Answer:
3003 number of 5-member chess teams can be chosen from 15 interested players.
Step-by-step explanation:
Given:
Number of the interested players = 15
To Find:
Number of 5-member chess teams that can be chosen = ?
Solution:
Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter. To calculate combinations, we will use the formula[tex]nCr = \frac{n!}{r!(n - r)!}[/tex]
where
n represents the total number of items,
r represents the number of items being chosen at a time.
Now we have n = 15 and r = 5
Substituting the values,
[tex]15C_5 = \frac{15!}{5!(15- 5)!}[/tex]
[tex]15C_5 = \frac{15!}{5!(10)!}[/tex]
[tex]15C_5 = \frac{15!}{5!(10)!}[/tex]
[tex]15C_5 = \frac{15\times \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 }{5 \times 4 \times 3 \times 2 \times 1(10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1)}[/tex]
[tex]15C_5 = \frac{15\times \times 14 \times 13 \times 12 \times 11}{(5 \times 4 \times 3 \times 2 \times 1)}[/tex]
[tex]15C_5 = \frac{360360}{120}[/tex]
[tex]15C_5 = 3003 [/tex]
Is the following relation a function?
Answer:
No
Step-by-step explanation:
A function is a relation in which no two ordered pairs have the same first element.
A function associates each element in its domain with one and only one element in its range.
Which number line best shows how to solve −8 − (−6)?
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 6.
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 6. Another arrow points from negative 6 to negative 8.
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 6. Another arrow points from negative 6 to 2.
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.
Answer:
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.
Step-by-step explanation:
find the number line best shows how to solve −8 − (−6)
In the number line first we start with -8 . negative and negative becomes positive
from -8 move 6 units to the right. So it ends at -2
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.
a 20.00 pair of jeans is discounted 20%. What is the final price of the jeans?
Answer:
16.00
Step-by-step explanation:
When you divide twenty percent(0.20) to 20.00 you will get sixteen or 4.00 dollars off
3x + 4x − 2x = − 76 + 96
Answer:
4
Step-by-step explanation:
first add up the xs that gives you 5x because first 3x+4x gives you 7 then minus that with 2x that gives you five,
now add the numbers -76+96 that gives you 20 now the equation becomes
5x=20
now divide 20 by 5 that gives you 4
here is an inequality 2x + 5 > 50 explain the steps you would use to solve the equation for x what would the graph look like
Answer:
[tex]x>22.5[/tex]
Step-by-step explanation:
Given linear inequality:
[tex]2x+5>50[/tex]
Solving for [tex]x[/tex]
Subtracting both sides by 5.
[tex]2x+5-5>50-5[/tex]
[tex]2x>45[/tex]
Dividing both sides by 2.
[tex]\frac{2x}{2}>\frac{45}{2}[/tex]
∴ [tex]x>22.5[/tex]
The graph of the inequality is shown below.
The line is represented by dotted line because the inequality sign is only greater than which means 22.5 is not included in the solution.
Janet charges an upfront fee of $20 plus $7.50 an hour for babysitting. Lisa does not charge an upfront fee, but charges $8.75 an hour. After how many hours will their charge be equal?
After 16 hours, the charges will be same.
Step-by-step explanation:
Given,
Janet's upfront fee = $20
Charges per hour = $7.50
Let,
x be the number of hours.
J(x) = 7.50x+20
Lisa has no upfront fee.
Charges per hour = $8.75
L(x) = 8.75x
For the charges to be equal;
J(x) = L(x)
[tex]7.50x+20=8.75x\\20=8.75x-7.50x\\20=1.25x\\1.25x=20[/tex]
Dividing both sides by 1.25
[tex]\frac{1.25x}{1.25}=\frac{20}{1.25}\\x=16[/tex]
After 16 hours, the charges will be same.
Keywords: function, division
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What is the slope of the line shown below?
Answer:
B
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 1, 8) and (x₂, y₂ ) = (2, - 4) ← 2 points on the line
m = [tex]\frac{-4-8}{2+1}[/tex] = [tex]\frac{-12}{3}[/tex] = - 4 → B
Answer:
The slope of the given line is -4.
So, option (B) is correct.
Step-by-step explanation:
We know that, slope (m) of a line passing through points (x₁, y₁) and (x₂, y₂) is given by,
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Now, the given line passes through the point (-1, 8) and (2,-4).
So, (x₁, y₁) = (-1, 8) and (x₂, y₂) = (2, -4)
So, by using the above formula, we get
Slope(m) of the given line passing through (-1, 8) and (2, -4) is given by,
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{-4-8}{2-(-1)}[/tex]
[tex]\implies\;m = \frac{-12}{3}=-4[/tex]
∴The slope of the given line is -4.
Hence, option (B) is correct.
1. Using n, n+1, and n+2 to represent three consecutive integers, write the statement of multiplying three consecutive integers and then adding the middle integer to the result of the multiplication as an expression.
2. Simplify the expression from problem 1 and write the answer in standard form.
3. Show that the answer from problem 2 is equivalent to the cube of the middle integer.
Answer:
1) Expression is
[tex](n+1)+(n^3+3n^2+2n)=n^3+3n^2+3n+1[/tex]
2) The standard form of the expression is
[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]
3) The expression is
[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]
Where [tex](n+1)^3[/tex] is the cube of the middle integer
Step-by-step explanation:
1) Given three consecutive integers are n. n+1, and n+2
Now multiplying the three consecutive integers
[tex](n)(n+1)(n+2)=(n^2+n)(n+2)[/tex]
[tex]=n^3+2n^2+n^2+2n[/tex]
[tex]=n^3+3n^2+2n[/tex]
Therefore [tex](n)(n+1)(n+2)=n^3+3n^2+2n[/tex]
Now adding the middle integer to the result of the multiplication.
ie, adding (n+1) to the result of the multiplication [tex]n^3+3n^2+2n[/tex]
[tex](n+1)+(n^3+3n^2+2n)=n+1+n^3+3n^2+2n[/tex]
[tex]=3n+1+n^3+3n^2[/tex]
Therefore [tex](n+1)+(n^3+3n^2+2n)=n^3+3n^2+3n+1[/tex]
2) Expression is [tex]n^3+3n^2+3n+1[/tex]
Now we simplify the above expression
[tex]n^3+3n^2+3n+1=n^3+3n^2(1)+3(n)(1)^2+1^3[/tex]
[tex]=(n+1)^3[/tex] (by using [tex](a+b)^3=a^3+3a^2b+3ab^2+b^3[/tex] , Here a = n and b=1)
[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]
3) The expression is
[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]
Where [tex](n+1)^3[/tex] is the cube of the middle integer.
ie, expression is equivalent to the cube of the middle integer
Please help! A chemist has 100ml of 25% acid solution. How much of the solution does she need to drain and replace with 70% acid solution to obtain 100ml of 60% acid solution?
Answer:
77.78
Step-by-step explanation:
Answer:
77.78
Step-by-step explanation:
i had this ? on rsm student portal.
find the area of the shape shown below
Answer:
6
Step-by-step explanation:
all you have to do is split the shape in half to create a square and a triangle then for the triangle the equation would be 2*2=4 then divide by 2 witch is 2 the do the square witch is 2*2=4 then you add 4+2=6 and i'm only in 7th grade.
Solve
2w+2(w+3.8)=58
Answer:
w=12.6
Step-by-step explanation:
2w+2(w+3.8)=58
2w+2w+7.6=58
4w+7.6=58
4w=58-7.6
4w=50.4
w=50.4/4
w=12.6
Determine the y-intercept of x 12 + y 3 = 2
The y-intercept of [tex]\(12x + y^3 = 2\) is at \((0, \sqrt[3]{2})\).[/tex]
To find the y-intercept of the equation [tex]\(12x + y^3 = 2\)[/tex], we first need to understand what the y-intercept represents. The y-intercept is the point where the graph intersects the y-axis, which means the x-coordinate of this point is 0.
To find the y-intercept, we set [tex]\(x = 0\)[/tex] in the equation and solve for y:
[tex]\[12(0) + y^3 = 2\][/tex]
[tex]\[y^3 = 2\][/tex]
To solve for y, we take the cube root of both sides:
[tex]\[y = \sqrt[3]{2}\][/tex]
So, the y-intercept of the equation is [tex]\((0, \sqrt[3]{2})\).[/tex]
Graph the inequality.
Match the graph to the correct inequality below.
(attatched)
x > 5
x < 5
x ≥ 5
x ≤ 5
Answer:
x<=5
Step-by-step explanation:
Two things
direction its pointing is always how the sign will look likeif the circle is shaded it will have an "or equals to" sign; if its blank, there is only the "greater/lesser" signA rectangular prism with a volume of 555 cubic units is filled with cubes with side lengths of \dfrac13
3
1
start fraction, 1, divided by, 3, end fraction unit.
How many \dfrac13
3
1
start fraction, 1, divided by, 3, end fraction unit cubes does it take to fill the prism?
135 cubes are required to fill the prism
Solution:
Given that a rectangular prism with volume of 5 cubic units is filled with cubes with side lengths of [tex]\frac{1}{3}[/tex] units
Then the number of cubes required to fill the prism will be given by:
[tex]\text { number of cubes }=\frac{\text {volume of rectangular prism}}{\text {volume of cube}}[/tex]
Volume of rectangular prism = 5 cubic units
[tex]\text{ Volume of cube}=(\text { side })^{3}$[/tex]
[tex]\text { Volume of cube }=\left(\frac{1}{3}\right)^{3}=\frac{1}{27}[/tex]
Therefore number of cubes required to fill the prism are:
[tex]\text { number of cubes }=\frac{5}{\frac{1}{27}}=5 \times 27=135[/tex]
Therefore 135 cubes are required to fill the prism
Answer:
135
Step-by-step explanation:
A relation is plotted as a linear function on the coordinate plane starting at point A (0, 3) and ending
at point B (2, 7)
What is the rate of change for the linear function and what is its initial value?
Answer:
initial value=2
Step-by-step explanation:
equation of line,
y-[tex]y_1[/tex]=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex][tex](x-x_1)[/tex]..............(1)
put co ordinate (0,3) and (2,7) in the equation (1)
y-3=[tex]\frac{7-3}{2-0}[/tex](x-0)
y-3=2x
y=2x+3
rate of change of linear equation=[tex]\frac{\partial (2x+3)}{\partial x}[/tex]
[tex]\frac{\partial y}{\partial x}[/tex]=2
hence, initial value=2 answer
Does anyone know how you work out this bearings question???
The bearing of A from B according to the diagram is 82.86°
Using trigonometric relations ;
Tan B = opposite/ AdjacentB = bearing of A from B
Now we have;
Tan B = 40 /5
Tan B = 8
Take the inverse value of the tangent ;
[tex]B = Tan^{-1} (8) [/tex]
B = 82.86°
Hence, the bearing of A from B is 82.86°
Higher Order Thinking A mother
manatee, pictured to the right, is three
times as long as her baby manatee.
a. How long is her baby manatee? Write
and solve an equation.
b. If a blue whale is 9 times as long as the
manatee shown, how much longer is
a blue whale than the manatee? Write
and solve equations.
12 feet
The equation for baby manatee is 3x = 12 and length is 4 feet and length of blue whale is 108 feet.
What is linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have given:
Length of Mother manatee = 12 feet.
Let's suppose the length of a baby manatee is 'x'.
So the equation can be framed as:
3x = 12
x = 4 feet
The length of blue whale is = 9(length of mother manatee)
The length of blue whale is = 9(12) = 108 feet
Thus, the equation for baby manatee is 3x = 12 and length is 4 feet and length of blue whale is 108 feet.
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Absolute value of 225
225
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Answer: 3x-x+2=4
Step-by-step explanation:
absolute value of 225 = | 225 | = 225
Which fraction is the reciprocal of 2 5/7 ASAP!!!
7/19
bc 2 5/7 = 19/7. the reciprocal is a fraction reversed. or upside down that is. So, your answer is 7/19
Answer:
7/19
Step-by-step explanation:
2 5/7=19/7
Coordinates of centroid of a triangle with vertices of (0,1) (2,6) (7,2)
Answer:
The centroid is located at (3,3)
Step-by-step explanation:
Centroid Of A Triangle
The centroid of a triangle is the point where its three medians intersect. It is also the center of gravity of the triangle. The medians are lines that go from each vertex to the midpoint of the opposite side.
Given A(ax,by), B(bx,by), C(cx,cy) the points of the vertices, then the coordinates of the centroid [tex]P(x_c,y_c)[/tex] are
[tex]\displaystyle x_c=\frac{ax+bx+cx}{3}[/tex]
[tex]\displaystyle y_c=\frac{ay+by+cy}{3}[/tex]
The vertices are (0,1) (2,6) (7,2), thus
[tex]\displaystyle x_c=\frac{0+2+7}{3}=3[/tex]
[tex]\displaystyle y_c=\frac{1+6+2}{3}=3[/tex]
The centroid is located at (3,3)
The coordinates of centroid are (3,3)
Step-by-step explanation:
The coordinates of centroid of a triangle are calculated by finding average of x-coordinates of vertices and the average of y-coordinates of vertices.
Given vertices are:
(0,1) (2,6) (7,2)
So,
x-coordinate of centroid:
[tex]x = \frac{0+2+7}{3}\\=\frac{9}{3}\\= 3[/tex]
y-coordinate of centroid:
[tex]y = \frac{1+6+2}{3}\\=\frac{9}{3}\\= 3[/tex]
Hence,
The coordinates of centroid are (3,3)
Keywords: Triangle, centroid
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Linda owns 4 shares of a certain stock. Yesterday the total value of her shares went down by 32 dollars. What was the change in value for each share?
Answer:
The value of each share decreased by $8.
Step-by-step explanation:
Number of shares of a certain stock Linda owned = 4
Total value of shares went down by = $32
So find the change in value of each share.
Solution:
Let the total value of each share in dollars be = [tex]x[/tex]
Value of 4 shares in dollars will be = [tex]4x[/tex]
The total value of shares went down by $32
So, new value of 4 shares = [tex]4x-32[/tex]
New value of each share = [tex]\frac{New\ value\ of\ total\ shares}{4}[/tex]
⇒ [tex]\frac{4x-32}{4}[/tex]
Splitting the denominators.
⇒ [tex]\frac{4x{{4}-\frac{32}}{4}[/tex]
⇒ [tex]x-8[/tex]
Original value of each share in dollars was = [tex]x[/tex]
New value of each share in dollars = [tex]x-8[/tex]
Thus, we can see that the value of each share decreased by $8.
How many 3/4 cup servings are in 12 cups of cherries?
Answer:
16 serving.
Step-by-step explanation:
Given: 3/4 cup servings.
Now, computing the number of serving in 12 cups of cherries.
Using unitary method to solve.
∴ Number of serving= [tex]total\ cups \times number\ of\ serving\ per\ cup[/tex]
Number of serving in one cup is [tex]\frac{4}{3}[/tex]
Number of serving in 12 cups = [tex]12\times \frac{4}{3} = 16 \ serving[/tex]
Number of serving in 12 cups= [tex]16\ serving[/tex]
∴ There are 16 serving is possible in 12 cups of cherries.
Final answer:
To calculate the number of 3/4 cup servings in 12 cups of cherries, divide 12 by 3/4, which equals 16 servings.
Explanation:
To determine how many 3/4 cup servings are in 12 cups of cherries, we can divide the total number of cups by the size of one serving.
First, we express the serving size and the total amount in the same units: 3/4 cup and 12 cups.
Next, we divide the total amount of cherries by the serving size: 12 cups ÷ 3/4 cup.
To perform the division, we can multiply 12 by the reciprocal of 3/4, which is 4/3 (12 × 4/3 = 16).
The result is that there are 16 servings of 3/4 cup in 12 cups of cherries.
solve the inequality for x: -3(2x+5) < -45
Answer:
x>5
Step-by-step explanation:
-3(2x+5)<-45
2x+5<-45/-3
2x+5<15
2x<15-5
2x<10
x<10/2
x<5
x>5
Demuestra que al utizar agrupaciones de terminos para factorizar el polinomio 6a2,+15a-4a-10 la respuesta es( 2a+5)(3a-2)
Answer:
Step-by-step explanation:
the rate of watering is Rs. 4 per ll.
6) Find the area of the cardboard required to make a closed box of length
25cm, 5m and height 15cm.
dim deep is to be made. It is open at the
Answer:
The area of cardboard required is 40750 cm².
Step-by-step explanation:
Given:
Length (L) = 25 cm
Width (W) = 5 m = 5 × 100 = 500 cm
Height (H) = 15 cm
Area of the cardboard is same as the total surface area of the closed rectangular box.
Total surface area of the rectangular box is given as:
[tex]SA=2(LW+WH+LH)\\\\SA=2(25\times 500+500\times 15+15\times 25)\\\\SA=2(12500+7500+375)\\\\SA=2\times 20375=40750\ cm^2[/tex]
So, the area of cardboard required is 40750 cm².
The base of a triangle is 10 cm greater than the height. The area is 28 cm2. Find the height and the
base.
PLEASE HELP! 20 POINTS!
What is the apparent solution to the system of equations? y=1/2x+2y=2x−1 Graph the system of equations using the Line tool. Plot a point at the apparent solution to the system using the Point tool.
Answer:
y=x/2−1/2
Step-by-step explanation:
Choose the point-slope form of the line passing through (3,5) with a slope of -3.
O y -3'= -3 (ix – 5)
0 -3(y – 5) = x - 3
y - 5 = -3 (0 - 3)
O 3x - 5y = -3
O
Answer:
answer is y-5=-3(x-3)
Step-by-step explanation:
your y-coordinate is 5 s you would write y-5 and your slope is -3 with your x-coordinate as 3 so that would be written as -3(x-3). The equation put together correctly would be y-5=-3(x-3)
Answer:
y-5=-3(x-3)
Step-by-step explanation:
y-y1=m(x-x1)
y-5=-3(x-3)
80 Point Offer, Help is required on these questions. Highest offer I've given.
Answer:
Answer 1.) f(x)=0x-4
Answer 2.) f(x)=2/3x+4
Answer 3.) i don't really get this one so sorry
Answer 4.) f(x)= -1/5x+2
hope this helped it took me a while to figure out this but looks like the guy ahead of me beat me to it
Step-by-step explanation:
HELP PLEASE!
Compare the function with the parent function. Without graphing, what are the vertex, axis of symmetry, and transformations of the given function?
Y= |6x-2|-7
A.)(1/3,7);x=1/3; translated to the right 1/3 unit and up 7 units
B.) (1/3,7);x=1/3; translated to the left 1/3 unit and down 7 units
C.) (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units
D.) (1/3,-7);x=1/3; translated to the left 1/3 unit and up 7 units
Answer:
C. (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units.
Step-by-step explanation:
The function is (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units.
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, codomain, and domain.
The parent function is:
g(x) = IxI
And we have:
f(x) = I6x - 2I - 7
Rearranging the function:
f(x) = 6Ix - 1/3I - 7
Then, now let's define some transformations:
If we start with g(x), a translation of N units to the right is:
f(x) = g(x - N)
if we start with g(x), a translation of N units up is:
f(x) = g(x) + N
A translation down would be:
f(x) = g(x) - N
And a vertical dilation of scale factor A is written as:
f(x) = A × g(x)
Then in this case we have:
A translation to the right of 1/3 units.
A dilation of scale factor 6.
A translation down of 7 units.
And the axis of symmetry will be when the absolute value part is equal to zero, or when
6Ix - 1/3I = 0
And that is when x = 1/3.
Therefore, the function is (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units.
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