Using the combination formula, it is found that:
There are 7750 different ways for the winners to be chosen.The probability that the first two students who signed up will be the winners is 1/7750.The order in which the students are chosen is not important, as for example, João and Elisa is the same outcome as Elisa and João, hence the combination formula is used to solve this question;
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula, involving factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
2 students are chosen from a set of 125, hence the number of combinations is:
[tex]C_{125,2} = \frac{125!}{2!123!} = 7750[/tex]
There are 7750 different ways for the winners to be chosen.
The first two students winning is only one outcome, hence:
The probability that the first two students who signed up will be the winners is 1/7750.
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What is the practical advantage of requiring a function to have exactly one output for each input?
A particular kind of relation called a function is one in which every input value has only one and only one output value. The value of an input is the independent value, but the value of an output is dependent on the value of the input.
What is an independent value?The independent variable is the cause. The other study factors have no impact on its value. The dependent variable is effect. Its value is affected by changes in the independent variable.
It is an independent variable that has no bearing on the other factors you are attempting to evaluate. For example, age may be an independent variable.
The graph's x-axis (horizontal line) should contain the independent variable, and the y-axis should contain the dependent variable (vertical line).
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pls help solve for x
Answer:
Step-by-step explanation:
x + 80° = 5x ( being corresponding angle )
80° = 5x - x
4x = 80°
x = 80° / 4
x = 20°
☘☘☘...
What is the slope of a line that is parallel to the line y = ?
0
5
undefined
Answer:
I think the answer is ∞ which is the third option, undefined.
Find the eighth term of each geometric sequence. -3,6,-12, . . . . .
The eighth term of the given geometric sequence is: 384.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.Now, given: -3, 6, -12, ....
Here, [tex]\frac{6}{-3}=\frac{-12}{6} = -2[/tex]
Thus this geometric progression has the common ratio = -2.
The nth term of a geometric sequence is given by: [tex]a_n=a_1(r^{n-1})[/tex]
For n = 8, a₈ = a₁ ( r⁸⁻¹)
=> a₈ = (-3)(-2)⁷
=> a₈ = 3 ( 128) = 384.
Hence, The eighth term of the given geometric sequence is: 384.
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Please help with this question asap (true or false question)
Answer:
Step-by-step explanation:
true if 10=x and y equals 33
HIGHLIGHT >
AND NOTES
(a) Taro costs $7.00 per kilogram.
What is the cost of a taro that weighs 510 grams?
$2.83
$3.57
$4.28
$5.10
(b) A taro costs $4.20. What is the weight of the taro in grams (g)?
Answer: a) $3.57 b) 600 g
Step-by-step explanation:
a) 1 kg=1000g
Let's do the proportion:
$7.00 - 1000 g
$x - 510 g
Hence,
[tex]\displaystyle\\x=\frac{7*510}{1000} \\\\x=\frac{3570}{1000} \\\\x=3.57\ dollars[/tex]
b)
Let's do the proportion:
$7.00 - 1000 g
$4.20 - x g
Hence,
[tex]\displaystyle\\x=\frac{4.2*1000}{7} \\\\x=\frac{4200}{7} \\\\x=600 g[/tex]
a) The cost of a taro that weighs 510 grams is, $3.57
b) The weight of the taro in grams (g) is, 600 g
a) Here, Taro costs $7.00 per kilogram.
Hence, the cost of a taro that weighs 510 grams is,
= 1000 grams = $7.00
510 grams = $7.00 x 510 / 1000
= $3.57
Hence, the cost of a taro that weighs 510 grams is, $3.57
b) Since, A taro costs $4.20
Now, WE can change the weight of the taro in grams (g) as,
$7.00 = 1000 g
Hence, $4.2 = 1000 x $4.2 / 7
= 600 grams
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Tammy is standing on a dock beside a lake. She drops a rock from her hand into the lake. After the rock hits the surface of the lake, the rock’s distance from the lake’s surface changes at a rate of -5 inches per second. If Tammy holds her hand 5 feet above the lake’s surface, how far from Tammy’s hand is the rock 4 seconds after it hits the surface?
Lisa's hand is located twenty-five feet distant from the rock.
This is further explained below.
How far from Tammy’s hand is the rock 4 seconds after it hits the surface?Generally, If the rock is falling at a rate of 5 inches per second, then you can easily calculate how deep below the surface of the lake it was after 5 seconds by multiplying 5 by 4.
After four seconds, the rock will have dropped -20 inches.
Because Lisa's hand is five feet above the water's surface, we need to add five to the distance between her hand and the rock in order to calculate how far away it is.
After four seconds, Lisa's hand is located twenty-five feet distant from the rock.
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The distance from Chicago to Cleveland to Cincinnati and back to Chicago is 900 miles. The distance from Chicago to Cleveland is 50 miles more than the distance from Cincinnati to Chicago, and the distance from Cleveland to Cincinnati is 50 miles less than the distance from Cincinnati to Chicago. Find each distance and classify the triangle formed by the three cities.
Answer:
Step-by-step explanation:
Hello, I have a Wonderfull website that can help you with this question. (Mathgenius.com) it should pull it up. its all and every subject you can imagine.
Answer:
Chicago to Cleveland- 350 miles
Cleveland to Cincinnati-250 miles
Cincinnati to Chicago-300 miles
Type of triangle formed? - Scalene
Step-by-step explanation:
so I first give each of them a letter, so I chose a for Chicago to Cleveland, b for Cleveland to Cincinnati, and c for Cincinnati to Chicago. Then I write some equations.
a+b+c =900
b=c-50
a=50+c
i then plug the a and b equation into the first one to get
50+c+c-50+c=900
The fifties cancel out, so we are left with 3c =900 so c=300
From this we can figure out the rest by substituting in 300 for c in the an and b equations.
300-50=250
300+50=350
Bob has a collection of 450 pens. If he gave 90 pens to his friend
Jenny, find the percent of pens left with Bob?
Answer: The answer is: 360
Step-by-step explanation:
Subtract 450 by 90
450 - 90 = 360.
Hope this helped <//3
Which of the following is most likely the next step in the series?
Answer:
Step-by-step explanation:
Im not so sure about this one but I think it is D
The most likely next step in the series is:
Blue color with 7 rays.
Option D is the correct answer.
What is a pattern in a series of figures?A series containing figures will have a pattern between each consecutive figure.
We have,
From the series,
First figure:
Blue color and 3 rays.
Second figure:
Red color and 5 rays
We can assume that the color alternates and the number of rays increases by 2.
So,
Third figure.
Blue color and (5 + 2) rays.
Thus,
Option D is the third figure in the series.
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Solve for x in the diagram below
Find x and the measure of each side.
Δ F G H is an equilateral triangle with F G=3 x-10, G H=2 x+5 , and H F=x+20 .
For given equilateral triangle ΔFGH, x = 15. And the measure of each side is 35 units.
In given question,
ΔFGH is equilateral triangle.
The sides of ΔFGH are:
FG = 3x - 10,
GH =2x + 5 ,
and HF = x + 20 .
We need to find the value of x.
Since ΔFGH is an equilateral triangle, FG = GH = FH
⇒ 3x - 10 = 2x + 5 = x + 20
Consider 3x - 10 = 2x + 5
⇒ 3x - 2x = 5 + 10
⇒ x = 15
Now we find the measure of each side.
FG = 3x - 10
FG = 3(15) - 10
FG = 35 units
But FG = GH = FH
So, the measure of each side is 35 units.
Therefore, for given equilateral triangle ΔFGH, x = 15. And the measure of each side is 35 units.
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If f(x)=-3 x+7 and g(x)=-7 x+3 , what is the value of f(-3)-g(3) ?
a. 40 b. 34 c. 8 d. -8
After solving the equation we have concluded that if f(x)=-3 x+7 and g(x)=-7 x+3 , then the value of f(-3)-g(3) is -8
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
f(x) = -3x + 7
f(-3) = -3(-3) + 7 = 9 + 7 = 16
g(x) = -7x + 3
g(-3) = -7(-3) + 3 = 21 + 3 = 24
f(-3) - g(-3) = 16 - 24 = -8
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the volume of a cube-shaped box for earrings is 125 cubic centimeters. what is the length of one edge of the box?
Answer:
s = 5
Step-by-step explanation:
V=s^3
125 = s^3
s = 125^(1/3) (cube root)
s = 5
Never mind got it wrong
Read the question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.
The Great Pyramid of Giza in Egypt originally had a height of about 148 meters. The base of the pyramid was a square with 230-meter sides. What was the original volume of the pyramid? Round to the nearest whole number.
A. 1,786,503m³
B. 2,609,733 m³
C. 104,128,752 m³
D. 122,716,907 m³
The correct choice is B
In the given statement is:
The Great Pyramid of Giza in Egypt originally had a height of about 148 meters. The base of the pyramid was a square with 230-meter sides.
To find the original volume of the pyramid.
We know that, the Volume of the Pyramid is V = 1/3 Bh,
Where B is the area of the base and h is the height of the pyramid.
Now, V = 1/3 Bh
V = [tex]\frac{1}{3}[/tex](230 x 230)148
V~ 2,609,733[tex]m^{3}[/tex]
Hence, The correct choice is B
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The graph below shows how the number of donations to a charity affects the expected total value of those donations.
In October, the charity received 80 donations.
If the graph continues in the same way, what is the expected total value of the donations in October?
Based on the graph, the expected total value of the donations in October would be $460.
What is the expected value?When donations were 5 in number, the expected value was £30.
When donations were 8, the expected value was £50.
When donations were 15, the expected value was £90.
The slope of the line is:
= (90 - 50) / (15 - 8)
= 5.71
The y-intercept as seen on the graph is 0.
The equation of the line is therefore:
y = 5.71x
The expected value of £80 in donations is therefore:
y = 5.71 x 80
= $460
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PLEASE HELP! rewrite the equation in standard form
Answer:
16x + 10y = 21
Step-by-step explanation:
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
given
[tex]\frac{4}{3}[/tex] x + [tex]\frac{5}{6}[/tex] y = [tex]\frac{7}{4}[/tex]
multiply through by 12 ( the LCM of 3, 6 and 4 ) to clear the fractions
16x + 10y = 21 ← in standard form
Simplify by combining like terms.
2 a+3 b+4 a
By combining the like terms, the simplified form of the the expression 2a+3b+4a is 6a+3b
Given,
The algebraic expression = 2a+3b+4a
Rearrange the terms
2a+3b+4a=2a+4a+3b
Combine the like terms
2a+4a+3b=6a+3b
Hence, by combining the like terms, the simplified form of the the expression 2a+3b+4a is 6a+3b
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Note: Please make sure to properly format your answers. All dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma
($2,354.67). All percentage values in the answers need to include a percentage sign (%). For all items without specific rounding instructions, round your answers to two decimal places,
show both decimal places (5.06).
Jerome deposits $3700, in a certificate of deposit that pays 1.8% interest, compounded annually. How much interest does Jerome earn in one year?
He get the approximately $67 as the amount of interest rate.
According to the statement
We have to find that the interest does Jerome earn in one year.
So, For this purpose, we know that the
A Interest is the amount paid by someone who borrows a certain amount of money.
From the given information:
Jerome deposits $3700, in a certificate of deposit that pays 1.8% interest, compounded annually. How much interest does Jerome earn in one year.
Then
The amount deposited = $3700
The interest pays by the bank = 1.8%
Amount he get by the interest rate = 1.8% of 3700
Amount he get by the interest rate = 1.8 / 100 * 3700
Amount he get by the interest rate = 0.018 * 3700
Amount he get by the interest rate = 66.6.
So, He get the approximately $67 as the amount of interest rate.
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Write the equation in slope-intercept form. What are the slope and y -intercept?
b. -7 x-5 y=35
The equation in slope-intercept form is y = - (7/5x - 7 ).
What is slope - intercept form?The equation of a line is found using the slope-intercept form of a straight line. We need to know the slope of the line and the intercept where the line crosses the y-axis in order to use the slope-intercept formula. Consider a straight line with y-intercept b and slope m. For a straight line with slope "m" and y-intercept "b," the slope intercept form equation is: y = mx + b.
Given the equation is -
-7 x-5 y=35
Divide the equation by 5
-7/5x - y = 7
Rearrange the equation -
y = - (7/5x - 7 ) which is the equation in slope-intercept form.
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An aquarium can be modeled as a right rectangular prism. Its dimensions are 17 in by 13 in by 12 in. How many cubic inches of water are in it when it is full? Round your answer to the nearest tenth if necessary.
Find the slope of the line through each pair of points. 3/2 , - (1/2) and -(2/3) , 1/3
The slope of the line of each pair of points 3/2 , - (1/2) and -(2/3) , 1/3 is zero
What is a slope of line?A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.
Therefore,
m = y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.
Be aware that tan ∅ = y/x.
We also refer to this tan as the line's slope.
We know that slope, slope = m = [tex]\frac{y_2 -y_1}{x_2 -x_1}[/tex]
For the pair of points 3/2 , - (1/2)
m = [tex]\frac{2-2}{-1-3}[/tex]
= 0/(-4)
Hence the slope is zero for these points.
For the pair of points -(2/3) , 1/3
m = [tex]\frac{3-3}{1-(-2)}[/tex]
= 0/3
Hence the slope is zero for these points.
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i need help solving this problem
Answer:
The answer is x=14
Step-by-step explanation:
(4x14 - 1)
(56 - 1)
Hope this helps ( ˊᵕˋ )♡
NEEEDDDD HELP ASSAP. This is about math help
So 1st off you divide 25.2 by 36 since it miles is the x and the cost is y
the unit rate is 0.7 since i divided those 2 numbers
now i just have to do 0.7 times 47
The answer is $ 32.9
sorry if its wrong?
☞ user58580~ ♥
I need to find the perimeter, can you help me?
The total price of a shirt and a cap is $10. If the price of the shirt was doubled and the price of the cap was four times its original price, the total price of a shirt and a
cap would be $26. The following system of equations models this scenario:
x+y=10
2x + 4y = 26
What is the price of each shirt and cap?
A)The price of a shirt is $9, and the price of a cap is $1.
B)The price of a shirt is $8, and the price of a cap is $2.
C)The price of a shirt is $7, and the price of a cap is $3.
D)The price of a shirt is $6, and the price of a cap is $4
Answer:
Step-by-step explanation:
c
C)The price of a shirt is $7, and the price of a cap is $3.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
x+y=10
2x + 4y = 26
solving, we get,
x=7 & y=3
Hence, C)The price of a shirt is $7, and the price of a cap is $3.
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A student has taken three math tests so far this semester. His scores for the first three tests were 75,79 , and 83 .
b. What will be his total score for all six tests?
The total score in the six tests (average) is:
P = 85
What are sequences?A sequence is defined by an order of values and/or elements that have a relationship of variation as a ratio or proportion that makes them predictable.
The first thing to do in this problem is to compare the behavior of the first three trials (variation between each number):
75, 79, 83
83 - 79 = 479 - 75 = 4We must find an expression that models a variable behavior of 4 starting at 75
An = A1 + (n - 1)x : Where x = 4
Fourth proof:A(4) = 75 + (4 - 1)4
A(4) = 87
Fifth test:A(5) = 75 + (5 - 1)4
A(5) = 91
Sixth test:A(6) = 95
Average to know the score of all tests
P = (75 + 79 + 83 + 87 + 91 + 95) / 6
P = 85
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Determine the distance between each pair of points. Then determine the coordinates of the midpoint M of the segment joining the pair of points.
S(6√3, 4,4√2) and T(4√3, 5, √2)
The midpoint is at ([tex]\frac{10\sqrt{3} }{2} , \frac{9}{2} , \frac{9\sqrt{2} }{2}[/tex])
In the given statement is
To find the midpoint of the line segment joining the pair of points
S(6√3, 4,4√2) and T(4√3, 5, √2)
Midpoint:
The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.
m = (A +B)/2
If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =( [tex]\frac{x_{1} +x_{2} }{2} , \frac{y_{1} +y_{2} }{2} , \frac{z_{1} +z_{2} }{2}[/tex] )
where:
(x1 , y1 ,z1) are the coordinates of the first point:
(x2 , y2 , z2) are the coordinates of the second point:
Now, We are given the three points S(6√3, 4,4√2) and T(4√3, 5, √2)
Solving for the midpoint , we have,
m = ([tex]\frac{6\sqrt{3}+4\sqrt{3} }{2} ,\frac{4+5}{2} , \frac{4\sqrt{2}+5\sqrt{2} }{2}[/tex])
m = ([tex]\frac{10\sqrt{3} }{2} , \frac{9}{2} , \frac{9\sqrt{2} }{2}[/tex] )
Therefore, the midpoint is at ([tex]\frac{10\sqrt{3} }{2} , \frac{9}{2} , \frac{9\sqrt{2} }{2}[/tex] )
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The midpoint of AB is (6, 3). If the coordinates of A are (4, -2),
what are the coordinates of B?
Answer:
Step-by-step explanation:
M(6,3)
A(4,-2)⇒A(x1,y1) just incase you understand
B(x2,y2),Now I will use the midpoint formula
[tex]M(\frac{x1+x2}{2} ,\frac{y1+y2}{2} )\\=(\frac{4+x2}{2} ,\frac{-2+y2}{2} )\\=separate(x)\\\frac{4+x2}{2} =6\\4+x2=12\\x2=12-4\\x2=8\\\\\frac{-2+y2}{2} =3\\-2+y2=6\\y2=3+2\\y2=5[/tex]
B(8,5)
Can someone help me with my geometry hw?
Given that line AT bisects angle CAR, the measure of angle TAR is 35 degree.
What is the measure of angle TAR?Given the data in the question;
Line AT bisects ∠CARm∠CAT = 5xm∠CAR = 9x + 7m∠TAR = ?Since Line AT bisects ∠CAR
m∠CAR = 2 × m∠CAT
9x + 7 = 2( 5x )
We solve for x
9x + 7 = 10x
10x - 9x = 7
x = 7
We know that a bisector divides a line or angle into two equal halves.
Hence, m∠CAT = m∠TAR
m∠TAR = m∠CAT = 5x
m∠TAR = m∠CAT = 5(7)
m∠TAR = m∠CAT = 35°
Given that line AT bisects angle CAR, the measure of angle TAR is 35 degree.
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