The 10 players can be chosen for each place on the lineups, so:
- For the first place he can choose between 10 players (and choose 1)
-for the second place he can choose between 9 players (because 1 is in the 1st place)
- for the 3rd place he can choose between 8 players and this repeat
-4th place - 7 players
-5th place - 6 players
- 6th place - 5 players
and the same for the other 3 places
now to get the amount of possibles lineups we need to multiply the options to be chosen on each place, so:
10*9*8*7*6*5*4*3*2= 3628800
So the answer is:
Option A. 3,628,800
Find an equivalent equation in rectangular coordinates.r(1 - 2 cos θ) = 1
SOLUTION
The given equation is:
[tex]r(1-2\cos\theta)=1[/tex]Rewrite the equation
[tex]r-2r\cos\theta=1[/tex]Recall that
[tex]r=\sqrt{x^2+y^2}x=rcos\theta[/tex]Substituting these values gives
[tex]\begin{gathered} \sqrt{x^2+y^2}-2x=1 \\ (\sqrt{x^2+y^2})^2=(1+2x)^2 \\ x^2+y^2=1+4x^2+4x \\ 1+4x^2+4x-x^2-y^2=0 \\ 3x^2-y^2+4x+1=0 \end{gathered}[/tex]Therefore the required equation is
[tex]3x^{2}-y^{2}+4x+1=0[/tex]107(a) Find an angle between 0 and 2n that is coterminal with3(b) Find an angle between 0° and 360° that is coterminal with -240°.
Given:
(a) Find an angle between 0 and 2π that is coterminal with 10π/3
The given angle (10π/3) > 2π
So, we will subtract 2π to get the coterminal angle
[tex]\frac{10π}{3}-2π=\frac{4π}{3}[/tex]So, the answer will be 4π/3
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(b) Find an angle between 0 and 360 that is coterminal with -240
The given angle is a negative value of the angle, to get the positive value add 360
So,
[tex]-240\operatorname{\degree}=-240\operatorname{\degree}+360\degree=120\operatorname{\degree}[/tex]So, the answer will be 120°
Question 4 of10If f(x) = 2x² + 1 and g(x)=x2-7, find (f- g)(x).
Solution:
Given the functions below
[tex]\begin{gathered} f(x)=2x^2+1 \\ g(x)=x^2-7 \end{gathered}[/tex]The composite function will be
[tex]\begin{gathered} (f-g)(x)=(2x^2+1)-(x^2-7) \\ (f-g)(x)=2x^2+1-x^2+7=2x^2-x^2+1+7=x^^2+8 \\ (f-g)(x)=x^2+8 \end{gathered}[/tex]Hence, the answer is x²+8
Use the rule to write the first 12 in the pattern. Discribe another pattern in the numbers. 1. Rule: Subtract 7 First Term: 95____________________________________________________________________________________________________2. Rule: Add 15 Subtract 10 First Term:4____________________________________________________________________________________________________
we have
1. Rule: Subtract 7 First Term: 95
so
a1=95
a2=95-7=88
a3=88-7=81
a4=81-7=74
a5=74-7=67
a6=67-7=60
a7=60-7=53
a8=53-7=46
a9=46-7=39
a10=39-7=32
a11=32-7=25
a12=25-7=18
we have that
the general equation in this arithmetic sequence is
an=a1+d(n-1)
we have
a1=95
d=-7
substitute
an=95-7(n-1)
an=95-7n+7
an=102-7n2. Rule: Add 15 Subtract 10 First Term:4
the rule add 15 and subtract 10 is the same that the rule add 5
so
a1=4
a2=4
Write an equation of the line containing the point (3,1) and perpendicular to the line 2x - 3y = 4.The equation of the line is____(Type an equation. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation. Simplify your answer. Do notfactor.)
Two lines are perpendicular when the multiplication of their slopes is equal to -1.
To find the slope of the line 2x - 3y = 4, we have to isolate y, as follows:
[tex]\begin{gathered} 2x-3y=4 \\ -3y=4-2x \\ y=\frac{4-2x}{-3} \\ y=\frac{4}{-3}+\frac{-2x}{-3} \\ y=-\frac{4}{3}+\frac{2}{3}x \end{gathered}[/tex]Its slope is 2/3, then the slope of the perpendicular line is:
[tex]\begin{gathered} m\cdot\frac{2}{3}=-1 \\ m=-1\cdot\frac{3}{2} \\ m=-\frac{3}{2} \end{gathered}[/tex]The slope-intercept form is:
y = mx + b
where m is the slope and b is the y-intercept.
Replacing with m = -3/2 and point (3,1):
1 = -3/2(3) + b
1 = -9/2 + b
1 + 9/2 = b
11/2 = b
The equation of the line is y = -3/2x + 11/2
Which is greater ? 3/5 or 0.14
3/5 = 0.60
0.6 > 0.14
Then, 3/5 is greater than 0.14
a college lacrosse team will play 18 games next fall. each game can result in one of 3 outcomes; a win, a loss, or a tie. find the total possible number of outcomes for the season record.
Each game has 3 possible outcome so there are 3 different outcomes for game 1
The same can happen for game 2
and for game 3 and so on for each game
There are 18 games
3 *3*3*3*3 .......*3 18 times
3^18
387420489 different possible outcomes
Ellen sells mugs that are in boxes in the shape of a cube. The edges of the boxes have a length of 1 foot. Ellen can completely fill a container in the shape of a rectangular prism with 378 boxes. What is the volume of her container? 471 ft 3 189 ft3 942 ft Ht 2 378 ft?
The side of the cubical box is 1/2 foot, so its volume is given by,
[tex]\begin{gathered} \text{Volume of cubical box=(side)}^3 \\ \text{Volume of cubical box=(}\frac{1}{2}\text{)}^3 \\ \text{Volume of cubical box=}\frac{1}{8} \\ \text{Volume of cubical box=0}.125 \end{gathered}[/tex]Given that the container can be filled with 378 boxes.
So the volume of the container is given by,
[tex]\begin{gathered} \text{Volume of Container=378}\times\text{ Volume of a single box} \\ \text{Volume of Container=378}\times\text{ 0}.125 \\ \text{ Volume of Container}=47.25 \\ \text{Volume of Container}=47\frac{1}{4} \end{gathered}[/tex]Thus, first option is the correct choice.
A trivia contest awards $102 for first place, $68 for second place, $34 for third place, and $17 for fourth place . The function can be written bas ordered pairs :{(1,102),(2,68),(3,34),(4,17)}. Express this function as a table, a graph, and a mapping diagram.
The function denoted by the ordered pairs, (1, 102), (2, 68), (3, 34), (4, 17) can be shown on a tale as follows
As a graph, this is shown below;
Note that the graph drawn above uses 25 units on 1 cm on the y-axis, and 1 unit to 1 cm on the x-axis. Also, its not drawn to perfection as the "points where the x any y values intersect should all fall perfectly on the line of the function.
Solve the following for a:-2 + a=1
a = 3
Explanations:The given equation is:
- 2 + a = 1
Collect like terms:
This means that the -2 will cross the equality sign to the Right Hand Side to become +2
The equation will then become:
a = 1 + 2
a = 3
⇒I will use the additive inverse to solve the problem.
[tex]-2+(2)+a=1+(2)\\a=3[/tex]
GOODLUCK!!
Susy had a square plot of grass in her backyard, but now part of the plot is taken up by a fountain. Each side of the plot has a length of 14.5 feet. One side of the plot has a semicircular fountain with a radius of 2.5 feet.What is the approximate area of the plot of grass after installing the fountain?
Given:-
Susy had a square plot of grass in her backyard, but now part of the plot is taken up by a fountain. Each side of the plot has a length of 14.5 feet. One side of the plot has a semicircular fountain with a radius of 2.5 feet.
To find:-
The approximate area of the plot of grass after installing the fountain.
Now we find the area of square plot,
[tex]14.5\times14.5=210.25[/tex]Now we find the area of semi circle. we get,
[tex]\begin{gathered} \frac{1}{2}\pi r^2=\frac{1}{2}\times\frac{22}{7}\times2.5\times2.5 \\ \text{ =}\frac{11}{7}\times2.5\times2.5 \\ \text{ =9.821} \end{gathered}[/tex]So to find the area of plot grass after installing the fountain. we substract both the areas. so we get,
[tex]210.25-9.821=200.429[/tex]So the area of plot is 200.429 square feet.
write the equation in STANDARD FORM!
y=2x+3/7
Standard form: [tex]Ax+By=C[/tex]
A, B and C are integersTo arrange a given linear equation into standard form, we are looking to put x and y onto one side of the equation.
Solving the QuestionWe're given:
[tex]y=2x+\dfrac{3}{7}[/tex]
⇒ Typically, we don't include any fractions in standard form. Multiply everything by 7 to get rid of the fraction:
[tex]7y=14x+3[/tex]
⇒ Move 14x to the other side:
[tex]-14x+7y=3[/tex]
⇒ A is typically positive. Divide everything by -1 to make A positive:
[tex]14x-7y=-3[/tex]
Answer[tex]14x-7y=-3[/tex]
117. 10 + 61 - 15i + 6 - 4i3i- 131 +1616 - 9
Answer: -13i + 16
We are given: 10 + 6i - 15i + 6 - 4i
Firstly, we need to collect the like terms
= 10 + 6 + 6i - 15i - 4i
= 16 - 9i -4i
= 16 - 13i
= -13i + 16
3n+6=15 please solve for n.
Isolate the variable term by subtracting 6 from both sides of the equation.
[tex]\begin{gathered} 3n=15-6 \\ 3n=9 \end{gathered}[/tex]Divide both sides of the equation by 3.
[tex]\begin{gathered} \frac{3n}{3}=\frac{9}{3} \\ n=3 \end{gathered}[/tex]Therefore, the value of n is 3.
Hello! I need help on solving this! Step by step. For the red one
To answer this question we will use the following property:
[tex](a^7)^{\frac{1}{7}}=a.[/tex]Subtracting 8 to the equation obtained on a) we get:
[tex]\begin{gathered} y-8=x^7(7)+8-8, \\ y-8=x^7(7). \end{gathered}[/tex]Dividing the above result by 7 we get:
[tex]\begin{gathered} \frac{y-8}{7}=\frac{x^7(7)}{7}, \\ \frac{y-8}{7}=x^7. \end{gathered}[/tex]Taking the above result to the power of 1/7 we get:
[tex](\frac{y-8}{7})^{\frac{1}{7}}=(x^7)^{\frac{1}{7}}.[/tex]Using the first property we get:
[tex]x=(\frac{y-8}{7})^{\frac{1}{7}}.[/tex]Answer: x=g(y)= ((y-8)/7)^(1/7).is
Find+Graph the equation parallel to y=4x-5 with a x-intercept of -5.
Line equations can be written in slope-intercept form. The slope-intercept form is
[tex]y=mx+b[/tex]Where m represents the slope and b the y-intercept.
The given line is
[tex]y=4x-5[/tex]Comparing this equation with the slope-intercept form, we have a line with slope equal to 4 and y-intercept equals to -5.
Parallel lines have the same slope, then, the equation for the line we want has the following form
[tex]y=4x+b[/tex]The x-intercept is -5, then, this means that x = -5 when y = 0. We can substitute those values in our form to find the coefficient b.
[tex]\begin{gathered} 0=4\cdot(-5)+b \\ 0=-20+b \\ -b=-20 \\ b=20 \end{gathered}[/tex]This means that our line is
[tex]y=4x+20[/tex]Graphing this equation, we have
The volume of this triangular prism is 144 cubic feet. What is the value of s?
1. In the Rocky Mountains the snow is 40 inches deep. After a snow storm, 2 the depth of the snow increased by 21%. How deep is the snow, in inches, after the snow storm? Explain your thinking. *
In the Rocky Mountains the snow is 40 inches deep
Intial depth of the snow on mountain = 40 inches
After the second snow storm
The depth of the snow increased by 21%.
i.e. depth of the snow increased by 21%. of intial depth = depth of the snow increased by 21%. of 40
So,
[tex]\begin{gathered} 20\text{ perecntage of 40 =}\frac{20\times40}{100} \\ 20\text{ percentage of 40=8 inch} \end{gathered}[/tex]Thus, depth of the snow increased by 21%. = 8 inches
So, the final depth of snow = Intial depth + Increased depth
The final depth of snow = 40 + 8
The final depth of snow = 48 inches
Answer: 48 inches
After the snow storm, the depth of snow is 48 inches
Which statement illustrates the distributive property?OA. 9+ (5i -12i) = (9 + 5i) — (9 + 12i)OB. 9(5i -12i) = 9(5i) — 12i--OC. 9(5i + 12i) = 9(12i + 5i)OD. 9(5i -12i) = 9(5i) — 9(12i)-
Given:
Four options are given.
Required:
Find the option that states the distributive property.
Explanation:
The distributive property is stated as:
[tex]a(b\pm c)=ab\pm ac[/tex]In the given options
[tex]9(5i-12i)=9(5i)-9(12i)[/tex]Final Answer:
Option D is the correct answer.
using the distance formula from above find the distance between (-15,-18) and (18,-2). round to the nearest tenth.using the distance formula from above find the distance between (5,9) and (-7,-7). round to the nearest tenth.using the distance formula from above find the distance between (3,8) and (9,10). round to nearest tenth.
Answer:
[tex]\begin{gathered} 1.\text{ }d=36.7 \\ 2.\text{ }d=20 \\ 3.\text{ }d=6.3 \end{gathered}[/tex]Step by step explanation:
The distance between two points is represented by the following expression:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]1. Then, for (-15, -18) and (18, -2)
[tex]\begin{gathered} d=\sqrt[]{(18-(-15))^2+(-2-(-18))^2} \\ d=\sqrt[]{(33)^2+(16)^2} \\ d=\sqrt[]{1089+256} \\ d=\sqrt[]{1345} \\ d\approx36.67 \\ \text{Rounding to the nearest tenth:} \\ d=36.7 \end{gathered}[/tex]2. Now, for (5,9) and (-7,-7)
[tex]\begin{gathered} d=\sqrt[]{(-7-5)^2+(-7-9)^2} \\ d=\sqrt[]{(-12)^2+(-16)^2} \\ d=\sqrt[]{144+256} \\ d=\sqrt[]{400} \\ d=20 \end{gathered}[/tex]3. Finally, for (3,8) and (9,10)
[tex]\begin{gathered} d=\sqrt[]{(9-3)^2+(10-8)^2} \\ d=\sqrt[]{6^2+2^2} \\ d=\sqrt[]{36+4} \\ d=\sqrt[]{40} \\ d=2\sqrt[]{10} \\ \text{Rounding to the nearest tenth:} \\ d=6.3 \end{gathered}[/tex]Scale the graph below and write down the absolute maximum value.
SOLUTION
Given the graph in the image on the question;
Explanation:
The one, true, largest value reached by the entire function is called the absolute maximum, or the global maximum.
Considering our question:
The absolute maximum from the graph above is 5.
8. A hair stylist at Pierre's hair salon earns $6.80 per hour plus tips.The stylist works 40 hours per week with tips of about $240 per week. Findthe total weekly earnings.A.493.00B.512.00C. $625.00
1) Gathering the data
6.80h + t=E
h=hours
t=tips
E=Earnings
2
If a cylinder has a volume of 1810 cubic feet and a radius of 12 feet, then find the height. (Hint: Solve the equation for h first!)
The rule of the volume of a cylinder is
[tex]V=\pi r^2h[/tex]Where:
r is the radius of its base
h is its height
The given is:
V = 1810 cubic feet
r = 12 feet
Substitute them in the rule above
[tex]\begin{gathered} 1810=\pi(12)^2h \\ 1810=144\text{ }\pi\text{ h} \end{gathered}[/tex]To find h divide both sides by 144 pi
[tex]\begin{gathered} \frac{1810}{144\pi}=144\pi\text{ h/144}\pi \\ 4.000978431=h \end{gathered}[/tex]h = 4 feet
What will be the first step to find the closest fractional equivalent for 2.784 using the given denominator ?A. Multiply the decimal number by the fraction 1 over 32 B. Multiply the decimal number by the fraction 32 over 32c. Multiply the decimal number by the number 32.
The given decimal number is 2.784.
Then, we need to multiply the given number by the following fractions with the given fractions.
(A). Multiply the decimal number by the fraction 1 over 32
So,
[tex]2.784\times\frac{1}{32}=\frac{2.784}{32}=\frac{1.392}{16}=\frac{0.696}{8}=0.087[/tex](B). Multiply the decimal number by the fraction 32 over 32
So,
[tex]2.784\times\frac{32}{32}=2.784\times1=2.784[/tex](C). Multiply the decimal number by the number 32.
So,
[tex]\frac{2.784}{32}=0.087[/tex]Hence, option B will be the first step.
what are the solutions to the equation (x+2)(x-7)=0
The given equation is :
(x+2)(x-7)=0
[tex]\begin{gathered} \mleft(x+2\mright)\mleft(x-7\mright)=0 \\ \text{either (x+2)=0 or (x-7)=0} \\ \text{if (x+2)=0} \\ \text{then, x+2=0} \\ x=-2 \\ \text{if (x-7)=0} \\ \text{then x-7=0} \\ x=7 \end{gathered}[/tex]Thus, the x have two values that are x =-2, 7
If Motown knows that it will sell many of these warranties, should it expect to make or lose money from offering them? How much?
We will have the following:
We know that there is a 7% chance that they would need to pay the car; that means that for each 100 people that pay the warranty 7 would need to be paid for it; so the total amount obtained from 100 people would be:
[tex]T=100(983)-7(13400)\Rightarrow T=4500[/tex]Now, from this we can determine the total amount of money gained from each warranty sold by dividing by the total of the hypothetical sales; in our case 100, that would be:
[tex]x=\frac{4500}{100}\Rightarrow x=45[/tex]So:
MotoWin can expect to make money from offering these warranties.
In the long run, they should expect to make 45 dollars on each warranty sold.
What is a system of equations? • An equation with no variables •An equation with more than one variable •Two or more equations with one variable •Two or more equations that share variables
A system of equations is two or more equations with the same variables.
Example:
[tex]\begin{gathered} y=3x+8 \\ 2y=5x-9 \end{gathered}[/tex]Two equations with variables x and y
Un givenue Coordinates . Problem 1 Dilation: Coordinates: A(2,-4), B(2,-2), C(4,0), D(4,-4)
To solve we appply dilation for each point
[tex]\begin{gathered} A(2,-4)\times\frac{1}{2}=A^{\prime}(1,-2) \\ \\ B(2,-2)\times\frac{1}{2}=B^{\prime}(1,-1) \\ \\ C(4,0)\times\frac{1}{2}=C^{\prime}(2,0) \\ \\ D(4,-4)\times\frac{1}{2}=D^{\prime}(2,-2) \end{gathered}[/tex]I need help with number 5 the same one that’s in black not blue
The vertex is the highest point if the parabola opens downward and the lowest point if the parabola opens upward.
The axis of symmetry is the line that cuts the parabola into 2 matching halves and the vertex lies on the axis of symmetry.
The function is given to be:
[tex]h(x)=-3x^2[/tex]The graph of the function is shown below:
Since the graph opens downwards, the highest point is (0, 0). The image below shows the axis of symmetry and vertex:
Therefore, we have
[tex]\begin{gathered} Vertex=(0,0) \\ Axis\text{ }of\text{ }symmetry\Rightarrow x=0 \end{gathered}[/tex]Use the following function rule to find f(162) f(x) = 9/x- 146 f(162) = Submit
We are given a function whic is
[tex]\begin{gathered} f(x)\text{ = 9}\sqrt[]{x\text{ - }146} \\ \text{This means this function is x dependent} \\ To\text{ find f(162)} \\ \text{This implies that substitute x = 162} \\ f(162)\text{ = 9}\sqrt[]{162\text{ - 146}} \\ f(162)\text{ = 9}\sqrt[]{16} \\ Then,\text{ }\sqrt[]{16\text{ = }}\text{ 4} \\ f(162)\text{ = 9 x 4} \\ f(162)\text{ = 36} \\ \text{The answer is 36} \end{gathered}[/tex]