2 people => 1 handshake (AB)
3 people => 3 handshakes (AB, BC, AC)
4 people => 6 handshakes (AB, AC, AD, BC, BD, CD)
Do you see a pattern here?
We can write a general formula for this
[tex]handshakes=\frac{n\cdot(n-1)}{2}[/tex]Since we are given that there were 15 handshakes
[tex]15=\frac{n\cdot(n-1)}{2}[/tex][tex]\begin{gathered} 2\cdot15=n\cdot(n-1) \\ 30=n\cdot(n-1) \\ 30=6\cdot(6-1) \\ 30=6\cdot(5) \\ 30=30 \end{gathered}[/tex]This means that n = 6 people were present at the party.
You can substitute n = 6 into the above formula and you will notice that it will give 15 handshakes
[tex]handshakes=\frac{n\cdot(n-1)}{2}=\frac{6\cdot(6-1)}{2}=\frac{6\cdot5}{2}=\frac{30}{2}=15[/tex]Find ca^2+b^2=c^2 3^2+2^2=c^29+4=13
Substituting with a = 3 and b = 2, we get:
[tex]\begin{gathered} 3^2+2^2=c^2 \\ 9+4=c^2 \\ 13=c^2 \\ \sqrt[]{13}=c \\ 3.6\approx c \end{gathered}[/tex]A small company produces baseball and racquetball by the function B(x)=-6x^2+2,556x-106,878. The profit made from the racquetball products can be represented by the function R(x)=-x^2+293x-16,770. If x is the total number of products made, which function best describes P(x), the profit the company makes from these two products?
profit made from the baseball products
[tex]B(x)=-6x^2+2556x-106878[/tex]Profit made from the racquetball products
[tex]R(x)=-x^2+293x-16770[/tex]Profit made from those 2 products is
[tex]\begin{gathered} P(x)=-6x^2-x^2+2556x+293x-106878-16770 \\ P(x)=-7x^2+2849x-123648 \end{gathered}[/tex]Nathan loved learning about earthquakes in science class. He told his brother that up until a 7.8-magnitude earthquake hit Nepal in 2015, Mount Everest had been moving northeast at a rate of 7.7×10^-6 centimeters per minute. What would be the most appropriate unit for Nathan to use instead of centimeters per minute?
The most appropriate unit for Nathan to use instead of centimeters per minute is centimeters per year.
What is an earthquake?An earthquake simply means a rapid motion of the solid layer of the Earth.
In this case, Nathan told his brother that up until a 7.8-magnitude earthquake hit Nepal in 2015, Mount Everest had been moving northeast at a rate of 7.7×10^-6 centimeters per minute.
Since the year is being discussed, the unit should be based on the year.
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Seventh grade > X.9 Reflections over the x- and y-axes: find the coordinates TF8 You have prizes to reveal The point D(-5, -3) is reflected over the y-axis. What are the coordinates of the resulting point, D'?
Answer
The coordinates of the resulting point, D' = (5, -3)
Explanation
When a given point with coordinates A (x, y) is reflected over the y-axis, the y-coordinate remains the same and the x-coordinate takes up a negative in front of it. That is, A (x, y) changes after being reflected across the y-axis in this way
A (x, y) = A' (-x, y)
So, for this question where the coordinate is D (-5, -3). it changes in the manner,
D (-5, -3) = D' (-(-5), -3) = D' (5, -3)
Hope this Helps!!!
Mario constructs a scale model of a building with a rectangular base. His model is 4.2 inches in length and 2 inches in width. The scale of the model is 1 inch = 15 feet What is the actual area, in square feet, of the base of the building?
First let's use two rules of three to determine the actual dimensions of the building.
For the length, we have:
[tex]\begin{gathered} 1\text{ inch}\to15\text{ feet} \\ 4.2\text{ inches}\to x\text{ feet} \\ \\ \frac{1}{4.2}=\frac{15}{x} \\ x=15\cdot4.2=63 \end{gathered}[/tex]For the width:
[tex]\begin{gathered} 1\text{ inch}\to15\text{ feet} \\ 2\text{ inches}\to x\text{ feet} \\ \\ \frac{1}{2}=\frac{15}{x} \\ x=15\cdot2=30 \end{gathered}[/tex]Now, calculating the area of the building base, we have:
[tex]\text{Area}=63\cdot30=1890\text{ ft2}[/tex]So the area of the building base is 1890 ft².
Can I get help w this pleaseThe dimensions of a rectangular prism are quadrupled.if the original surface area was 225ft^2 was is the new surface area?
Answer:
Concept:
Doubling the dimensions of a prism will increase the new area by 4 times the original area
Tripling the the dimensions of the prism will increase the new area by 9 times the original area
Quadrupling will increase the new area by 16 times the original area
Given that the original area given is
[tex]=225ft^2[/tex]The new area therefore will be
[tex]\begin{gathered} 16\times225 \\ =3600ft^2 \end{gathered}[/tex]Hence,
The final answer will be
[tex]\rightarrow3600ft^2[/tex]Question
Refer to section 1.3.2, Credit scores, beginning on page 22 of the report.
Arrange the five tiers of credit scores in order, starting with the lowest tier of credit scores.
The five credit score tiers are listed in ascending order, starting with the lowest tier:
Deep Subprime < Subprime < near prime < prime < super prime
A consumer's credit score may have a big impact on their ability to receive credit. These interactive infographics show how lending practices have changed for borrowers with various credit score profiles.
We focus on the five credit score levels that are commercially available.
The range of subprime credit scores is 580 to 619.
The range of Prime's credit score is from 660 to 719.
Deep subprime credit scores fall below 580.
Near prime credit scores range from 620 to 659.
Super prime credit is defined as having a score of 720 or higher.
The following are the five credit scores, listed from lowest to highest:
Deep Subprime < Subprime < near prime < prime < super prime
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What is the inverse function of y = (x-4)^2+2
One way to find the inverse of a function is by first swapping x and y, then solving for y, like this:
[tex]\begin{gathered} y=(x-4)^2+2\text{ }\Rightarrow x=(y-4)^2+2 \\ \end{gathered}[/tex]Now, let's solve for y, like this:
[tex]\begin{gathered} x=(y-4)^2+2 \\ x-2=(y-4)^2+2-2 \\ (y-4)^2=x-2 \\ \sqrt[]{\mleft(y-4\mright)^2}=\sqrt[]{x-2} \\ y-4=\sqrt[]{x-2} \\ y-4+4=\sqrt[]{x-2}+4 \\ y=\sqrt[]{x-2}+4 \end{gathered}[/tex]Then, the inverse function of y = (x-4)^2+2 is:
[tex]y=\sqrt[]{x-2}+4[/tex]Classwork Area of Algebra Tiles 1 An If the side lengths of a tile can be measured exactly, then the area of the tile can be calculated by multiplying these two lengths together. The area is measured in square units. For example, the tile at right measures 1 unit by 5 units, so it has an area of 5 square units. 1 The next tile at right has one side length that is exactly one unit long. If the other side length cannot have a numerical value, what can it be called? ?
The other side of a tile can be called as width of hte tile
Match the following reasons to the statements given.Given:ABEF isEBDCProve:ACDF is
Solution
For this case we can do the following:
2. Part of lines FE and AB
4. Transitive
1. Given
5. Definition of parallelogram
3. Opposite sides of a parallelogram are II
A focus group of 12 people is to be chosen randomly from among 24 right-handed people and 5 left-handed people. In order to find the probability that 3 of the people chosen are right-handed, you should use
Let 1 and 2 mean that a person is right-handed or left-handed, respectively.
Consider the probability space as the different groups of 12 people that can be formed with the 29 total people. {(1,1,1,1,1,...1),(2,1,1,1,1,...,1),...}
We need to use the binomial distribution in order to find the answer.
Consider X to be the number of right-handed people in the group.
The probability of X=3 is then:
[tex]Pr(X=3)=\text{ binomial coefficien(}12,3\text{)}(\frac{24}{29})^3(1-\frac{24}{29})^{12-3}[/tex]We used the formula
[tex]\begin{gathered} Pr(X=k)=\text{ binomial coefficient(n,k)}\cdot p^k(1-p)^{n-k} \\ \text{where } \\ k=3 \\ n=12 \\ p=\frac{24}{29} \end{gathered}[/tex]Finally, we need to simplify the expression, as shown below
[tex]\Rightarrow P(X=3)=220(\frac{24}{29})^3(\frac{5}{29})^9=0.0000167[/tex]This is the answer one obtains using the binomial distribution; nevertheless, the actual probability is equal to zero because it is not possible to form a group of 12 people that only contains 3 right-handed people as there are only 5 left-handed people (3+5=8).
- What is the closed linear form of the sequence 3, 4,5, 6, 7, ...?
AcuveDetermining If a Number Is a SolutionQUICK CHECKWhich values are solutions to the inequality -3x – 4< 2? Check all of the boxes that apply.-4-2OOO03DONE
We have the next inequality given:
[tex]-3x-4<2[/tex]Solve the x variable:
Add both sides 4
[tex]\begin{gathered} -3x-4+4<2+4 \\ -3x<6 \end{gathered}[/tex]Divide both sides by 3
[tex]\begin{gathered} \frac{-3}{3}x<\frac{6}{3} \\ -x<2 \end{gathered}[/tex]Finally, multiply both sides by -1:
[tex]\begin{gathered} (-1)(-x)<2(-1) \\ x>-2 \end{gathered}[/tex]Hence, x can take any value greater than -2.
So, the solutions that apply are 0 and 3.
I will send u a picture of my equation
Answer:
where is the picture????
In a middle school with 300 students, there are 40% boys, 1/3 of the students wear glasses, and 15% of the girls wear glasses. What is the probability (= how many percent is it) that a randomly selected student does not wears glasses? (Round the percentage to the nearest hundredth) *
We know that
• There are 300 students.
,• 40% are boys (this means 60% are girls).
,• 1/3 of the students wear glasses.
If 1/3 of the students wear glasses, then 2/3 of the students don't wear glasses. Let's find 2/3 of 300.
[tex]\frac{2}{3}\cdot300=\frac{600}{3}=200[/tex]Therefore, 200 students don't wear glasses.
Then, we divide to find the probability.
[tex]P=\frac{200}{300}=0.6667[/tex]Then, we multiply by 100.
[tex]0.6667\cdot100=66.67[/tex]Therefore, the probability is 66.67%.which calculation does not show the surface area of the cube?
Given: A cube with side 6.5 cm
Required: Which calculation does not show the surface area of the cube.
Explanation:
Surface area of cube with side a is 6a².
So here the surface area of cube is
[tex]6(6.5)^2[/tex]Oprion 2, 3 and 4 reflects the calculation correctly.
But option A is actually the volume of the cube, it is not a correct way to show surface area of the cube.
Final Answer: option A is correct.
Write 6.5123 x 10^8 in standard
The standard form is a standard method of writing numbers such that we have it in the form:
[tex]a\times10^b[/tex]where
[tex]0Therefore, 6.5123 x 10^8 in standard form is:[tex]6.5123\times10^8[/tex]You must show your work as you... determine whether QR and ST are parallel, perpendicular, or neither. Q(9, 10), R(-5, 2), S(-8, -2), T(-1, 2) Parallel Perpendicular Neither
WILL MARK BRAINLIEST
PLS HELP ASAP
Slope of QR = 4/7; Slope of ST = 4/7, therefore, the lines are parallel to each other.
How to Determine if Two Lines are Parallel or Perpendicular?To determine if two given lines are perpendicular to each other or parallel to each other, find their slopes.
Slope, m = change in y / change in x.
If they have the same slope, m, then they are parallel lines. If they have slopes that are negative reciprocal to each other, then they are perpendicular lines.
Given:
Q(9, 10)
R(-5, 2)
S(-8, -2)
T(-1, 2)
Find the slope of QR and ST:
Slope of QR = (10 - 2)/(9 -(-5)) = 8/14 = 4/7
Slope of ST = (-2 - 2)/(-8 -(-1)) = -4/-7 = 4/7
The slope are the same, therefore they are parallel to each other.
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Jan 10, 7:17:08 PM Which equation represents a line which is perpendicular to the line x - 2y = -14? Oy= -27 -1 Oy= 2x + 8 Submit Answer Oy=x+4 Oy = -x + 2
You need to determine which line is perpendicular to the line
[tex]x-2y=-14[/tex]For two lines to be considered perpendicular their slopes must be the inverse positive, that is, if, for example, you have the lines
[tex]y_1=mx_1+b[/tex][tex]y_2=nx_2+c[/tex]For them to be perpendicular one slope must be the inverse negative of the other such as
[tex]n=-\frac{1}{m}[/tex]The first step is to write the given line in slope-intercept form:
1) Pass the x term to the right side of the equal sign
[tex]\begin{gathered} x-2y=-14 \\ x-x-2y=-14-x \\ -2y=-x-14 \end{gathered}[/tex]2) Divide both sides of the expression by "-2"
[tex]\begin{gathered} -\frac{2y}{-2}=-\frac{x}{-2}-\frac{14}{-2} \\ y=\frac{1}{2}x+7 \end{gathered}[/tex]The slope of the line is
[tex]m=\frac{1}{2}[/tex]So the slope of a line perpendicular to it will be the inverse negative of it
[tex]\begin{gathered} n=-(\frac{1}{\frac{1}{2}}) \\ n=-2 \\ \end{gathered}[/tex]The correct option is the one that has slope -2
Which of the equations below could be the equation of this parabola? A. y = 1/2 x² B. x-1/2 y2 c. y = -1/2 x² D. x = 1/2 y2SUBMIT
The equation of the parabola is given as;
[tex]y=\frac{1}{2}x^2[/tex]The correct answer is option A.
Use the graph of y = f (x) to find the following value of f. f(2) =
Answer:
f(2)=4
Explanation:
Consider the graph below:
When x=2, the value of f(x) = 4 (the poiny circled in blue above).
Therefore:
[tex]f(2)=4[/tex]The value of f(2) is 4.
a. Solve for c: E = mc^2
ANSWER
[tex]\text{c = }\sqrt[]{\frac{E}{m}}[/tex]EXPLANATION
We want to solve for c in:
[tex]E=mc^2[/tex]To do that, we will make c the subject of the formula:
[tex]\begin{gathered} E=mc^2 \\ \Rightarrow\text{ }\frac{E}{m}=c^2 \\ Find\text{ the square root of both sides:} \\ \Rightarrow\text{ c = }\sqrt[]{\frac{E}{m}} \end{gathered}[/tex]We have solved for c.
-353-0-- * GR-35-21-2700-3s 6 - 2y-6- - +28+82-80 -592-35-07-2+27-35-30 9815+ Seesters << RB- --3-1-1-12) 6-5-3= LG - 5+13-2225 SVE -3-5y+6=-24 -*- 4y +50=-21 5r - 55 - 5 = 3r-S-=
Explanation:
5x - 4y + 2z = 21 ...equation 1
-x - 5y + 6z = -24 ....equation 2
-x - 4y + 5z = -21 ...equation 3
Using elimination method:
multiply equation 2 by 5:
-5x - 25y + 30z = -120 ....equation 2a
add equation 2a from 1:
5x - 5x -4y -25y + 2z + 30z = 21 - 120
0 - 29y + 32z = -99
-29y + 32z = - 99 ....equation 4
multiply equation 3 by 5:
-5x - 20y + 25z = -105 ...equation 3a
add equation 1 and 3a
5x - 5x - 4y - 20y + 2z +25z = 21 - 105
0 - 24y + 27z = -84
-24y + 27z = -84 ...equation 5
-29y + 32z = - 99 ....equation 4 (×-24)
-24y + 27z = -84 ...equation 5 (×-29)
696y - 768x = 2376 ...(4a)
696y -783x = 2436 ...(5a)
subtract 5a from 4a
696y - 696y -768x -(-783x) = 2376 - 2436
0 - 768x + 783x = -60
15x = -60
x = -60/15
x = -4
substitute for x in equation 4a:
696y - 768(-4) = 2376
696y + 3072 = 2376
696y = 2376 -3072
696y = -696
y = -696/696
y = -1
substitute for y in equation 4:
-29(-1) + 32z = -99
29 + 32z = -99
32z = -99 - 29
32z = -128
z = -128/32
z = -4
absolute value of v-5>3
Answer: v=8
Step-by-step explanation:
-5+5=0
3+5=8
v=8
the triangle in the figure had a hypotenuse equal to 40 units what is the approximate length of x
25.7 units
30.6 units
47.7 units
52.2 units
(Srry I’m spamming I know nothing on this test)
If the triangle in the figure has a hypotenuse equal to 40 units, then the approximate length of x is 30.64 units
The length of the hypotenuse = 40 units
The angle = 50 degrees
Here we have to apply the trigonometric function
we know
sin θ = Opposite side / Hypotenuse
cos θ = Adjacent side / Hypotenuse
tan θ = Opposite side / Adjacent side
Here we have to use the equation of sin θ
Substitute the values in the equation
sin 50 = x/40
x = 40×sin 50
x = 30.64 units
Hence, if the triangle in the figure has a hypotenuse equal to 40 units, then the approximate length of x is 30.64 units
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Two ships are sailing across the Atlantic ocean at the equator. The dofference in solar time between them is two hours. How many degrees of longitude are they apart?
Answer:
30 degrees
Step-by-step explanation:
There are 360 degrees of longitude ( 360 degrees is a complete circle)
It takes 24 hours to complete a complete rotation of the earth
360 degrees / 24 hours = 15 degrees / hr
15 degrees/ hr * 2 hr = 30 degrees
A company produces 11 times as many rings on shift 1+ shift to if I total of 12,000 rings were produced how many were produced on each shift
Shift 1 produced 11000 rings and Shift 2 produced 1000 rings.
What does "parent company" mean and how Do Parent Companies Work?
A single firm that owns a majority stake in another company or groups of companies is known as a parent company.
Parent corporations are created through acquisition, merger, spin-off, or carving out of subsidiaries.
A parent company is a business that controls a significant portion of another business, giving it operational authority over that business.
Given :-
Production of Shift 1 = 11 times of Production of Shift 2
total production = 12,000 rings
production of ( Shift 1 + Shift 2 ) = Total production
on solving we get,
Production of Shift 1 = 11,000 rings
Production of Shift 2 = 1,000 rings
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| 5-6x | -12 = 0Solve the absolute. equation for 2 values of x
Given
[tex]|5-6x|-12=0[/tex]To solve this equation for both possible values of x, you have to separate it into two calculations.
1) One will be for the case that the values inside the absolute term are multiplied by "+1":
[tex]\begin{gathered} 1\cdot(5-6x)-12=0 \\ 5-6x-12=0 \\ -6x+5-12=0 \\ -6x-7=0 \\ -6x=7 \\ -\frac{6x}{-6}=\frac{7}{-6} \\ x=-\frac{7}{6} \end{gathered}[/tex]The first value of x is -7/6
2) The second will be the case that the absolute values are negative, that is as if they are multiplied by -1
[tex]\begin{gathered} (-1)(5-6x)-12=0 \\ -5+6x-12=0 \\ 6x-5-12=0 \\ 6x-17=0 \\ 6x=17 \\ \frac{6x}{6}=\frac{17}{6} \\ x=\frac{17}{6} \end{gathered}[/tex]The second value of x is 17/6
So for this absolute equation, the possible values of x are -7/6 and 17/6
Solve the system using the elimination method:2x - y + z = -26x + 3y - 4z = 8-3x + 2y + 3z = -6
multiply 2x - y + z = - 2 for 3
[tex]6x-3y+3z=-6[/tex]then sunstract the equation 1 and 2
[tex]\begin{gathered} 6x+3y-4z=8 \\ 6x-3y+3z=-6 \\ 6y-7z=14 \end{gathered}[/tex]multiply -3x+2y+3z=-6 for 2
[tex]-6x+4y+6z=-12[/tex]adding
[tex]\begin{gathered} -6x+4y+6z=-12 \\ \underline{6x-3y+3z=-6} \\ y+9z=-18 \end{gathered}[/tex]multiply y+9z=-18 for 6
[tex]6y+54z=-108[/tex]Subtracting
[tex]\begin{gathered} 6y+54z=-108 \\ \underline{6y-7z=14} \\ 61z=-122 \end{gathered}[/tex]then solve
[tex]\begin{gathered} 61z=-122 \\ \frac{61z}{61}=\frac{-122}{61} \\ z=-2 \end{gathered}[/tex][tex]\begin{gathered} 6y-7\mleft(-2\mright)=14 \\ 6y+14=14 \\ 6y+14-14=14-14 \\ 6y=0 \\ y=0 \end{gathered}[/tex][tex]\begin{gathered} 6x-3\cdot\: 0+3\mleft(-2\mright)=-6 \\ 6x-6=-6 \\ 6x-6+6=-6+6 \\ 6x=0 \\ x=0 \end{gathered}[/tex]answer is: x = 0, y = 0 and z = - 2
2/5m = 1/2 what is the m stand for ?
we can interpret m as a constant of proportionality.