The mean, median and mode are as follows:
1. 11.75
2. 11.5
3. 11 and 14
4. 16.75
5. 13 and 16
6. 23
7. 32
8. 79
9. 35
10. 14
11. 2
What are mean, median and mode ?The three measures of central tendency used in statistics are mean, median, and mode. While describing a set of data, we always specify the focal point of any data set. The measure of central tendency is this. Every day, data are presented to us. We discover them in books, articles, bank statements, phone and utility bills, as well as in newspapers. There are so many; they are all around us. The challenge now is if we can identify some key characteristics of the data by focusing on only a few data points. The means, medians, and modes—measures of central tendency or averages—can be used to do this. When describing a set of data, a measure of central tendency locates the set's center.
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Math
Classify each algebraic expression below as polynomial or non-polynomial
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.
How are polynomials and non-polynomials categorized?
There are two ways to categorize polynomials: by degree and by number of terms. According to degree, polynomials can be classified as zero, linear, quadratic, or cubic. Monomials, binomials, trinomials, etc. are the different types of polynomials based on the quantity of terms.
A polynomial is, in general, an expression containing more than one term and non-negative integral exponents of a variable. A polynomial expression might look like this: ax + by + ca, x3 + 2x + 3, etc.
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can someone help me please!!!!!!!
A number was tripled, then decreased by 10, then doubled, and then increased by 2. The result was 5 times the original number.
If the original number was x, the equation will be
x=
Answer:
x = 18
The number is 18.
Step-by-step explanation:
Convert the words into an equation.
let x;
( 3x - 10 )( 2 ) + 2 = 5x;
6x - 20 + 2 = 5x;
6x - 18 = 5x;
Subtract both sides by 5x.
6x - 5x - 18 = 5x - 5x;
x - 18 = 0;
Add 18 to both sides.
x - 18 + 18 = 18;
x = 18;
If cos∠E = sin∠F and m∠E = 26°, what is m∠F?
Step 1
Given;
[tex]\begin{gathered} cosE=sinF \\ measure\text{ of angle E=26}^o \end{gathered}[/tex]Required; To find the measure of angle F
Step 2
[tex]\begin{gathered} cos26=sinF \\ \sin\left(90^{\circ\:}-26^{\circ\:}\right)=cos26 \end{gathered}[/tex][tex]\begin{gathered} \sin\lparen F)=\sin\left(90^{\circ\:}-26^{\circ\:}\right) \\ sin(F)=sin(64) \end{gathered}[/tex]Answer;
[tex]m\angle F=64[/tex]Write the equation 2(x + 3 )= 2x + 6 as a system of equations
Answer:
y=2x+6
y=2x+6
Explanation:
Given the equation:
[tex]2\mleft(x+3\mright)=2x+6[/tex]The equation written as a system of equations is:
[tex]\begin{gathered} y=2\mleft(x+3\mright) \\ y=2x+6 \end{gathered}[/tex]Opening the bracket in the first equation gives:
[tex]\begin{gathered} y=2x+6 \\ y=2x+6 \end{gathered}[/tex]Whats the midpoint of line segment (-1,6), (3,0)
Answer:
(1,3)
Step-by-step explanation:
You can use the distance formula to help you solve the answer
Answer:
(1; 3)
Step-by-step explanation:
x = (-1 + 3)/2 = 1
y = (6 + 0)/2 = 3
Simplify: I3 - 6| - (12 ÷ 6 + 1)3
Solution
The question would like us to evaluate the following expression
[tex]|3-6\left|-(12\div6+1\right)^2[/tex]- We should deal with the modulus and bracket separately.
- After that, we can then perform the subtraction operation on the results of the modulus and bracket.
- This is done below:
[tex]\begin{gathered} |3-6|=|-3\left|\right? \\ |-3\left|\right?=3\text{ \lparen Because the modulus always returns a positive number\rparen} \end{gathered}[/tex]Also,
[tex]\begin{gathered} \lparen12\div6+1)^2 \\ By\text{ the rules of PEDMAS,} \\ Division\text{ comes before Addition, thus, we should perform the division operation first} \\ 12\div6=2 \\ \\ \lparen2+1)^2=3^2=9 \end{gathered}[/tex]Thus, combining both results, we have:
[tex]\begin{gathered} 3-9 \\ =-6 \end{gathered}[/tex]Final Answer
The answer is -6
Answer:
-6 hope it helps
thank you
Write the equation of the line that is perpendicular to the x-axis and contains point (0,
4).
The line of the equation which passes through the point (0, 4) and is parallel to the x-axis is 2y = 8.
What are equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 = 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. A mathematical equation is a formula that uses the equals sign to express the equality of two expressions.So, the equation is as:
A line formed needs to be parallel to the x-axis which means x = 0.Should pass through points (0, 4)Then, the equation can be:
2y = 8(Refer to the graph attached below)
If you solve will become:
2y = 8y = 4Therefore, the line of the equation which passes through the point (0, 4) and is parallel to the x-axis is 2y = 8.
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Based on the given diagram, complete the sentence below.
Point D is the centroid of ΔABC, since we know that A.F, BC, and CE are all medians.
What is the Median of a Triangle?A median of a triangle is the line segment that connects the vertex of a triangle to the midpoint of the opposite side. There are usually three medians of a triangle.
What is the Centroid of a Triangle?The point where the three medians of a triangle intersect each other or meet at is referred to as the centroid of the triangle.
The diagram shows a triangle with three medians that meets at point D in the triangle. Therefore, point D is the centroid of the tringle because lines A.F, BC, and CE are all medians of the given triangle.
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PLEASE FOLLOW THE DIRECTIONS IN THE PICTURES. PLEASE HURRY. Thank you very much
Answer:
E
Step-by-step explanation:
[tex]\sqrt{144} = 12\\ \frac{234}{3}= 78\\[/tex]
12, 68.12, 78
x + 6Identify the vertical asymptotes of f(x)(1 point)- 9x + 18O x= -6 and x = -3O x= -6 and x = 3oO x = 6 and x = -3O x = 6 and x = 3
So we want to find the vertical asymptotes of the function:
[tex]f(x)=\frac{x+6}{x^2-9x+18}[/tex]Remember that there's a vertical asymptote at points of x where the denominator of the rational function is 0.
So, equal the denominator to zero:
[tex]x^2-9x+18=0[/tex]And solve this equation for x as follows:
We could factor
[tex]\begin{gathered} x^2-9x+18=0 \\ (x-6)(x-3)=0 \end{gathered}[/tex]Now, notice that any of both factors could be zero, so:
[tex]\begin{cases}x-6=0\to x=6 \\ x-3=0\to x=3\end{cases}[/tex]Therefore, the function has vertical asymptotes at x=6 and x=3.
The radius of the base of a cylinder is 10 centimeters, and its height is 20 centimeters. A cone is used to fill the cylinder with water. The radius of the cone's base is 5 centimeters, and its height is 10 centimeters
The number of times one needs to use completely filled cone to completely fill the cylinder with water is...
The number of times one needs to use completely filled cone to completely fill the cylinder with water is 24
What is volume of cone and cylinder?The volume of cylinder is equal to the product of the area of the circular base and the height of the cylinder.
Given that radius of the base of a cylinder is 10 centimeters, and its height is 20 centimeters.
The radius of the cone's base is 5 centimeters, and its height is 10 centimeters.
The volume of cylinder is πr²h
For a volume of cone it is 1⁄3πr²h.
So volume of cylinder = 22/7×(10)2×20=3.142×100×20
=6284
volume of cone it is 1⁄3πr²h=1/3×3.142×(5)^2×10=261.16
Number of times one needs to use the completely filled cone to completely fill the cylinder with water =
= Volume of cylinder/Volume of cone
6284 / 261.16 = 24
Hence the number of times one needs to use completely filled cone to completely fill the cylinder with water is 24
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Is this relation a function? Justify your answer.
A. Yes because every x- and y-value is positive.
B. No because two points with the same y-value have different x-values.
C. No because two points with the same x-value have different y-values.
D. Yes because the number of x-values is the same as the number of y-values
Answer:
C. No because two points with the same x-value have different y-values.
Step-by-step explanation:
(view my screenshot attachment too please)
A function can't have same x-values that appear for multiple different y-values.
In the diagram, (10, 6) and (10, 9) indicate that it isn't a function.
This is because the same 10 appears twice (x-value) but with multiple different y-values (6 and 9).
I just need the answer
At x=0
[tex]\begin{gathered} f(x)=14 \\ c=14 \end{gathered}[/tex]at x=1
[tex]\begin{gathered} f(x)=10.5 \\ a+b=10.5-14 \\ a+b=-3.5 \end{gathered}[/tex]at x=2
[tex]\begin{gathered} f(x)=8 \\ 4a+2b=8-14 \\ 4a+2b=-6 \end{gathered}[/tex]a=1/2
So correct option is (c).
the hypotenuse of a right triangle is growing at a constant rate of a centimeters per second and one leg is decreasing at a constant rate of b centimeters per second. how fast is the acute angle between the hypotenuse and the other leg changing at the instant when both legs are 1 cm?
The acute angle between the hypotenuse and the other leg changing at the instant when both legs are 1 cm is dθ/dt = -b - a/[tex]\sqrt{2}[/tex] fast.
Differentiation is a process to find the instantaneous rate of change in function based on one of its variables.
The hypotenuse of a right triangle is growing at a constant rate of a centimeters per second
[tex]\frac{dH}{dt} = a[/tex]
One leg is decreasing at a constant rate of b centimeters per second
[tex]\frac{dy}{dt} = -b[/tex]
From the right triangle
sin θ = [tex]\frac{y}{H}[/tex] (y is the perpendicular and H is the hypotenuse)
Differentiate both sides with respect to t
cos θ*dθ/dt = (H*dy/dt - y*dH/dt) / H²
cos θ*dθ/dt = [H(−b)−y(a)] / H²........................(1)
If the both legs are 1 cm.
∴ H= [tex]\sqrt{ 2[/tex],cosθ=sinθ=1/[tex]\sqrt{2}[/tex]
Thus , Equation (1)
cos θ*dθ/dt = [H(−b)−y(a)] / H²
1/√2*dθ/dt = [√2 (−b)−(a)] / 2
dθ/dt = √2 [(√2 (−b)−(a)) / 2]
Therefore, we can conclude that the acute angle between the hypotenuse and the other leg changing at the instant when both legs are 1 cm is dθ/dt = -b - a/[tex]\sqrt{2}[/tex] fast.
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three ratios that are equivelent to 11 : 1
Answer: 22:2, 33:3 and, 44:4
Step-by-step explanation:
Answer:
Step-by-step explanation:
22 : 2
33 : 3
44 : 4
can someone please answer this step by step asap? im confused and dont know how to solve this
3 equations that can be used to solve the given scenario are:
10x + 15x + 20x = 500045x = 500010x + 15x + 20x = 300What exactly are equations?In mathematical equations, the equals sign is used to show that two expressions are equal.An equation is a mathematical statement that uses the word "equal to" in between two expressions of the same value.As an illustration, 3x + 5 equals 15.There are many different types of equations, including linear, quadratic, cubic, and others.The three primary types of linear equations are slope-intercept, standard, and point-slope equations.So, equations that can be used to solve the following scenario are:
Let, the number of students in each group is 'x'.Then,
10x + 15x + 20x = 500045x = 500010x + 15x + 20x = 300Therefore, 3 equations can be used to solve the given scenario are:
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determine the equation of line from the graph
Answer:
y = -x
Step-by-step explanation:
Answer: Y=-X
Step-by-step explanation:
Please helpppppp!!!!!!!!!!!!!!!!!!!!!!!!3|x_5|-|4y|/|x+y|when x=8 & y=4
Answer:
29/49
Step-by-step explanation:
x:y = 3:4
let x = 3x , y = 5k
3x+4y/8x+5y
= 3(3k)+4(5k)/8(3k)+5(5k)
= 9k+20k/24k+25k
=29/49
A line has a slope of – 1 and includes the points (9,2) and (8,p). What is the value of p?
Answer:
p = 3
Step-by-step explanation:
y = mx + b They gave us the slope of -1. We need to find the y intercept. We will use the x of 9 and the y of 2 to find b. We will plug these numbers in to find b.
y = mx + b
2 = -1(9) + b
2 = -9 + b Add 9 to both sides
11 = b
y = -x +11
Now, plug in 8 for x
y = -1(8) + 11
y = -8 + 11
y = 3
In this case p is 3.
albert brought a blanket for 32.75, a pillow for 12.75,and a glove for 16.25. he paid 50 and the rest he borrowed from his friend. if albert for 5.25 in change from the cashier, how much did he borrow from his friend to pay for all of the items.
Albert borrowed $17 from his friend.
Given,
Albert brought some items:
Cost of blanket = $32.75
Cost of pillow = $12.75
Cost of glove = $16.25
Amount paid by Albert = 50
Amount borrowed by Albert from his friend = x
Cashier gave back the change = $5.25
We have to find the amount borrowed by Albert from his friend:
This is simply arithmetic operations:
Total cost in shop = 32.75 + 12.75 + 16.25 = $61.75
Total amount given to the cashier = 61.75 + 5.25 = 67
Amount borrowed by Albert from his friend = Total amount given to the cashier - Amount paid by Albert
x = 67 - 50
x = 17
That is,
Albert borrowed $17 from his friend.
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Please help me i dont the answer
[tex] \huge\underline\mathcal{Answer \: -} [/tex]
We know that ,
exterior angle equals sum of two interior opposite angles.
therefore ,
[tex]\bold{x + x + 14 = 136\degree} \\ \\ \longrightarrow \: 2x + 14 = 136\degree \\ \\ \longrightarrow \: 2x = 136\degree - 14 \\ \\ \longrightarrow \: 2x = 122\degree \\ \\ \longrightarrow \: x = \cancel\frac{122}{2} \\ \\ \longrightarrow\boxed{ \: x = 61\degree}[/tex]
hence , the first option is correct.
hope helpful ! ;-;
Answer:
First find the last angle of the triangle.
180 - 136 = 44° (sum of angles on a straight line=180)
Form an equation with the unknown angles with the knowledge that sum of angles in a triangle add up to 180°.
x + (x + 14) + 44 = 180
Simplify and solve for x.
2x + 58 = 180
2x = 122
x = 61
ships a and b leave port together. for the next two hours, ship a travels at 20 mph in a direction 30o west of north while the ship b travels 20o east of north at 25 mph. a) what is the distance between the two ships two hours after they depart? b) what is the speed of ship a as seen by ship b?
Two hours after depart, the distance between two ships is 39.2 miles and the relative speed of ship A seen by ship B is 19.6 mph heading to 18.4⁰ South of East.
The situation can be depicted on the attached picture.
Let North - South be the y-axis and East - West ne the x-axis.
The velocities vector can be represented as:
Ship A, 20 mph 30⁰ west of north:
vA = - 20 . cos( 60⁰) i + 20 . sin( 60⁰) j
vA = -10 i + 10√3 j
Ship B, 25 mph 20⁰ east of north:
vB = 25 . cos( 70⁰) i + 25 . sin( 70⁰) j
vB = 8.55 i + 23.5 j
b) The speed of ship A relative to ship B is:
vAB = vA - vB
= ( -10 i + 10√3 j) - (8.55 i + 23.5 j)
= -18.55 i - 6.18 j
or vAB = sqrt (18.55² + 6.18²) = 19.6 mph with the angle tan⁻¹ (6.18/18.55) = 18.4⁰ South of East.
a) The distance between 2 ships after 2 hours:
d = vAB . 2 hours
d = 19.6 . 2 = 39.2 miles
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What is the maximum volume of a rectangular prism (or box) if the prism has a square base and a total surface area of 100 cm^2?
A) First, let x = the side length of the base and h = the height of the prism. Write and solve the equation for h.
B) Write a function for the volume of the box, V, in terms of x.
Answer: A. 100/x^2 = h, B. v(x) = x^2*h
Step-by-step explanation:
A. Volume = b * h
100 cm^2 = x^2 * h
100/x^2 = h
B. v(x) = x^2*h
Please answer quick! i'm stuck on th is and it is due today! (equation is on the bottom on the picture)
4 - 1/3x = x + 2x
2 1/3 - 4/7
what is the answer to this question
The solution for the algebraic expression 2 1/3 - 4/7 is 37/21
Given,
The algebraic expression ; 2 1/3 - 4/7
We have to solve this expression;
First lets solve the mixed fraction 2 1/3
2 1/3 = (2 x 3) + 1 / 3 = 6 + 1 / 3 = 7/3
Mixed fraction;
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
Now,
7/3 - 4/7 = (7 x 7) / (3 x 7) - (4 x 3) / (7 x 3) = 49/21 - 12/21
That is,
49/21 - 12/21 = (49 - 12) / 21 = 37/21
That is,
The solution for the algebraic expression 2 1/3 - 4/7 is 37/21
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Determine whether each order pair is a solution of the equation
Answer:
Given equation is, x+3y=6
To determine whether each order pair is a solution of the equation
(3,1)
we have that, when x=3 we get y=1
Let us check this in the equation.
Put x=3, we get
[tex]3+3y=6[/tex][tex]\begin{gathered} 3y=6-3 \\ 3y=3 \end{gathered}[/tex][tex]y=1[/tex]Hence (3,1) is the solution of the equation.
(6,0)
Put x=6, we get,
[tex]6+3y=6[/tex][tex]y=0[/tex]
Hence (6,0) is the solution of the equation.
(-2,2/3)
Put x=-2, we get,
[tex]-2+3y=6[/tex][tex]3y=6+2[/tex][tex]y=\frac{8}{3}[/tex]Hence (-2,2/3) is not the solution of the equation.
The table shows pizza prices at Papi's Pizzeria.
Pizza Size Price
small $9.99
medium $11.99
large $13.99
On Saturday, Papi's sold 39 small pizzas, 62 medium pizzas, and 83 large pizzas.
Which equation represents the total amount of money Papi's made selling pizzas on Saturday?
A.
(
39
+
62
+
83
)
×
(
$
9
.
99
+
$
11
.
99
+
$
13
.
99
)
=
$
6
,
618
.
48
B.
(
$
9
.
99
×
39
)
+
(
$
11
.
99
×
62
)
+
(
$
13
.
99
×
83
)
=
$
2
,
294
.
16
C.
(
39
×
62
×
83
)
÷
(
$
9
.
99
+
$
11
.
99
+
$
13
.
99
)
=
$
5
,
579
.
48
D.
1
3
(
$
9
.
99
+
$
11
.
99
+
$
13
.
99
)
×
(
39
+
62
+
83
)
=
$
2
,
206
.
16
The equation that represents the total amount of money Papi's made selling pizzas on Saturday is (39 x $9.99) + (62 x $11.99) + (83 x $13.99)
Equation:
An equation is the mathematical statement which is made up of two expressions connected by an equal sign.
For example, 3x – 2 = 16 is an equation.
Given,
There are three types of pizza varieties are small, medium and large. And the price of them are $9.99, $11.99 and $13.99 respectively.
On Saturday, Papi's sold 39 small pizzas, 62 medium pizzas, and 83 large pizzas.
So, we have to write the equation for the total amount of money Papi's made selling pizzas on Saturday.
To calculate the price of the pizza we have to multiply it by the number of items sold by the cost.
So, the equation to calculate the cost of pizza,
=> number of items sold x cost.
Here we have to write the equation for three types and we have to find the total cost for it,
So, the equation is looks like,
=> (39 x $9.99) + (62 x $11.99) + (83 x $13.99)
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What is the value of in if the remainder of /is 2?
O A. 1
OB. i
O C. -1
O D. -1
The value of i where remainder of n/ 4 is 2 is :
i² = -1 .
What is i?I has the value √-1.The complex numbers are expressed using the imaginary unit number, where I is defined as imaginary or unit imaginary. An imaginary number is a complex number component that can be written as a real number multiplied by the imaginary unit I where i² = -1. When the imaginary number is multiplied by itself, the result is negative. Consider the imaginary number 3i, which, when multiplied by itself or divided by its square, yields 9i², or -9.z = a + ib .i² = -1
i⁰ = 1
i¹ = i
i² = -1
i³ = i² x i
= -1 x i
= -i
i⁴ = i² x i²
= -1 x -1
= 1
The pattern repeats.
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help!!
I'm not sure if i'm right...
are these the steps to solve for x?
-5 *4 +3 /2
Yes, you are right!
First of all, we will subtract [tex]5[/tex] from each side.
[tex]\frac{2x-3}{4}=5[/tex]Then we multiply both sides by [tex]4[/tex].
[tex]2x-3=20[/tex]Then add [tex]3[/tex] to each side.
[tex]2x=23[/tex]Finally, we divide each side by [tex]2[/tex].
[tex]x=\frac{23}{2}=11.5[/tex][tex]\boldsymbol{\sf{\cfrac{2x-3}{4}+5=10 }}[/tex]
Multiply the two sides of the equation by 4.
2x - 3+20 = 40
Add −3 and 20 to get 17.
2x+17 = 40
It remains 17 on both sides.
2x = 40−17
Subtract 17 of 40 to get 23.
2x = 23
Divide both sides by 2.
[tex]\boldsymbol{\sf{x=\dfrac{23}{2} \ \ \longmapsto \ Answer }}[/tex]