Answers
Explanation
We are required to determine the value of the following:
[tex]_{15}C_3[/tex]This is achieved thus:
We know that the combination formula is given as:
Therefore, we have:
[tex]\begin{gathered} _{15}C_3=\frac{15!}{3!(15-3)!} \\ _{15}C_3=\frac{15!}{3!12!} \\ _{15}C_3=\frac{15\cdot14\cdot13\cdot12!}{3!12!} \\ _{15}C_3=\frac{15\cdot14\cdot13}{3!}=\frac{15\cdot14\cdot13}{3\cdot2\cdot1} \\ _{15}C_3=5\cdot7\cdot13 \\ _{15}C_3=455 \end{gathered}[/tex]Hence, the answer is:
[tex]455[/tex]
Related Questions
write an equation if a circle has a center of (3,-1) and the diameter 8
Answers
Answer:
[tex](x-3)^2+(y+1)^2=16[/tex]Explanation:
The equation of a circle with center (h, k) and radius of r is generally given as;
[tex](x-h)^2+(y-k)^2=r^2[/tex]Given the center of the circle as (3, -1) and the diameter of 8 (r = d/2 = 8/2 = 4), the equation of the circle can then be written as shown below;
[tex]\begin{gathered} (x-3)^2+\lbrack y-(-1)\rbrack^2=4^2 \\ (x-3)^2+(y+1)^2=16 \end{gathered}[/tex]The first three terms of an arithmetic sequence are as follows.3, -1, -5
Answers
We will take a look at how we go about with arithmatic progressions.
Arithmmetic sequences are caetgorized by the following two parameters:
[tex]\begin{gathered} a\text{ = First term} \\ d\text{ = common difference} \end{gathered}[/tex]Where,
[tex]\begin{gathered} \text{The value of the first term is called ( a )} \\ \text{The common difference between each and every successive value in a sequence is called ( d )} \end{gathered}[/tex]We are given the following arithmetic sequence:
[tex]3\text{ , -1 , -5 , }\ldots[/tex]Now we will try to determine the values of the two parameters ( a and d ) from the given sequence as follows:
[tex]\begin{gathered} a\text{ = 3 }(\text{ first term value )} \\ d\text{ = (-1 ) - ( 3 ) = (-5 ) - ( -1 ) = -4 ( common difference )} \end{gathered}[/tex]Now to determine the value of any term number ( n ) in an arithmetic sequence we use the following formula:
[tex]a_n\text{ = a + ( n - 1 )}\cdot d[/tex]Where,
[tex]n\text{ is the term number}[/tex]So if we plug in the values of arithmetic sequence parameters into the general equation above we get:
[tex]\textcolor{#FF7968}{a_n}\text{\textcolor{#FF7968}{ = 3 + ( n - 1 ) }}\textcolor{#FF7968}{\cdot}\text{\textcolor{#FF7968}{ ( -4 )}}[/tex]Now we are to determine the values of term numbers ( n = 4 ) and ( n = 5 ). We will evaluate the ( an ) for each term number as follows:
[tex]\begin{gathered} \text{\textcolor{#FF7968}{For n = 4}} \\ a_4\text{ = 3 + ( 4 - 1 )}\cdot(-4\text{ )} \\ a_4\text{ = 3 - 12} \\ \textcolor{#FF7968}{a_4}\text{\textcolor{#FF7968}{ = -9}} \\ \\ \text{\textcolor{#FF7968}{For n = 5}} \\ a_5\text{ = 3 + ( 5 - 1 )}\cdot(-4\text{ )} \\ a_5\text{ = 3 - 1}6 \\ \textcolor{#FF7968}{a_5}\text{\textcolor{#FF7968}{ = -}}\textcolor{#FF7968}{13} \end{gathered}[/tex]Hence, the next two consecutive numbers in the arithmetic sequence would be:
[tex]3\text{ , -1 , -5 ,}\text{\textcolor{#FF7968}{ -9}}\text{ , }\text{\textcolor{#FF7968}{-13}}[/tex]If the diameter of a quarter is 24.26 mm and the width of each quarter is 1.75 mm, to the nearest tenth, what is the approximate surface areaof the roll of quarters? Hint there are 40 quarters in a roll of quarters.A)14,366,2 mm
Answers
For this problem, we are given the dimensions of a quarter and we need to determine the surface area of a roll of quarters.
We can approximate the roll as a cylinder, where the height is the sum of the heights of all the quarters and the dimater is equal to the diameter of one quarter. Therefore we have:
[tex]\begin{gathered} A_{base}=\pi r^2=\pi(\frac{24.26}{2})^2=462.24\text{ mm^^b2}\\ \\ h=40\cdot1.75=70\text{ mm}\\ \\ L_{base}=2\pi(\frac{24.26}{2})=76.22\text{ mm}\\ \\ A_{lateral}=70\cdot76.22=5335.4\text{ mm^^b2}\\ \\ A_{surface}=2\cdot462.24+5335.4=6259.88\text{ mm^^b2} \end{gathered}[/tex]The surface area is equal to 6259.88 mm, the correct option is C.
Point L is on line segment KM. Given KL = 15 and LM = 3, determine the
length KM.
Answers
Answer: KM = 18
Step-by-step explanation:
K---------------L---M
15 + 3 = 18
I have no clue what I'm supposed to do I need helpFind the equation of line.
Answers
The general equation of line with slope m and point (x_1,y_1) is,
[tex]y-y_1=m(x-x_1)[/tex]Determine the equation of line.
[tex]\begin{gathered} y-1=3(x+2) \\ y-1=3x+6 \\ y=3x+6+1 \\ =3x+7 \end{gathered}[/tex]So equation of line is y = 3x +7.
△VWY is equilateral, VZ≅WX, and ∠XWY≅∠YVZ. Complete the proof that △VYZ≅△WYX.VWXYZ
Answers
The statement
[tex]VY\cong WX[/tex]is true because
[tex]\Delta VWY[/tex]is an equilateral triangle.
Now, the last statement is true because the triangles have 2 sides and one angle congruent, therefore, by the SAS criterion, the triangles are congruent.
Answer:4.- Triangle VWY is an equilateral triangle.
5.- SAS criterion.
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!
Answers
Answer:
To find the perimeter of the triangle, you would add p + m + n. To find the area of the triangle you would use (p x m) /2. To find a missing side of the triangle, given that it is a right triangle, you would use p^2 + m^2 = n^2
The ratio of girls to
boys in a math club
was 1:7. There were
6 girls. How many
boys
Were there in the
club?
Answers
Answer: 42
Step-by-step explanation: If the ratio is 1 girl for 7 boys and there are 6 girls you do 6x7=42
When 80% of a number is added to the number, the result is 162.
Answers
Given:
80% of a number is added to the number, the result is 162.
Required:
To find the number.
Explanation:
80% of a number is added to the number
[tex]\begin{gathered} \frac{80}{100}x+x \\ \\ =0.8x+x \end{gathered}[/tex]The result is 162, so
[tex]\begin{gathered} 0.8x+x=162 \\ \\ 1.8x=162 \\ \\ x=\frac{162}{1.8} \\ \\ x=90 \end{gathered}[/tex]Final Answer:
The number is 90.
The formula, = / + , converts temperatures between Celsius and Fahrenheit degrees. What is the temperature in degrees Celsius that is equivalent to 14 degrees FahrenheitA) -10B) -9 C) -8D) -7
Answers
Hello there. To answer this question, we need to plug in the value given by the question and solve for C, the temperature in Celsius.
We want to find the equivalent temperature in Celsius to 14 degrees Fahrenheit.
Knowing that F = 9/5C + 32, making F = 14 lead us to:
14 = 9/5C + 32
Subtract 32 on both sides of the equation
9/5C = -18
Multiply both sides of the equation by a factor of 5/9, in order to get:
C = 5/9 (-18) = -10.
This is the equivalent temperature we were looking for.
if 2 angles from a line
Answers
If two angles form a linear pair, then they form a straight line, and the sum of their measures is 180 degrees.
This illustrated below;
In the illustration above, angle measure 1 and 2 both equal to 180 degrees. Angle 1 and angle 2 are refered to as a linear pair.
7. Find the slope of a line which passes through the origin and point (2,4).A 0.5B -0.5C 2D 4
Answers
Answer:
C
Step-by-step explanation:
the slope of a line is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
in our case here we are going e.g. from the origin (0, 0) to (2, 4).
so, x changes by +2 (from 0 to 2).
y changes by +4 (from 0 to 4).
therefore, the slope is
+4/+2 = 2
FYI - the direction is not important. it works the same way in the other direction. but what is important : once you pick a direction for one coordinate, you have to use the same direction for the second one. you cannot go e.g. for x in one direction and for y in the other.
The population of a country dropped from 52.5 million in 1995 to 44.2 million in 2007. Assume that P(t), the population, in millions, t years after 1995, is decreasing according to the exponential decay model.a) Find the value of k, and write the equation.b) Estimate the population of the country in 2018.c) After how many years will the population of the country be million, according to this model?
Answers
we have the exponential decay function
[tex]P(t)=52.5(e)^{-0.0143t}[/tex]Part b
Estimate the population of the country in 2018
Remember that
t=0 -----> year 1995
so
t=2018-1995=23 years
substitute in the function above
[tex]\begin{gathered} P(t)=52.5(e)^{-0.0143\cdot23} \\ P(t)=37.8\text{ million} \end{gathered}[/tex]Part c
After how many years will the population of the country be 2 million, according to this model?
For P(t)=2
substitute
[tex]2=52.5(e)^{-0.0143t}[/tex]Solve for t
[tex]\frac{2}{52.5}=(e)^{-0.0143t}[/tex]Apply ln on both sides
[tex]\begin{gathered} \ln (\frac{2}{52.5})=\ln (e)^{-0.0143t} \\ \\ \ln (\frac{2}{52.5})=(-0.0143t)\ln (e)^{} \end{gathered}[/tex][tex]\ln (\frac{2}{52.5})=(-0.0143t)[/tex]t=229 years
Find the area of the triangle. 30 cm 15 cm cm2
Answers
Area of the triangle is 225 sq. cm.
Given:
The base of the triangle is, b = 30cm.
The height of the triangle is, h = 15cm.
The objective is to find the area of the triangle.
The formula to find the area of the triangle is,
[tex]A=\frac{1}{2}\times b\times h[/tex]Now, substitute the given values in the above formula.
[tex]\begin{gathered} A=\frac{1}{2}\times30\times15 \\ A=225cm^2 \end{gathered}[/tex]Hence, the area of the triangle is 225 sq. cm.
A bridge AB is to be built across a river. The point C is located 62m from B, and angle A is 80 degrees, angle C is 60 degrees. How long is the bridge
Answers
The points A, B, and C form a triangle.
From the given information in the question, the triangle ABC can be drawn to have the following parameters:
Recall the Sine Rule. Applied to the triangle above, the rule is stated as follows:
[tex]\frac{BC}{\sin A}=\frac{AC}{\sin B}=\frac{AB}{\sin C}[/tex]The length of the bridge is AB. Given that the measures of angles A and C, and side BC are known, the following ratio is used to solve:
[tex]\frac{BC}{\sin A}=\frac{AB}{\sin C}[/tex]Substituting known values, the length of AB is calculated as follows:
[tex]\begin{gathered} \frac{62}{\sin80}=\frac{AB}{\sin60} \\ AB=\frac{62\times\sin60}{\sin80} \\ AB=54.52 \end{gathered}[/tex]The bridge is 54.52 m long.
consider the following linear equation 5x-5y=15 determine the slope and Y-intercept (entered as an ordered x and y pair) of the equation
Answers
The first step to solve this problem is to rewrite the equation in slope intercept form, to do it, solve the given equation for y:
[tex]\begin{gathered} 5x-5y=15 \\ -5y=-5x+15 \\ y=x-3 \end{gathered}[/tex]According to this, the slope of the line is 1.
The y intercept is (0,-3).
The line graphed should look like this:
in the diagram of BED below, FC||ED,BF=6,FE=18, and BC=22. What is the length of BD
Answers
we know that
The side splitter theorem states that if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally
so
18/6=DC/11
solve for DC
DC=3*11
DC=33
Find the length of BD
BD=BC+DC
BD=11+33=44 units
therefore
the answer is 44 units
B. Are the graphs of y = a|x| and y = |ax| the same when a is negative? Why?
Answers
The absolute value gives always a positive number.
If a is negative, then a|x| is negative and |ax| is positive.
Therefore, the graph of y=a|x| won't be the same as the graph of y=|ax|.
Another way to see it, is by using the property:
[tex]\mleft|ax\mright|=\mleft|a\mright|\cdot\mleft|x\mright|[/tex]Since a is negative, then |a| = -a. So, |ax| = -a|x|, which is clearly different from a|x|.
i need help with this pls
Answers
Mathematically speaking, the linear pair postulate and linear pair theorem both express the same thing.
A linear pair is made up of two angles, and the sum of their measures is 180°.What is the formula for linear pairs?A two-variable linear equation of the form axe + by + c, with a, b, and c all being real numbers and not equal to zero.The Transitive Property states that if all real numbers x, y, and z are equal, then x=z. Substituting characteristics. If x=y, then x can be swapped to y in any equation or formula.Mathematically speaking, the linear pair postulate and linear pair theorem both express the same thing. A linear pair is made up of two angles, and the sum of their measures is 180°.Line pairs can be congruent. Adjacent angles are joined by a vertex. Angles that are similar cross across. A linear pairing is unnecessary.
Therefore, mathematically speaking, the linear pair postulate and linear pair theorem both express the same thing.
A linear pair is made up of two angles, and the sum of their measures is 180°.To learn more about the Linear pair theorem refer to:
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solve and reduce 10÷2/9
Answers
We have the following:
[tex]10\div\frac{2}{9}[/tex]solving:
[tex]\frac{10}{\frac{2}{9}}=\frac{\frac{10}{1}}{\frac{2}{9}}=\frac{10\cdot9}{2\cdot1}=\frac{90}{2}=45[/tex]The answer is 45
I need help with this problem. Quick answer is fine
Answers
[tex]a^{\frac{-m}{n}}=\frac{1}{a\frac{m}{n}}=\frac{1}{\sqrt[n]{a^m}}[/tex]
what is the measure in radians of central angle 0 in the circle below
Answers
For this exercise you need to use the following formula:
[tex]\theta=\frac{S}{r}[/tex]Where θ is the Central angle in radians, "S" is the arc length and "r" is the radius of the circle.
In this case, you can identify that:
[tex]\begin{gathered} S=8\pi cm \\ r=8\operatorname{cm} \end{gathered}[/tex]Knowing these values, you can substitute them into the formula and then evaluate, in order to find the measure of the Central angle in radians. This is:
[tex]\begin{gathered} \theta=\frac{8\pi cm}{8\operatorname{cm}} \\ \\ \theta\approx\pi radians \end{gathered}[/tex]The answer is:
[tex]\pi radians[/tex]Stacia has 28 red and blue marbles. The ratio of red to blue marbles is 1: 6.
How many blue marbles does Stacia have?
Answers
Answer:You have 24
Step-by-step explanation:
I need to order the numbers least to greatest for the numbers: sq root of 144 234/3 and 68.12
Answers
So, the order would be 8.25, 8.832 and 12
I need help with this answer can you explain it
Answers
The solution.
The correct answer is y-intercept at (0,1) and decreasing over the interval
[tex]\lbrack-\infty,\infty\rbrack[/tex]Hence, the correct answer is the last option (option D)
Complete the equation of the line through (-7,-3) and (-2,4)
Answers
If one line passes through the points (x₁, y₁) and (x₂, y), the slope of the line can be calculated using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}...(1)[/tex]Additionally, the equation can be expressed in point-slope form as:
[tex]y-y_2=m(x-x_2)...(2)[/tex]From the problem, we identify:
[tex]\begin{gathered} (x_1,y_1)=(-7,-3) \\ \\ (x_2,y_2)=(-2,4) \end{gathered}[/tex]Then, we calculate the slope of the line using (1):
[tex]m=\frac{4-(-3)}{-2-(-7)}=\frac{4+3}{-2+7}=\frac{7}{5}[/tex]Finally, we find the equation of the line using (2):
[tex]\therefore y-4=\frac{7}{5}(x+2)[/tex]EspañolAt a football game, a vender sold a combined total of 249 sodas and hot dogs. The number of sodas sold was 55 more than the number of hot dogs sold. Findthe number of sodas sold and the number of hot dogs sold.Number of sodas sold:Number of hot dogs sold:1Х5?
Answers
Given:
Vender sold a combined total of 249 sodas and hot dogs.
The number of sodas sold was 55 more than the number of hot dogs sold.
Let x and y be the number of sodas and hot dogs sold.
[tex]x+y=249\ldots\text{ (1)}[/tex][tex]x=y+55\ldots\text{ (2)}[/tex]Substitute equation (2) in (1)
[tex]y+55+y=249[/tex][tex]2y=249-55[/tex][tex]2y=194[/tex][tex]y=97[/tex][tex]x=97+55[/tex][tex]x=152[/tex]Number of sodas sold is 152.
Number of hot dogs sold is 97.
Drag the tiles to the correct boxes. Not all tiles will be used.
Match each equation with a value of x that satisfies it.
18
1
9
2
5
(x - 2) = 2
√²+7=4
V1-x
= -1
-3
Answers
For a given exponential expression, the determined value is x=3,0,6.
What are exponential expressions?A component of an exponential expression is an exponent. Powers can be expressed succinctly using exponential expressions. The exponent represents the number of times the base has been multiplied.Powers can be expressed succinctly using exponential expressions. The exponent represents the number of times the base has been multiplied. Exponential expressions or the representation of multiplication with exponents can be streamlined to produce the most efficient notation possible.Each exponential expression's x value is evaluated.
Therefore,
1. [tex]$ \sqrt{x^2+7}=4 \\[/tex]
[tex]&\left(x^2+7\right)=4^2 \\[/tex]
[tex]&\left(x^2+7\right)=16 \\[/tex]
simplifying the above equation, then we get
x² = 16 - 7 = 9
x = 3
2. [tex]$\sqrt[2]{1-x}=-1$[/tex]
(1 -x) = (-1)²
1 - x = 1
x = 0
3. [tex](x-2)^{\frac{1}{2}}=2 \\[/tex]
(x - 2) = 2²
x - 2 = 4
x = 6
The determined value is x=3,0,6 for a given exponential expression.
To learn more about exponential expression, refer to:
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If AACB = ADCE, ZCAB = 63°,ZECD = 52°, and ZDEC = 5xDE(c сx = [?]
Answers
Since angles ACB and ECD are vertical angles, they are congruent, so we have
Calculating the sum of internal angles in triangle ABC, we have:
[tex]\begin{gathered} ABC+ACB+CAB=180 \\ ABC+52+63=180 \\ ABC=180-52-63 \\ ABC=65 \end{gathered}[/tex]Since triangles ACB and DCE are congruent, we have [tex]\begin{gathered} DEC=ABC \\ 5x=65 \\ x=13 \end{gathered}[/tex]
Solve the equation for y.1/3 x + y = 4
Answers
In order to solve the equation for y, we just need to isolate the variable y in one side of the equation. So we have:
[tex]\begin{gathered} \frac{1}{3}x+y=4 \\ y=4-\frac{1}{3}x \end{gathered}[/tex]So the answer is y = 4 - 1/3 x