The new average of the students is 25.368.
What is the average?In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
Given that, in a group of 24 students attending a party, the average age is 25.3 years.
A 27-year-old student joins the party.
So, the new average is (24×25.3+27)/25
= 634.2/25
= 25.368
Therefore, the new average of the students is 25.368.
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A regular hexagon whose perimeter is 12 can be inscribed in a certain rectangle, as shown. What is the area of this rectangle?
The area of this rectangle is 4 * √11 square units
What is the area of this rectangle?The perimeter of a regular hexagon can be divided equally into the lengths of its six sides.
So, the length of each side of the hexagon is 12 / 6 = 2 units.
Since the hexagon is inscribed in a rectangle, the length of the rectangle is equal to the length of two sides of the hexagon, or 2 * 2 = 4 units.
Let's call the height of the rectangle "h."
Then, the length of one side of the equilateral triangle is 2 units and the height is h, so using the Pythagorean theorem:
h^2 + (2/2)^2 = (2 * √3)^2
h^2 + 1 = 12
h^2 = 11
h = √11
So, the area of the rectangle is equal to its length multiplied by its width:
4 * √11 square units
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A health club charges a one-time sign-up fee and a monthly membership fee. The equation
�
=
37
�
+
50
y=37x+50 represents what the health club charges. Find the rate of change.
Solve for x. Justify which angle relationships
you used.
The value of x in the quadrilateral is 112 degrees and the angle relationship is vertical angles.
How to find angles in a quadrilateral?A quadrilateral is a plane figure that has four sides , and also has four corners or vertices. The sum of angles in a quadrilateral is 360 degrees. Examples of quadrilateral are parallelograms, rectangle, square, rhombus etc.
The quadrilateral above has two diagonals that intersect each other. The diagonal AC and BD intersect each other at a points.
The relationship formed are vertically opposite angles. Vertically opposite angles are congruent.
Hence, the sum of angles in a point is 360 degrees.
Let's find x as follows;
2x + 68 + 68 = 360
2x = 360 - 136
2x = 224
x = 224 / 2
x = 112 degrees.
Therefore,
x = 112 degrees
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Given: DEF
Prove: DEF is isosceles.
Both the side of triangle DEF have equal distance DF = DE. so it is isosceles triangle.
How can you demonstrate that an isosceles triangle is made up of the specified vertices?
The distance between any two of the supplied points must be the same for two pairs of the given points in order to determine whether the given points are the vertices of an isosceles triangle. We can infer that DF = DE from the DF, FE, and DE data mentioned above.
we have 3 coordinates of triangle .
D(x1,y1) = D(1 , 2)
F(X2,Y2) = F(-2 , -2)
E(X3,Y3) = E(-3 , -1)
if given triangle is isosceles triangle than distance DF = DE.
Distance between two points :-
Distance (DF) =[tex]\sqrt{((x_1 - x_2)^{2} + (y_1 - y_2)^{2})} = \sqrt{((1 + 2)^{2} + (2 +2)^{2})} = 5[/tex].
Distance (DE)= [tex]\sqrt{((x1 - x3)^{2} + (y1 - y3)^{2})}= \sqrt{((1 + 3)^{2} + (2 + 1)^{2})} = 5[/tex]
hence, both the side have equal distance DF = DE. so it is isosceles triangle.
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Assume that a national restaurant chain called BBQ builds 10 new restaurants at a cost of $1 million per restaurant. It outfits each
restaurant with an additional $400,000 of equipment and furnishings. To help partially defray the cost of this expansion, BBQ issues
and sells 200,000 shares of stock at $40 per share.
Instructions: Enter your answers rounded to 1 decimal place.
a. What is the amount of economic investment that has resulted from BBQ's actions?
b. How much purely financial investment took place?
the total economic investment by BBQ is $(10 +2=)12 million and purely financial investment accounts for $6 million.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given,a national restaurant chain called BBQ builds 10 new restaurants at a cost of $1 million per restaurant.
Economic investment is the amount of money used to increase the productivity or output of the economy. Since BBQ builds 10 new restaurants at the cost of $1 million per restaurant, the total capital investment in all restaurants by BBQ is $1 million × 10 = $10 million.
Also, the BBQ makes an additional investment of $200,000 in each restaurant to increase the productivity of restaurants. Therefore, total economic investment in all the restaurants is
$200,000 × 10 = $2,000,000.
Hence, the total economic investment by BBQ is $(10 +2=)12 million.
Financial investment by BBQ
The financial investment includes investments in bonds, shares, real estate, or any financial assets. The cost per share is $30, and the total number of shares issued is 200,000.
Thus, the total funds raised from shares are
$30 × 200,000 = $6,000,000.
Therefore, purely financial investment accounts for $6 million.
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A pump fills a pool at a constant rate. At the end of 12 minutes it has filled 3 gallons of water. Which table represents the relationship between the number of minutes and the number of gallons of water in the pool?
The table D represents the relationship between the number of minutes and the number of gallons of water in the pool.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.
Given:
A pump fills a pool at a constant rate.
At the end of 12 minutes,
it has filled 3 gallons of water.
From the given choices:
The table D represents the relationship between 12 minutes and 3 gallons of water in the pool.
Therefore, the table D is the correct table.
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The points O(4,4), P(-4,0), Q(-2,-4), and R(6,0) form quadrilateral OPQR.
On solving the provided question, we can say that none of the segments are parallel or perpendicular, and they are all different lengths. The image is a quadrilateral scalene figure.
what is quadrilateral?A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
FG: slope: -4/5, length: √41 ≈ 6.40
GH: slope: -5, length: √26 ≈ 5.10
HI: slope: -1, length: 3√2 ≈ 4.24
IF: slope: 4, length: √17 ≈ 4.12
None of the segments are parallel or perpendicular, and they are all different lengths. The image is a quadrilateral scalene figure.
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Ruby has a collection of square blocks and triangular blocks, which are lined up as shown below. She wants to have all the squares on the left and all the triangles on the right. Ruby can switch the position of any two adjacent blocks. What is the minimum number of switches that Ruby needs to make?
The minimum number of switches that Ruby needs to make would be = 39,916,800
What is permutation?Permutation is defined as the arrangement of different values of a data set into a definite order.
The total number of the shapes of the blocks are = 11
Therefore, the minimum number of switches that Ruby needs to make would be the permutation of the total number = 11*10*9*8*7*6*5*4*3*2*1 = 39,916,800.
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y=-4/5x-2 standard form
Answer:
[tex] y = - \frac{5}{4}x - \frac{5}{2} [/tex]
Step-by-step explanation:
Don't know if it's right but yeah that's what I got.
first interchange x and y second swap the the sides of the equationthird multiply both sides of the equation by 55th move the constant to the right-hand side and change its sign Divide both sides of the equation by -4The graph shows the location of the entrance to a state park. Each unit on the graph represents 1 kilometer. Rodrigo uses the graph to locate a waterfall. The waterfall is located 3 kilometers to the left and 4 kilometers down from the park entrance. Rodrigo says the ordered pair for the waterfall is (3,9). Use the drop-down menus to explain Rodrigo's error.
The location of the waterfall on the graph will be (3,1). Instead of going down down, Rodrigo goes 4 units upward direction.
How to interpret Cartesian Coordinates?Coordinates are defined as a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x-axis (horizontal) and y-axis are the two axes that make up a coordinate plane (vertical).
Given that the location of the entrance is at (6, 5).
To reach the waterfall, you need to go 3 km to the left and 4 km down from the park entrance.
The x-coordinate decreases to the left side of a point and increases to the right side of a point.
The y-coordinate decreases to a downward point and increases upward a point.
The x-coordinate of the waterfall is 6 - 3 =3
The y-coordinate of the waterfall is 5 - 4 = 1.
The coordinate that represents the location of a point is (3,1).
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Help please, this is for ib math.
The ratio of consecutive terms of the Fibonacci sequence 2/1, 3/2, 5/3, 8/5, 13/8 and so on is 0.75.
What is Fibonacci sequence?The Fibonacci series is the sequence of numbers (also called Fibonacci numbers), where every number is the sum of the preceding two numbers, such that the first two terms are '0' and '1'. In some older versions of the series, the term '0' might be omitted. A Fibonacci series can thus be given as, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, . . .
1) To represent any (n+1)th term in this series, we can give the expression as, Fₙ=Fₙ₋₁+Fₙ₋₂.
2) A sequence in which every number in the Fibonacci sequence is the sum of two numbers preceding it in the sequence.
Yes, the Fibonacci sequence written using a formula that connects successive terms of the sequence.
3) The Fibonacci sequence in nature:
A perfect example of this is the nautilus shell, whose chambers adhere to the Fibonacci sequence's logarithmic spiral almost perfectly. This famous pattern shows up everywhere in nature including flowers, pinecones, hurricanes, and even huge spiral galaxies in space.
4) The ratio of consecutive terms of the Fibonacci sequence 2/1, 3/2, 5/3, 8/5, 13/8 and so on.
Now, the ratio is 3/2 ÷ 2/1
= 3/2 × 1/2
= 3/4
= 0.75
Therefore, the ratio of consecutive terms of the Fibonacci sequence 2/1, 3/2, 5/3, 8/5, 13/8 and so on is 0.75.
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I NEED HELP
Which of the following best describes the technique used to graph the equation y = 9x + 4 using the slope and y-intercept?Mark a point at 9 on the y-axis, go up 4 and left one and mark this point.
Mark a point at 9 on the y-axis, go up 4 and left one and mark this point.
Mark a point at 9 on the y-axis, go up 4 and right one and mark this point.
Mark a point at 9 on the y-axis, go up 4 and right one and mark this point.
Mark a point at 4 on the y-axis, go down 9 and right one and mark this point.
Mark a point at 4 on the y-axis, go down 9 and right one and mark this point.
Mark a point at 4 on the y-axis, go up 9 and right one and mark this point.
Answer:
The technique used to graph the equation y = 9x + 4 using the slope and y-intercept is to mark a point at 4 on the y-axis, go up 9 and right one and mark this point. This is because the slope of the equation is 9 and the y-intercept is 4, so the graph can be plotted by starting at the y-intercept and moving up 9 units and right 1 unit. Unfortunately I need to wrap this conversation up and can only talk a little more. Is there anything you'd like to discuss before we close?
Step-by-step explanation:
PLEASE HELP !!!!!!!!!
The ages of 12 runners in a recent marathon are listed.
35, 17, 34, 14, 28, 20, 18, 15, 14, 19, 17, 31
Find the median and interpret its meaning as it relates to the runners.
The median is 18.5, and it represents the typical age of the runners.
The median is 20.5, and it represents the typical age of the runners.
The median is 21.5, and it represents the difference in the lowest and highest ages of runners.
The median is 23.5, and it represents the difference in the lowest and highest ages of runners.
Question 10(Multiple Choice Worth 2 points)
The median and its meaning as it relates to the runners include the following: A. The median is 18.5, and it represents the typical age of the runners.
What is a median?In Mathematics, a median can be defined as the middle number (center) of a sorted data set, which is when the data set is either arranged in a descending order from the greatest to least or an ascending order the least to greatest.
How to calculate the median age?First of all, we would sort the observations (data set) from the least to greatest as follows:
14,14,15,17,17,18,19,20,28,31,34,35
The median for 12 observations is the average of the 6th and 7th number:
Median = (18 + 19)/2
Median = 37/2
Median = 18.5.
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The median and its meaning as it relates to the runners include the following: A. The median is 18.5, and it represents the typical age of the runners.
What is a median?
In Mathematics, a median can be defined as the middle number (center) of a sorted data set, which is when the data set is either arranged in a descending order from the greatest to least or an ascending order the least to greatest.
How to calculate the median age?
First of all, we would sort the observations (data set) from the least to greatest as follows:
14,14,15,17,17,18,19,20,28,31,34,35
The median for 12 observations is the average of the 6th and 7th number:
Median = (18 + 19)/2
Median = 37/2
Median = 18.5.
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Find p and q , if X1 = 23, n1 = 43, X2 = 29, and n2 = 52.
The values:
[tex]\bar p[/tex] = 0.547.
And [tex]\bar q[/tex] = 0.453.
What is the mean?The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
Given:
The values,
X₁ = 23,
X₂ = 29,
n₁ = 43,
And n₂ = 52.
Now, using the formula for mean,
[tex]\bar p[/tex] = (X₁ + X₂) / (n₁ + n₂)
=(23 + 29) / (52 + 43)
= 0.547.
And [tex]\bar q[/tex] = 1 - [tex]\bar p[/tex] = 1 - 0.547 = 0.453.
Therefore, all the required values are given above.
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Find the equation, in standard form, of the line passing through the point (0,-3) and parallel
to x-5y = 75.
The equation in standard form when the line is passing through point (0,-3) and parallel to x - 5y = 75 is 5y - x + 15
What is equation of a straight line ?
Equation of straight line as follows , y = mx + b
where m is the slope of line.
Given equation ,
x - 5y = 75
and the points are (0,-3)
First lets find the slope of a line
we get,
x - 5y = 75
5y = x - 75
y = 1/5 x - 15
m = 1/5
Here the point (0,-3) and slope m = 1/5
Therefore,
The equation of the line
y + 3 = 1/5 (x-0)
5y + 15 = x
5y - x + 15
Therefore, The equation in standard form when the line is passing through point (0,-3) and parallel to x - 5y = 75 is 5y - x + 15
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You use a coordinate plane to design a poster for the Florida Strawberry Festival. The vertices of the design are A(2,4),B(34,4), C(2,-44) , and D(34,-44) . The coordinates are measured in inches. Find the least number of square yards of paper you need to make the poster.
The least number of square yards of paper required to make the poster is 11 square yards.
How did we get the value?The area of a rectangle can be found by multiplying the length of its sides. To find the length and width of the rectangle, we can subtract the x and y values of the opposite vertices.
The length of the rectangle is 34 - 2 = 32 inches, and the width is -44 - 4 = -48 inches. We will have to make the width positive to find the area, so the area is 32 * 48 = 1536 square inches.
Since 1 square yard is equal to 144 square inches, we need to divide 1536 by 144 to find the number of square yards: 1536 / 144 = 10.67 square yards.
Therefore, the least number of square yards of paper required to make the poster is 11 square yards.
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5 inches : 2 feet. If the gym is 170 inches wide in the drawing, how wide is the actual gym?
5 in :2ft
170 in :68ft
A person cycles from their home to a library which is 8 kilometers away. It takes them 20 minutes to reach the library. They stay there for 30 minutes to read, and then
walk to their friend's home which is 4 kilometers from the library and reach there in 20 minutes. Which graph best represents this situation?
Answer:
The third option
Step-by-step explanation:
Use point-slop form to write the equation of a one that passes through the point (16, -16) with slip 1/2
Step-by-step explanation:
you made so many typos.
let's see :
the point-slope form of a line is
y - y1 = a(x - x1)
"a" being the slope, (x1, y1) being a point on the line.
in our case
y - -16 = 1/2 × (x - 16)
y + 16 = x/2 - 16/2 = x/2 - 8
y = x/2 - 24
or
y = (1/2)x - 24
3 is the same as the sum of times a number and -3
A. 3+ (-3)
B.
3+ (-3x)
C. 3+ (-x) = -3
-
D. 3+ (-¹/2) = - 3x
-
The equation is 3 = 3x + (-3) which represents the given statement "3 is the same as the sum of times a number and -3".
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.
Let the x represents the number.
The statement is given in the question, as follows:
3 is the same as the sum of times a number and -3
As per the given statement, we can write the algebraic form as
3 = 3x + (-3)
Thus, the equation is 3 = 3x + (-3) which represents the given statement.
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Mrs. Mortlock uses a calculator program to select students at random to answer questions during class. Each of the 28 students in her class is equally likely to be chosen every time she runs the program. Suppose Mrs. Mortlock runs the program for five different questions.
(a) In how many different ways can the program select which students will answer the five questions?
(b) How many of the selections in part (a) include 5 different students?
a) 17210368 different ways can the program select which students will answer the five questions
b) 11,793,600 different ways.
What is Permutation?The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.
Given:
Each of the 28 students in her class is equally likely to be chosen every time she runs the program.
a) The number of ways can the program select which students will answer the five questions
= [tex]28^5\\[/tex]
= 17210368
b) using Permutation
[tex]P^{28}_2[/tex] = 28! / (28-5)!
= 28! / 23!
= 28 x 27 x 26 x 25 x 24 x 23! / 23!
= 11,793,600
So, there are 11,793,600 different ways.
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Find g (7) if g (x) = - 10x - 7
Given:-
[tex] \rm{g ( x ) = -10x - 7 eqⁿ}[/tex][tex] \rm \bold{x = 7}[/tex][tex] \: [/tex]
now , put the value of x = 7 in da eqⁿ
[tex] \: [/tex]
[tex] \rm{g ( 7 ) = -10(7)-7}[/tex][tex] \: [/tex]
[tex] \rm{g ( 7 ) = -70-7}[/tex][tex] \: [/tex]
[tex] \underline{ \boxed{ \rm{ \red{ \bold{g ( 7 ) = -77}}}}}[/tex][tex] \: \: [/tex]
hope it helps!:)
1.2 : 3/2
so confused what's it asking for? can't seem to find anything on it could someone please explain?
Answer:
is that the question?
Step-by-step explanation:
Henry is moving and needs to open a new checking account. He is trying to decide between three banks using the chart below:
Bank X
Bank Y
Bank Z
No monthly fees if balance stays above $500, otherwise $7 per month
No monthly fees if check card is used less than 6 times per month
$5 monthly fee
No minimum balance
$25 minimum balance
No minimum balance
Online banking services
Online banking services
Online banking services
Non-Bank X ATM fee - $2.00 per transaction
Non-Bank Y ATM fee - $1.50 per transaction
Non-Bank Z ATM fee - $2.00 per transaction
Henry usually has about $300 in his account at any given time during the month. He limits his ATM visits to one per week and is interested in banking online options. Bank X and Bank Z have 5 ATMs within a 5 mile radius of Henry’s work and his new home. Which bank should he choose?
Henry has to choose bank Z.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given there are three banks Bank X, Bank Y and Bank Z
For bank X, No monthly fees if balance stays above $500, otherwise $7 per month.
No monthly fees if check card is used less than 6 times per month
$5 monthly fee, No minimum balance, $25 minimum balance, No minimum balance
Has Henry has about $300 in his account at any given time during the month. He limits his ATM visits to one per week and is interested in banking online options he has to choose bank Z.
Hence, Henry has to choose bank Z.
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Answer: Bank Z
Step-by-step explanation:Bank Z is his best option
you get 26 points out of 32 total points on your test, write "26 out 32" as a simplified fraction, decimal, and percent
As a fraction: 26/32 = 13/16
As a decimal: 26/32 = 0.8125
As a percent: 26/32 * 100 = 81.25%
what are factors of 10^3.
Answer:
2^3 x 5^3
Step-by-step explanation:
Explain why -7 is NOT a solution of x > -5.
Answer: The result can be shown in multiple forms.
Inequality Form:
x>−5
Interval Notation:
(−5,∞)
Step-by-step explanation:
Answer:because if we plug this in it will be -7 > -5, this is false because this is saying that -7 has a greater value that -5.
Step-by-step explanation:
hope the helps<3
at which values of x does the graph of the function f(x) have a vertical asymptote? check all that apply. F(x) = x+2/X^2+2x-24
The graph of f(x) has a vertical asymptote at x = -2 and x = 6, as the denominator of the fraction approaches zero and the numerator approaches a finite value as x approaches those values from either direction.
Answer:
The graph of the function F(x) has vertical asymptotes at x = 2 and x = 6. This is because the denominator of the function (x2 + 2x - 24) is equal to 0 when x = 2 and x = 6.
Step-by-step explanation:
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Graph the functions f(x) = -6x+2 and g(x) =-2^x^+^2 + 6 whst are the solutions of the equation -6x+2=-2^x^+^2 +6
The solution of the system of equation -6x + 2 = -2^{x + 2} + 6 is equal to the ordered pair (0, 2).
How to graph the solution to this system of inequalities?In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
f(x) = -6x + 2 ......equation 1.
g(x) = -2^{x + 2} + 6 ......equation 2.
Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is given by the ordered pair (0, 2)
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