex]
We have two roots:
[tex]x_ {1} = \frac {-3- \sqrt {19}} {-2}\\x_ {2} = \frac {-3+ \sqrt {19}} {2}[/tex]
Answer:
[tex]x_ {1} = \frac {-3- \sqrt {19}} {2}\\x_ {2} = \frac {-3+ \sqrt {19}} {2}[/tex]
Higher Order Thinking Jamie says
that 19 - 10 is equal to 20 – 10
because both use subtraction. Is Jamie
correct? Explain why or why not.
**1st grade question**
Answer: Jamie is incorrect
Step-by-step explanation:
The same number 10 is subtracted from both numbers 19 and 20. There result will only be the same if both numbers are equal.
We compare both numbers;
19 and 20
On the number line 19 comes before 20, which means 20 is greater than 19. Hence the result of subtracting the same number 10 from both of them cannot be the same.
So Jamie is incorrect.
Answer:
she is wrong 19-10 equals to 9
Step-by-step explanation:
you subtract 19 from 10 and get 9:)
Select the correct answer from each drop-down menu.
In the figure, AC and BD bisect each other. Complete the statements to prove that quadrilateral ABCD is a parallelogram.
Reason options for 3rd statement:
•Alternate Interior Angles Theorem
•Vertical Angles Theorem
•Alternate Exterior Angles Theorem
Reason options for 9th statement:
•Converse of Alternate Exterior Angles Theorem
•Converse of Alternate Interior Angles Theorem
•Converse of Corresponding Angles Theorem
•Converse of Exterior angle theorem
Answer:1Vertical angles theoram
Step-by-step explanation:2 coverse of alternate interior angles theoram
Answer:
1. Reason options for 3rd statement:
Alternate Interior Angles Theorem
2.Reason options for 9th statement:
Converse of Alternate Interior Angles Theorem
Step-by-step explanation:
what is 5 more than the sum
Answer:
5 more of the sum would be + 5 to the final answer you are adding
Step-by-step explanation:
1. Determine if the set of ordered pairs is a relation or a function.
{(0,0), (0, 2), (0, 3), (0,4)}
Answer:
This is just a relation.
Step-by-step explanation:
It is easy to see if a set of ordered pairs is a relation or a relation that is a function.
If all the points are distinct, then you just have to look at the [tex]x[/tex]-coordinates.
If all the [tex]x[/tex]-coordinates are different, then it is a function. Otherwise, it is a just a relation.
So this cannot be a function because there is at least two different points that have [tex]x=0[/tex].
Which expression correctly represents eight times the difference of 4 and a number
The correct mathematical expression for eight times the difference of 4 and a number is 8(4 - n), where 'n' is the variable representing the number.
Explanation:The expression that represents eight times the difference of 4 and a number can be written as 8(4 - n), where 'n' represents the number in question. In this expression, '4 - n' is the difference between 4 and the number, and by multiplying this difference by eight, we are following the order of operations where the subtraction within the parentheses is performed first before the multiplication.
Grace diides 6 cups of fruit juice equally among 8 freinds two of her freinds do not drink the juice how much is left over?
Answer:
Amount of juice left over is 1.5 cups.
Step-by-step explanation:
Given:
Amount of juices Grace has = 6 cups
Number of friends = 8
She divides the juice equally among her friends.
Now we will first find Amount of juice each friend will have.
Amount of juice each friend will get can be calculated by dividing Amount of juices with total number of friends.
Framing in equation form we get;
Amount of juice each friend will have = [tex]\frac{6}{8}= \frac{3}{4}\ cups \ \ \ OR \ \ \ \ 0.75\ cups[/tex]
Number of friends who do not drink = 2
Amount of juice left will be equal to Number of friends who do not drink multiplied by Amount of juice each friend will have.
Framing in equation form we get;
Amount of juice left = [tex]2\times \frac{3}{4} = \frac{3}{2} \ cups \ \ \ \ OR \ \ \ \ 1.5\ cups[/tex]
Hence Amount of juice left over is 1.5 cups.
Donte is 138 centimeters tall . This is three times the height of his dog.what is the height of his dog
Answer:
46 centimetres tall
Step-by-step explanation:
Since Donte is 138cm tall and his height is three times that of his dog; his dog's height is 138cm/3 = 46cm tall.
Therefore, Donte's dog is 46cm tall.
how many solutions does this equation have -2x+9-3x=-5x+3
Answer:
There is No Solution for the equation.
Step-by-step explanation:
Given:
[tex]-2x+9-3x=-5x+3[/tex]
We need to find number of solutions for above equation.
Now Solving the equation we get;
[tex]-5x+9=-5x+3[/tex]
Now adding both side by 5x we get;
[tex]-5x+9+5x=-5x+3+5x\\\\9=3[/tex]
Which can't be true.
Hence There is No Solution for the equation.
What is the least common multiple of 2x3x5x7 and 2x3x3x5
Answer:
6 × 35
2×3×5×7
6 × 15
2×3×3×5
So your least common multiple is 2
Answer: 2
Step-by-step explanation:
Answer:
6 × 35
2×3×5×7
6 × 15
2×3×3×5
So your least common multiple is 2
PLEASE SHOW ALL WORK!
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An amusement park charges admission plus a fee for each ride. Admission plus four ride cost $22. Admission plus seven ride cost $31. What is the charge for admission and the cost for each ride
Answer:
Admission fee charged = $3
Cost of each ride = $10
Step-by-step explanation:
Let admission fee charged by amusement park in dollars be =[tex]x[/tex]
Let cost of each ride in dollars be =[tex]y[/tex]
Given:
Admission plus four rides cost $22
If each ride cost in dollars = [tex]y[/tex]
Cost of 4 rides in dollars will be = [tex]4y[/tex]
So, the total cost in dollars will be given as =[tex]x+4y[/tex]
So, we have
[tex]x+4y=22[/tex]
Admission plus seven ride cost $31.
If each ride cost in dollars = [tex]y[/tex]
Cost of 7 rides in dollars will be = [tex]7y[/tex]
So, the total cost in dollars will be given as =[tex]x+7y[/tex]
So, we have
[tex]x+7y=31[/tex]
So, we have the system of equation as:
A) [tex]x+4y=22[/tex]
B) [tex]x+7y=31[/tex]
Solving the system by elimination method.
Eliminating [tex]x[/tex] by subtracting equation A from B.
[tex]x+7y=31[/tex]
- [tex]x+4y=22[/tex]
- - - [Sign of each term of subtract-ant gets reversed]
-----------------------------
[tex]3y=9[/tex]
Dividing both sides by 3.
[tex]\frac{3y}{3}=\frac{9}{3}[/tex]
∴ [tex]y=3[/tex]
Plugging in [tex]y=3[/tex] in equation A.
[tex]x+4(3)=22[/tex]
[tex]x+12=22[/tex]
Subtracting both sides by 12.
[tex]x+12-12=22-12[/tex]
∴ [tex]x=10[/tex]
Thus, admission fee charged = $3
Cost of each ride = $10
type the outputs of these ordered pairs from greatest to least:(-1,2),(-3,-1),(6,0),(-1,4)
Answer:
4,2,0,-1
Step-by-step explanation:
Let
x ----> the independent variable or input value
y ----> the dependent variable or output value
we have the ordered pairs
(-1,2),(-3,-1),(6,0),(-1,4)
The input values are -1,-3,6,-1
The output values are 2,-1,0,4
Orders the output values from greatest to least
4>2>0>-1
therefore
4,2,0,-1
Answer:
4,2,0,-1
hope this helps
Savannah and her children went into a grocery store and she bought $22 worth of
peaches and mangos. Each peach costs $1.75 and each mango costs $1.50. She bought
6 more mangos than peaches. Write a system of equations that could be used to
an peaches Write a custom of educational
determine the number of peaches and the number of mangos that Savannah bought.
Define the variables that you use to write the system.
Answer:
Step-by-step explanation:
p = peaches, m = mangos
1.75p + 1.50m = 22
m = p + 6
1.75p + 1.50(p + 6) = 22
1.75p + 1.50p + 9 = 22
1.75p + 1.50p = 22 - 9
3.25p = 13
p = 13 / 3.25
p = 4 <====== she bought 4 peaches
m = p + 6
m = 4 + 6
m = 10 <===== she bought 10 mangos
check...
1.75p + 1.50m = 22
1.75(4) + 1.50(10) = 22
7 + 15 = 22
22 = 22 (correct)
The number of peaches and the number of mangos that Savannah bought
are 4 and 10 respectively.
The variable use to write the equation is x and it is the number of peaches
Savannah and her children bought
let
the number of peaches Savannah and her children bought = x
Therefore
the number of mangoes Savannah and her children bought = x + 6
The total worth of what they bought = $22
Therefore,
1.75x + 1.50(x + 6) = 22
1.75x + 1.50x + 9 = 22
3.25x + 9 = 22
3.25x = 22 - 9
3.25x = 13
x = 13 / 3.25
x = 4
Therefore,
number of peaches bought = 4
number of mangoes bought = 4 + 6 = 10
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