Answer: The number of possibilities = 380
Step-by-step explanation:
Given, There are 20 players on a soccer team. From them, a captain and an alternate captain have to be chosen.
Since, captain and alternate captain comes in order.
Number of ways to choose r things out of n things (when order matters) :
[tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
Number of ways to choose 2 players ( for captain and alternate captain ) from 20 players :
[tex]^{20}P_2=\dfrac{20!}{18!}=20\times19=380[/tex]
Hence, the number of possibilities = 380
"Use what you know about zeros of a function and end behavior of a graph that matches the function f(x)=(x-3)(x-2)(x+1)." Choices below:
Explanation:
The x intercepts here are -1, 2 and 3. This is where the graph crosses the x axis. We can determine these three values by solving f(x) = 0.
In other words, set (x-3)(x-2)(x+1) equal to zero and solve for x.
(x-3)(x-2)(x+1) = 0
x-3 = 0 or x-2 = 0 or x+1 = 0
x = 3 or x = 2 or x = -1
x = -1 or x = 2 or x = 3
When we expand out (x-3)(x-2)(x+1), there will only be one x^3 term and the coefficient for this term is positive 1. The positive leading coefficient indicates that the graph goes up forever as we move to the right. In other words, the graph grows forever after passing that dip between x = 2 and x = 3.
Another way you could phrase it is that "as x goes to infinity, y also goes to infinity". An informal way is to say "the graph rises to the right" to describe the end behavior.
circle the equations that represent quadratic functions a. y=3x+1 b. y=x^2+3 c. y=x^3-3 d. x^2+3y=8
Answer:
[tex]B. y=x^2+3 \\\\D.$ $x^2+3y=8[/tex]
Step-by-step explanation:
A quadratic function is a function in which the highest power of the unknown variable is 2.
Formally, a quadratic function is defined as a function of the form:
[tex]f(x)=ax^2+bx+c, a\neq 0[/tex]
From the given options, only B and D has the highest power as 2. Therefore, the equations that represent quadratic functions are:
[tex]B. y=x^2+3 \\\\D.$ $x^2+3y=8[/tex]
please solve this using quadratic formula :")
Answer:
Step-by-step explanation:
The given equation is expressed as
(x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12
Simplifying the right hand side of the equation, it becomes
[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)
x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)
(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)
4x/(x - 1)(x + 1)
Therefore,
4x/(x - 1)(x + 1) = 7/12
Cross multiplying, it becomes
4x × 12 = 7(x - 1)(x + 1)
48x = 7(x² + x - x - 1)
48x = 7x² - 7
7x² - 48x - 7 = 0
Applying the quadratic formula,
x = - b ± √(b² - 4ac)]/2a
from our equation,
b = - 48
a = 7
c = - 7
Therefore
x = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)
x = [48 ± √(2304 + 196]/14
x = (48 ± √2500)/14
x = (48 ± 50)/14
x = (48 + 50)/14 or x = (48 - 50)/14
x = 98/14 or x = - 2/14
x = 7 or x = - 1/7
Answer: The given equation is expressed as (x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12Simplifying the right hand side of the equation, it becomes[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)4x/(x - 1)(x + 1)Therefore, 4x/(x - 1)(x + 1) = 7/12Cross multiplying, it becomes4x × 12 = 7(x - 1)(x + 1)48x = 7(x² + x - x - 1)48x = 7x² - 77x² - 48x - 7 = 0Applying the quadratic formula,x = - b ± √(b² - 4ac)]/2a from our equation, b = - 48a = 7c = - 7Thereforex = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)x = [48 ± √(2304 + 196]/14x = (48 ± √2500)/14x = (48 ± 50)/14x = (48 + 50)/14 or x = (48 - 50)/14x = 98/14 or x = - 2/14x = 7 or x = - 1/7
Step-by-step explanation:
Two different radioactive isotopes decay to 10% of their respective original amounts. Isotope A does this in 33 days, while isotope B does this in 43 days. What is the approximate difference in the half-lives of the isotopes?
Answer:
A. 3 Days
Step-by-step explanation:
Just took the test hope this helps :)
Answer:
the answer on edge is A.3
I really need help with this, so could you help a little girl...?
Answer:
Option 3
Step-by-step explanation:
The curve goes infinitely downwards, so y is infinitely negative while x is limited at the y axis, or x=0 which is the asymptote.
use the graph to find the cost of 8 shirts
Answer:
Option B
Step-by-step explanation:
When we compare the number of shirt with it's cost, we find out that 8 shirts cost $120.
For more understanding, see the attached file.
Simplify.
A12 over a7
Answer:
a^5.
Step-by-step explanation:
a^12 / a^7 = a^(12 - 7) = a^5.
Hope this helps!
Complete the table for the given rule. hi guys this is question is Rule: y is 1/3 times as large as x x y 0 6 12 y need to know y by the rule i need this quilky plz
Answer:
The completed table is
x | 0 | 6 | 12
y | 0 | 2 | 4
Step-by-step explanation:
It is given that y is (1/3) as large as x. That is,
y = (x/3)
x | 0 | 6 | 12
y | ? | ? | ?
y = (x/3)
When x = 0,
y = (0/3) = 0
when x = 6,
y = (6/3) = 2
when x = 12,
y = (12/3) = 4
The completed table is thus
x | 0 | 6 | 12
y | 0 | 2 | 4
Hope this Helps!!!
The values of x will be 0 , 18 , 36 respectively when the value of y is 0, 6, 12.
Given,
y is 1/3 times as large as x.
So, [tex]x=3y[/tex].
We have to calculate the value of x when y is given .
1. when [tex]y=0[/tex]
Then, [tex]x=0[/tex]
2.when, [tex]y=6[/tex]
Then, [tex]x=18\\[/tex]
3. When [tex]y=12[/tex]
[tex]x=3\times 12\\x=36[/tex]
Hence, the values of x will be 0 , 18 , 36 respectively when the value of y is 0, 6, 12.
For more details follow the link:
https://brainly.com/question/11897796
solve for n: 5n-14<1
Answer: n< 3
Step-by-step explanation:
5n - 14 < 1 . add 14 to both sides
5n -14 +14 < 1 + 14
5n +0 < 15
5n < 15 divide both sides by 5 .5n/5 = 15/5
n < 3
(ILL MARK BRAINLIEST) The following two-way table shows the data for the students of two different grades in a school:
Member of Public Library Not Member of Public Library Total
Grade 6
25
3
28
Grade 7
23
7
30
Total
48
10
58
Based on the relative row frequency, the students of which grade are more likely to be members of the public library?
Answer:
6th
Step-by-step explanation:
the chart says not, 7th has majority
Solve x4 – 17x2 + 16 = 0. Let u = .
To solve the equation, we need to let u = x²
What is a quadratic equation?A quadratic equation is an algebraic expression that takes the power of the second degree.
From the given parameter:
x⁴ - 17x² + 16 = 0For us to be able to solve the given equation, we need to reduce the equation to a quadratic form.
This can be achieved by making an assumption that:
u = x²So, we will replace x² with u in the given equation.
By doing so, we have:
u² - 17u + 16 = 0Learn more about quadratic equations here:
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Answer: Solve x4 – 17x2 + 16 = 0.Let u = xX 17x²✔ x²X -17x².
let u = x^2
Step-by-step explanation: just did it
8³=512 indique a base
Answer:
8
Step-by-step explanation:
8^3 = 8*8*8 = 512
la base = base = 8
Which equation represents a linear function?
x = 3
y = 16
y = -3x + 10
y = 3x2 + 1
Please help me!!
Answer:
y = 16 and y = -3x + 10Step-by-step explanation:
The equation of a linear function:
y = mx + b
m - slope
b - y-intercept
x = 3 - it's a vertical line. It's not equation of a linear function
y = 16 - it's a horizontal line. It's an equation of a linear function
where m = 0, b = 16
y = -3x + 10 - it's an equation of a linear function
where m = -3, b = 10
y = 3x² + 1 - it's a quadratic function ( x² ).
Answer:
y = 16 and y = -3x + 10
Step-by-step explanation:
hello
what is the slope of the line shown below (2 2) (4 8) a. 3 b. 1/3 c. -1/3 d. -3
Answer:
Option A.3
Step-by-step explanation:
If its rise over run the fraction should be right 2 up 6 makeing a fraction of
6/2 which equals 3
The line has a slope of 3
HELP Classify the following: 3 + 9 + 27 + ... arithmetic sequence arithmetic series geometric sequence geometric series
Answer:
Geometric sequence
Step-by-step explanation:
Because this is not adding or subtraction, but multiplication, this would be a geometric sequence.
Una empresa exportadora de frutas vende dos variedades de frambuesas: estándar y de lujo. Una caja de freses estándar se vende en US$7 y una de lujo en US$10. Si la empresa vende 135 cajas de frambuesas por un total de US$1.100, ¿Cuántas cajas de cada tipo vendió?
Answer:
83.33 cajas estándar de frambuesas y 51.67 cajas de lujo de frambuesas.
Step-by-step explanation:
Representemos el número de cajas como
A = caja estándar de frambuesas
B = caja de lujo de frambuesas
Caja estándar de frambuesas = $ 7 Caja de lujo de frambuesas = 10.
A + B = 135 ......... Ecuación 1
B = 135 - A
7A + 10B = 1100 ........... Ecuación 2
Sustituir
135 - A para B en la ecuación 2
7A + 10 (135 - A) = 1100
7A + 1350 -10A = 1100
7A - 10A = 1100-1350
-3A = - 250
A = 250/3
A = 83.33 cajas
Sustituye 83.33 por A en la ecuación 1
A + B = 135
83,33 + B = 135
B = 135 - 83.33 = 51.67 cajas
Por lo tanto, vendió,
83.33 cajas estándar de frambuesas y 51.67 cajas de lujo de frambuesas.
Which expressions are equivalent
Answer:
Options (B) and (C)
Step-by-step explanation:
The given expression is [tex](d^{\frac{1}{8}})^5[/tex]
By simplifying this expression,
[tex](d^{\frac{1}{8}})^5[/tex]
= [tex](\sqrt[8]{d})^{5}[/tex]
Option (B)
Similarly,
[tex](d^{\frac{1}{8}})^5[/tex]
= [tex]d^{\frac{5}{8}}[/tex]
= [tex](d^{5})^{\frac{1}{8}}[/tex]
Option (C)
Therefore, Options (B) and (C) will be the correct options.
PLEASE HELP NOW --- >N is a 2-digit even number. If the last two digits of N^2 is the same as N, what is the sum of digits of N?
Answer:
76.
Step-by-step explanation:
It is given that N is a 2-digit number.
Last two digits of N^2 is the same as N.
We know that, a number is even if it ends with 0,2,4,6,8.
[tex]2^2=4,4^2=16,6^2=36,8^2=64[/tex]
If 0 is in end then we get two zeros in the square of that number.
It is clear that, number should ends with 6 to get the same number at the end.
[tex]16^2=256[/tex]
[tex]26^2=676[/tex]
[tex]36^2=1296[/tex]
[tex]46^2=2116[/tex]
[tex]56^2=3136[/tex]
[tex]66^2=4356[/tex]
[tex]76^2=5776[/tex]
[tex]86^2=7396[/tex]
[tex]96^2=9216[/tex]
It is clear that last two digits of (76)^2 is the same as 76.
Therefore, the required number is 76.
Which set of ratios could be used to determine if one triangle is a dilation of the other? A triangle has side lengths of 4, 6, 8.5. A second triangle has side lengths of 6, 9, 12.5. StartFraction 4 Over 6 EndFraction = StartFraction 6 Over 9 EndFraction = StartFraction 8.5 Over 12.5 EndFraction StartFraction 6 Over 4 EndFraction = StartFraction 6 Over 9 EndFraction = StartFraction 8.5 Over 12.5 EndFraction StartFraction 4 Over 6 EndFraction = StartFraction 9 Over 6 EndFraction = StartFraction 8.5 Over 12.5 EndFraction StartFraction 4 Over 6 EndFraction = StartFraction 8.5 Over 9 EndFraction = StartFraction 6 Over 12.5 EndFraction
Answer:
[tex]A.\ \frac{4}{6} = \frac{6}{9} = \frac{8.5}{12.5}[/tex]
Step-by-step explanation:
Given
Let the two triangles be A and B
Sides of A: 4, 6 and 8.5
Sides of B: 6, 9 and 12.5
Required
Which set of ratio determines the dilation
To determine the dilation of a triangle over another;
We simply divide the side of a triangle by a similar side on the other triangle;
From the given parameters,
A ------------------B
4 is similar to 6
6 is similar to 9
8.5 is similar to 12.5
Ratio of dilation is as follows;
[tex]Dilation = \frac{4}{6}[/tex]
[tex]Dilation = \frac{6}{9}[/tex]
[tex]Dilation = \frac{8.5}{12.5}[/tex]
Combining the above ratios;
[tex]Dilation = \frac{4}{6} = \frac{6}{9} = \frac{8.5}{12.5}[/tex]
From the list of given options, the correct option is A,
Answer:
a
Step-by-step explanation:
The value of a family's home, in Camrose AB, is given by the following exponential function f(x), where x is the number of years after the family purchases the house for $130,000. What is the best estimate for the instantaneous rate of change in the value of the home when the family has owned it for 5 years?
f(x) =130000(1.06)^x
Answer:
$173,969Step-by-step explanation:
Given the value of a family's home, in Camrose AB, given by the following exponential function f(x) = 130000(1.06)^x, where x is the number of years after the family purchases the house for $130,000. In order to calculate the best estimate for the instantaneous rate of change in the value of the home when the family has owned it for 5 years, we will have to substitute x =5 in the given function and solve as shown;
f(x) = 130000(1.06)ˣ
f(5) = 130000(1.06)⁵
f(5) = 130000*(1.06)⁵
f(5) = 130000*1.338226
f(5) = 173,969.38
Hence, the instantaneous rate of change in the value of the home when the family has owned it for 5 years is approximately $173,969
Identify the zeros of f(x)= (x-7)(x+4)(3x-2) Choices:
Answer:
second option
Step-by-step explanation:
Given
f(x) = (x - 7)(x + 4)(3x - 2)
To find the zeros let f(x) = 0, that is
(x - 7)(x + 4)(3x - 2) = 0
Equate each factor to zero and solve for x
x - 7 = 0 ⇒ x = 7
x + 4 = 0 ⇒ x = - 4
3x - 2 = 0 ⇒ 3x = 2 ⇒ x = [tex]\frac{2}{3}[/tex]
zeros are x = - 4, x = [tex]\frac{2}{3}[/tex], x = 7
help please thank you
Answer:
(0,-3)
Step-by-step explanation:
Ruth left her home at 9 am and walked to the library. She got to the library at 10 30 am. Ruth walked at a speed of 4 mph. (a) Work out the distance Ruth walked.
Answer:
she walked 6 miles.
Step-by-step explanation:
We know that Ruth walks at a speed of 4 mph and it took her 1.5 hours to walk from her home to the library (from 9 to 10.30).
We can solve this using a rule of three:
If she walks 4 miles in 1 hour, how many hours did she walk in 1.5 hours?
1 hour 4 miles
1.5 hours x miles
Solving for x we get:
[tex]x=\frac{1.5(4)}{1} =6[/tex] miles
Thus, she walked a distance of 6 miles
The distance between her home and the library is the number of meters between them.
The distance walked is 6 m
The speed is given as:
[tex]\mathbf{Speed = 4mph}[/tex]
The time spent walking is calculated as:
[tex]\mathbf{Time = 10:30am - 9:00am}[/tex]
[tex]\mathbf{Time = 1.5\ hrs}[/tex]
So, the distance is calculated as:
[tex]\mathbf{Distance = Speed \times Time}[/tex]
Substitute known values
[tex]\mathbf{Distance = 4mph \times 1.5hrs}[/tex]
[tex]\mathbf{Distance = 6m}[/tex]
Hence, the distance walked is 6 m
Read more about distance at:
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PLEASE! I need help! I am really confused with this.
Answer:
It's the first option
Step-by-step explanation:
They've constructed two angle bisectors and have shown you where they meet. Their point of intersection is the center of the inscribed circle (the incenter). Therefore, the last step is finding the altitudes (perpendicular lines) from the incenter to all the sides.
What is the slope of the line?
Answer:
4/5
Step-by-step explanation:
Slope(m) = (y2-y1)/(x2-x1)
Pick two points on your graph that are closest to clear values. (By that I mean you shouldn't pick points that aren't obvious unless you have to.)
For instance, I see the points (-2,0) and (3,4) to be clear; so we don't have to approximate anything.
You could plug these in in a any order but I'm going to let Point 1=(-2,0) and Point 2=(3,4). So:
m=(4-0)/(3--2)=(4/5)
Slope=4/5
Provide an appropriate response. At a college there are 120 freshmen, 90 sophomores, 110 juniors, and 80 seniors. A school administrator selects a random sample of 12 of the freshmen, a random sample of 9 of the sophomores, a random sample of 11 of the juniors, and a random sample of 8 of the seniors. She then interviews all the students selected. Identify the type of sampling used in this example.
Answer: Stratified Sampling
Step-by-step explanation: Stratified Sampling involves creating subdivisions of the population such that each subdivisions is seen as a subgroup or smaller chunk of the population which is split based on certain criteria or attribute. The stratified random sampling may be employed in delineating certain characteristics or to investigate further how a feature or characteristics vary between one subdivision to the other.
In the scenario above, the researcher made use of the stratified sampling by performing a random sampling selection of its subjects based on the different subdivisions of students available in the college
Colin leaves school to go home. He walks 3 blocks south and then 9 blocks west. If Colin could walk in a straight line to the school, what is the exact distance between Colin and the school?
Answer:
9.48*
Step-by-step explanation:
This is a right triangle. The formula for solving the Hypotenuse, or the longest side of the right triangle is A^2 + B^2 = C^2. If we put the numbers from the problem into the formula this is what we get :
3^2 + 9^2 = C^2
9 + 81 = C^2
90 = C^2
9.48 = C
* This is rounded, the exact number is closer to 9.486832980505138. Your class should tell you what to round to.
Answer:
The answer would be A. 3√10 blocks
Step-by-step explanation:
I have had this question and its 3√10 blocks.
Hope this helps you other people :))
WILL GIVE BRAINLIEST A rocket is launched vertically from the ground with an initial velocity of 64. Write a quadratic function that shows the height, in feet, of the rocket t seconds after it was launched. Graphon the coordinate plane.
Answer:
[tex]h=64t-4.9t^{2}[/tex]
Please refer to the attached graph.
Step-by-step explanation:
Given that
Initial velocity of rocket = 64 and is launched vertically.
To find:
Quadratic equation in time to represent the height of rocket in feet.
Solution:
Unit of initial velocity is not given in the question statement, let the velocity be in feet/second only.
Initial velocity, u = 64 feet/s
The acceleration will be = -g because it is going opposite to gravitational force so it will be negative acceleration motion (speed will be decreasing) so -g will be the acceleration.
Formula for distance traveled is given as:
[tex]s=ut+\dfrac{1}{2}at^2[/tex]
Here Let us represent s by 'h'
a = -g = 9.8 m/[tex]s^2[/tex]
Let us put the known values in the formula:
[tex]h=64t+\dfrac{1}{2}(-9.8)t^2\\\Rightarrow h =64t-4.9t^2[/tex]
It is a quadratic equation, the equation represents the graph of a parabola.
Please refer to the attached graph.
Value of height is 0 at 0 second and ~13 seconds
factor the equation. 2x+13x-15
Answer:
(2x+15)(x−1)
Step-by-step explanation:
Factor 2x2+13x−15
2x2+13x−15
=(2x+15)(x−1)
Here is the answer good sir
Answer:
(x - 1)(2x + 15)
Step-by-step explanation:
Well let's make the square look at the image below ↓
By looking at the image we can tell that the given equation factored is
(x - 1)(2x + 15).
Hope this helps :)
The registrar keeps an alphabetical list of all undergraduates, with their current addresses. Suppose there are 10,000 undergraduates in the current term. Someone proposes to choose a number at random from 1 to 100, count that far down the list, taking that name and every 100th name after it for the sample.
a) Is this a probability method?
b) Is it the same as simple random sampling?
c) Is there selection bias in this method of drawing a sample?
Answer:
The answer to this question can be defined as follows:
Step-by-step explanation:
Following are the description of the given points:
(a) This is a system of probability, which possibility occurs inside an intended manner whenever they choose this specific point of origin from 1 to 100 with no one reserve the possibility about who gets throughout the survey.
(b) Its method is different from the random sampling technique with the base available. For example, two individuals whose names identical to both the list have no chance to join within the survey.
(c) its sample is objective to its everyone can enter the test in equal measure.