Answer:
Solving the system of linear equations Mark tries to apply elementary transformations in order to eliminate one variable.
He makes such steps:
1. He multiplies equation (1) x+y+z=2 by 7 and adds it to equation (3) 4x-y-7z=16. This gives him:
7x+7y+7x+4x-y-7z=14+16,
11x+6y=30.
2. He multiplies equation (3) 4x-y-7z=16 by 2 and adds it to equation (2) 3x+2y+z=8. This step gives him:
8x-2y-14z+3x+2y+z=32+8,
11x-13z=40.
Thus, he did not eliminate the same variables in steps 1 and 2.
Answer: correct choice is he did not eliminate the same variables in steps 1 and 2.
Hope this helps you :)! If you would mark me brainliest, that would be awesome!
Answer:
correct answer is c
Step-by-step explanation:
edge 2020
How many real roots and how many complex roots exist for the polynomial
F(x) - X4+ x2 - 5x2 + x -- 6?
O A. 2 real roots and 2 complex roots
B. O real roots and 4 complex roots
O c. 3 real roots and 1 complex root
D. 4 real roots and 0 complex roots
Answer:
D. 4 real roots and 0 complex roots
Step-by-step explanation:
If I assume that the function you are saying is
[tex]F(x)=x^4+x^3-5x^2+x-6[/tex]
There should be up to "4 roots," there can't be more or less than 4 total solutions. First, we need to check how many sign changes are there in this function. There are 3 positive real roots. Now lets check for negative roots.
[tex]F(-x)=x^4-x^3-5x^2-x-6[/tex]
There are is only 1 negative real root. Since we basically have 4 real roots, and the max is 4. There should be 4 real roots and 0 complex roots.
I hope u can understand help asap
i think u can see sho T=5n+20
Answer:
T(n) = 5n + 20
Step-by-step explanation:
1 candy has a mass of 5 g.
n candies have a mass of 5n grams.
The box has a mass of 20 grams.
total mass = mass of candies + mass of box
T(n) = 5n + 20
n T(n)
0 20
25 145
50 270
75 395
100 520
A rectangular parking lot has an area of 7/10 km 2.The width is 1/3 km 2 .What is the length of the parking lot written as a improper fraction ,in kilometers
Answer:
[tex]\dfrac{21}{10}\text{ km}[/tex].
Step-by-step explanation:
It is given that,
Area of rectangular plot [tex]=\dfrac{7}{10}\text{ km}^2[/tex]
Width of rectangular plot [tex]=\dfrac{1}{3}\text{ km}[/tex]
We need to find the length of the parking lot.
We know that,
[tex]\text{Area of rectangle}=length\times width[/tex]
[tex]\dfrac{7}{10}=length\times \dfrac{1}{3}[/tex]
[tex]\dfrac{7\times 3}{10}=length[/tex]
[tex]length=\dfrac{21}{10}[/tex]
Therefore, length of the parking lot is [tex]\dfrac{21}{10}\text{ km}[/tex].
what’s the opposite of negative two
Answer: The answer is two
Step-by-step explanation: If you look for opposites of a number its either negative or positive. So when the answer is negative, the opposite is positive and if the answer is positive, the opposite is negative.
Answer:
[tex]\boxed{2}[/tex]
Step-by-step explanation:
The opposite of a number is the number that is the same distance from 0 on the number line.
-2 opposite is 2.
PLEASE HELP QUICK! Determine x value of: sqrt x + 8 - sqrt x - 4 = 2
Answer:
x=8
Step-by-step explanation:
[tex]\sqrt{x+8}-\sqrt{x-4}=2\\\sqrt{x+8}=2+\sqrt{x-4}\\\left(\sqrt{x+8}\right)^2=\left(2+\sqrt{x-4}\right)^2\\x+8=x+4\sqrt{x-4}\\8=4\sqrt{x-4}\\8^2=\left(4\sqrt{x-4}\right)^2\\64=16x-64\\x=8[/tex]
The amount of time to complete a physical activity in a PE class is approximately normally normally distributed with a mean of 32.9 seconds and a standard deviation of 6.4 seconds.
A) What is the probability that a randomly chosen student completes the activity in less than 33.2 seconds?
B) What is the probability that a randomly chosen student completes the activity in more than 46.6 seconds?
C) What proportion of students take between 35.5 and 42.8 seconds to complete the activity?
D) 75% of all students finish the activity in less than____seconds.
Answer:
The answer is below
Step-by-step explanation:
Given that mean (μ) of 32.9 seconds and a standard deviation (σ) of 6.4 seconds.
The z score is used to measure by how many standard deviation the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}\\[/tex]
a) For x < 33.2 seconds
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{33.2-32.9}{6.4} =0.05[/tex]
From the normal distribution table, the probability that a randomly chosen student completes the activity in less than 33.2 seconds = P(x < 33.2) = P(z < 0.05) = 0.5199 = 51.99%
b) For x > 46.6 seconds
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{46.6-32.9}{6.4} =2.14[/tex]
From the normal distribution table, the probability that a randomly chosen student completes the activity in more than 46.6 seconds = P(x > 46.6) = P(z > 2.14) = 1 - P(z < 2.14) = 1 - 0.9927 = 0.0073 = 0.73%
c) For x = 35.5 seconds
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{35.5-32.9}{6.4} =0.41[/tex]
For x = 42.8 seconds
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{42.8-32.9}{6.4} =1.55[/tex]
From the normal distribution table, the proportion of students take between 35.5 and 42.8 seconds to complete the activity = P(35.5 < x < 42.8) = P(0.41< z< 1.55) = P(z < 1.55) - P(z < 0.41) = 0.9332 - 0.6591 = 0.2741 = 27.41%
d) A probability of 75% = 0.75 corresponds to a z score of 0.68
[tex]z=\frac{x-\mu}{\sigma}\\\\0.68=\frac{x-32.9}{6.4} \\\\x-32.9=4.4\\x=4.4+32.9\\x=37.3[/tex]
75% of all students finish the activity in less than 37.3 seconds
what is this? 15.8 = d/25
Answer:
395
Step-by-step explanation:
15.8=d/25
multiply both sides by 25 to remove the denominator
25×15.8=d
d=395
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Second-degree, with zeros of −7 and 6, and goes to −∞ as x→−∞.
Answer:
Step-by-step explanation:
Hello, because of the end behaviour it means that the leading coefficient is negative so we can construct such polynomial function as below.
[tex]\large \boxed{\sf \bf \ \ -(x+7)(x-6) \ \ }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The polynomial function will be f ( x ) = - x² - x + 42
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax²+ bx + c = 0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
Given data ,
The polynomial function is of second degree with zeros of -7 and 6
So , x = -7 and x = 6
Let the function be f ( x ) where f ( x ) = ( x + 7 ) ( x - 6 )
Now , as x tends to infinity , the negative makes no such difference on the zeros of the function f ( x ) ,
And , f ( x ) = - ( x + 7 ) ( x - 6 )
Therefore , to find the polynomial function , f ( x ) = - ( x + 7 ) ( x - 6 )
f ( x ) = - [ x² - 6 x + 7 x - 42 ]
= - [ x² + x - 42 ]
= - x ² - x + 42
Hence , the polynomial function f ( x ) = - x ² - x + 42
To learn more about polynomial function click :
https://brainly.com/question/25097844
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Mai invests $20,000 at age 20. She hopes the investment will be worth $500,000 when she turns 40. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal? Round to the nearest tenth of a percent.
Answer:16.1%
Step-by-step explanation:
Answer:
The investment needs the rate of growth to be approximately 16.1%.
Step-by-step explanation:
Which linear inequality is represented by the graph?
Answer:
A. y ≤ 1/2x + 2
Step-by-step explanation:
Well look at the graph,
It is a solid line with it shaded down,
meaning it is y ≤,
So we can cross out B. and D.
So the y intercept is 2, we know this because the y intercept is the point on the line that touches the y axis.
now the slope can be found by seeing how far away each points are from each other,
Hence, the answer is A. y ≤ 1/2x + 2
Find the slope of the line passing through the points (-3, -8) and (4,6).
Answer:
slope = 2Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have
[tex](-3;\ -8)\to x_1=-3;\ y_1=-8\\(4;\ 6)\to x_2=4;\ y_2=6[/tex]
Substitute:
[tex]m=\dfrac{6-(-8)}{4-(-3)}=\dfrac{6+8}{4+3}=\dfrac{14}{7}=2[/tex]
The formula for the slope m of the line that passes through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is the following:
[tex]m=\dfrac{y_1-y_2}{x_1-x_2}[/tex]
We have points (4,6) and (-3,-8). Let's plug these values into the formula for slope:
[tex]m=\dfrac{6-(-8)}{4-(-3)}[/tex]
[tex]=\dfrac{14}{7}=2[/tex]
The slope of the line passing through the two points is 2. Let me know if you need any clarifications, thanks!
What is viscosity?
O A measure of the oil's quality
O An oil's resistance to flow at different temperatures
A reference to synthetic oil; all oils with viscosity are synthetic
O A new motor oil ingredient
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Answer:
viscosity is the state of being thick, sticky, and semifluid in consistency, due to internal friction.
"cooling the fluid raises its viscosity"
a quantity expressing the magnitude of internal friction, as measured by the force per unit area resisting a flow in which parallel layers unit distance apart have unit speed relative to one another.
plural noun: viscosities
"silicone oils can be obtained with different viscosities"
Step-by-step explanation:
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. hope this helps you :)
Answer:
O An oil's resistance to flow at different temperatures
Step-by-step explanation:
Internal friction of a moving fluid .
The cost of plastering the 4 walls of a room which is 4m high and breadth one third of its length is Rs. 640 at the rate of Rs. 5/m². What will be the cost of carpeting its floor at the rate of Rs. 250/m².
Answer:
Rs. 32,000
Step-by-step explanation:
height = 4m
let length = x m
breadth = x/3 m
Area of the 4 walls = 2(length × height) + 2(breadth × height)
Area = 2(4×x) + 2(4 × x/3) = 8x + (8x)/3
Area = (32x)/3 m²
1 m² = Rs. 5
The cost for an area that is (32x)/3 m²= (32x)/3 × 5 Rs.
The cost of plastering 4 walls at Rs.5 per m² = 640
(32x)/3 × 5 = 640
(160x)/3 = 640
x = length = 12
Area = (32x)/3 m² = (32×12)/3 = 128m²
The cost of carpeting its floor at the rate of Rs. 250/m²:
= 128m² × Rs. 250/m² = 32,000
The cost of carpeting its floor at the rate of Rs. 250/m² = Rs. 32,000
WILL MARK BRAINLIEST If Alan and Zack can clean a room in 30 minutes when working together, and Alan cleans twice as fast as Zack, how long would it take Alan to clean the room by himself?
Answer:
45 min
Step-by-step explanation:
Here,
the we take the work as W and Alan's speed as A and Zack's speed as Z.
A = 2Z
W = 30 ( A+Z)
if the time for Alan to done cleaning alone is t then t = W ÷ A
t = ( 30 (A+(A÷2)))÷ A
t = 45 min
I am done .
21.65 to 1 decimal place
Answer:
21.7
Step-by-step explanation:
When anything is 5 or above in a decimal place you round up to the next number for example
2.35 this would round up to be 2.4
21.65
Place value of 1 = ones place
Face value of 1 = 1
Note : The face value of a number will not change at all
Hope it helps you..If it's wrong plz say and I'll try to recorrect it :)
McKenzie has a bag contains six red marbles four blue marbles and 14 yellow marbles if she chooses one marble from the bag what is the probability that the marble is not yellow
Answer:
5/12
Step-by-step explanation:
Total number of marbles in the bag
6red+ 4blue + 14 yellow = 24 marbles
Not yellow marbles = 10 marbles
P ( not yellow ) = number of not yellow marbles / total marbles
=10/24
= 5/12
Answer:
5/12
Step-by-step explanation:
6 red marbles
4 blue marbles
14 yellow marbles
total marbles = 6 + 4 + 14 = 24 marbles
24 - 14 = 10 marbles
10 marbles are not yellow.
P(not yellow) = 10/24 = 5/12
Find the probability of each event. A six-sided die is rolled seven times. What is the probability that the die will show an even number at most five times?
Answer:
[tex]\dfrac{15}{16}[/tex]
Step-by-step explanation:
When a six sided die is rolled, the possible outcomes can be:
{1, 2, 3, 4, 5, 6}
Even numbers are {2, 4, 6}
Odd Numbers are {1, 3, 5}
Probability of even numbers:
[tex]\dfrac{\text{Favorable cases}}{\text{Total cases }} = \dfrac{3}{6} = \dfrac{1}{2}[/tex]
This is binomial distribution.
where probability of even numbers, [tex]p =\frac{1}{2}[/tex]
Probability of not getting even numbers (Getting odd numbers) [tex]q =\frac{1}{2}[/tex]
Probability of getting r successes out of n trials:
[tex]P(r) = _nC_r\times p^r q^{n-r}[/tex]
Probability of getting even numbers at most 5 times out of 7 is given as:
P(0) + P(1) +P(2) + P(3) +P(4) + P(5)
[tex]\Rightarrow _7C_0\times \frac{1}{2}^0 \frac{1}{2}^{7}+_7C_1\times \frac{1}{2}^1 \frac{1}{2}^{6}+_7C_2\times \frac{1}{2}^2 \frac{1}{2}^{5}+_7C_3\times \frac{1}{2}^3 \frac{1}{2}^{4}+_7C_4\times \frac{1}{2}^4 \frac{1}{2}^{3}+_7C_5\times \frac{1}{2}^5 \frac{1}{2}^{2}[/tex]
[tex]\Rightarrow (\dfrac{1}{2})^7 (_7C_0+_7C_1+_7C_2+_7C_3+_7C_4+_7C_5)\\[/tex]
[tex]\Rightarrow (\dfrac{1}{2})^7 (1+7+\dfrac{7 \times 6}{2}+\dfrac{7 \times 6 \times 5}{3\times 2}+\dfrac{7 \times 6 \times 5}{3\times 2}+\dfrac{7 \times 6}{2})\\\Rightarrow \dfrac{120}{128} \\\Rightarrow \dfrac{15}{16}[/tex]
Ash Lee bought a new Brunswick boat for $17,000. He made a $2,500 down payment on it. The bank's loan was for 60 months. Finance charges totaled $4,900. His monthly payment is:
Answer: $323.33
Step-by-step explanation:
($17,000 + $4,900 - $2,500) ÷ 60 months = $323.33 per month
↓ ↓ ↓
price finance down payment
Question 3 (5 points)
POINT
-POINT A
POINT B
What are the coordinates of the point labeled B in the graph shown above?
A) (3, 2)
B) (-3,2)
OC) (-2,3)
D) (-2, -3)
Question 4 (5 points)
Answer:
(D) -2,-3
Step-by-step explanation:
From the origin, we can find the current position of point B by counting.
B is 2 to the left of the y-axis, meaning that it's x value is -2.
B is 3 down of the x-axis, making it's y value -3.
Therefore, the coordinates of point B are -2,-3.
Hope this helped!
Answer: (D) -2,-3
Step-by-step explanation:
Find the difference of functions at x= - 3, (g - f)(-3), given f(x) and g(x): g(x) = x^2−15, and f(x) =2x
Answer:
0
Step-by-step explanation:
Solution:-
We are given two functions as follows:
[tex]f ( x ) = x^2 - 15\\\\g ( x ) = 2x[/tex]
We need to determine the composite function defined as ( g - f ) ( x ). To determine this function we need to make sure that both function exist for all real positive value of x.
The function f ( x ) is a quadratic function which has real values for all values of x. Similarly, function g ( x ) is a linear line that starts from the origin. Hence, both functions are defined over the domain ( -∞, ∞ )
We will perform arithmetic operation of subtracting function f ( x ) from g ( x ) as follows:
[tex][ g - f ] ( x ) = g ( x ) - f ( x )\\\\\\( g - f ) ( x ) = x^2 - 15 - 2x\\\\[/tex]
Now evaluate the above determined function at x = -3 as follows:
[tex]( g - f ) ( -3 ) = ( -3 )^2 - 2 ( -3 ) - 15\\\\( g - f ) ( -3 ) = 9 + 6 - 15\\\\( g - f ) ( -3 ) = 0[/tex]
Determine the t critical value for a lower or an upper confidence bound in each of the following situations. (Round your answers to three decimal places.)
a. Confidence level = 95%, df = 10
b. Confidence level = 95%, df = 15
c. Confidence level = 99%, df = 15
d. Confidence level = 99%, n = 5
e. Confidence level = 98%, df = 23
f. Confidence level = 99%, n = 32
Answer:
A. 1.812
B. 1.753
C. 2.602
D. 3.747
E. 2.069
F. 2.453
Step-by-step explanation:
A. 95% confidence level, the level of significance = 5% or 0.05
Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 10 degrees of freedom = 1.182
B. 95% confidence interval = 0.05 level of significance
Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 15 degrees of freedom = 1.753
C. 99% confidence interval = 0.01 level of significance
Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 15 degrees of freedom = 2.602
D. 99% confidence interval = 0.01 level of significance; DF (n - 1) = 5- 1 = 4
Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 4 degrees of freedom = 3.747
E. 98% confidence interval = 0.02 level of significance
Using t-table, the critical value for a lower or an upper confidence bound at 0.02 significance level with 23 degrees of freedom = 2.069
F. 99% confidence interval = 0.01 level of significance; df (n - 1) = 32 - 1 = 31
Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 31 degrees of freedom = 2.453
Please help. I’ll mark you as brainliest if correct!
Answer:
Quantity (lbs) of type 1 candy x = 8
Quantity (lbs) of type 2 candy y = 17,5
Step-by-step explanation:
Let´s call "x" quantity (in pounds) of candy type 1 in the mixture, and "y" quantity (in pounds ) of candy type 2, then according to the problem statement.
x + y = 25,5
2,20*x + 7,30*y = 5,70 * 25,5 ⇒ 2,20*x + 7,30*y = 145,35
Then we have a two equation system
x + y = 25,5 ⇒ y = 25,5 - x
2,20*x + 7,30*y = 145,35 ⇒ 2,20*x + 7,30* (25,5 - x ) = 145,35
2,20*x + 186,15 - 7,30*x = 145,35
5,1*x = 40,8
x = 40,8/5,1
x = 8 lbs
And y = 25,5 - 8
y = 17,5 lbs
At time, t=0, Billy puts 625 into an account paying 6% simple interest. At the end of year 2, George puts 400 into an account paying interest at a force of interest, δt=16+t for t≥2. If both accounts continue to earn interest indefinitely at the levels given above, the amounts in both accounts will be equal at the end of year n. Calculate n.
Answer:
26
Step-by-step explanation:
Given that:
At time, t=0, Billy puts 625 into an account paying 6% simple interest
At the end of year 2, George puts 400 into an account paying interest at a force of interest, 1/(6+t), for all t ≥ 2.
If both accounts continue to earn interest indefinitely at the levels given above, the amounts in both accounts will be equal at the end of year n. Calculate n.
In order to calculate n;
Let K constant to be the value of time for both accounts
At time, t=0, the value of time K when Billy puts 625 into an account paying 6% simple interest is:
[tex]K = 625 \times (1+ 0.06 K)[/tex]
[tex]K = 625 +37.5 K[/tex]
At year end 2; George amount of 400 will grow at a force interest, then the value of [tex]K = 400 \times e^{\int\limits^2_k {\dfrac{1}{6+t}} \, dx }[/tex]
[tex]K =400 \times \dfrac{6+K}{6+2}[/tex]
[tex]K =400 \times \dfrac{6+K}{8}[/tex]
[tex]K =50 \times ({6+K})[/tex]
[tex]K =300+50K[/tex]
Therefore:
If K = K
Then:
625 + 37.5 = 300 +50 K
625-300 = 50 K - 37.5 K
325 = 12.5K
K = 325/12.5
K = 26
the amounts in both accounts at the end of year n = K = 26
How to calculate a circumference of a circle?
Answer: Pi multiplied by the diameter of the circle
Step-by-step explanation:
Answer:
The formula for finding the circumference of a circle is [tex]C = 2\pi r[/tex]. You substitute the radius of the circle for [tex]r[/tex] and multiply it by [tex]2\pi[/tex].
The dot plots show the number of hours a group of fifth graders and seventh graders spent playing outdoors over a one-
week period.
Time Spent Playing Outdoors
for Fifth Graders and Seventh Graders
.
5th Grade
0
ta
1 2 3 4 5
Hours
7
8
9 10
7th Grade
.
Answer: B
Step-by-step explanation:
Answer:B
Step-by-step explanation: I took the edge quiz and it was right.
What is the value of s in the equation 3 r equals 10 plus 5 s, when r equals 10? 4 8 100 200
Answer
4Step-by-step explanation:
Given,
r = 10
Let's create an equation,
[tex]3r = 10 + 5s[/tex]
plugging the value of r
[tex]3 \times 10 = 10 + 5s[/tex]
Multiply the numbers
[tex]30 = 10 + 5s[/tex]
Move 5s to L.H.S and change its sign
Similarly, Move 30 to R.H.S and change its sign.
[tex] - 5s = 10 - 30[/tex]
Calculate
[tex] - 5s = - 20[/tex]
The difference sign ( - ) should be cancelled on both sides
[tex]5s = 20[/tex]
Divide both sides of the equation by 5
[tex] \frac{5s}{2} = \frac{20}{5} [/tex]
Calculate
[tex]s = 4[/tex]
The value of s is 4.
Hope this helps..
Best regards!!
Answer:
A. 4 (on edgenuity)
Step-by-step explanation:
Hi I need this question please asap.
The exact heights of different elephants Choose the correct answer below. A. The data are continuous because the data can only take on specific values. B. The data are discrete because the data can take on any value in an interval. C. The data are discrete because the data can only take on specific values. D. The data are continuous because the data can take on any value in an interval.
Answer:
Option d: The data are continuous because the data can take on any value in an interval.
Step-by-step explanation:
The data are continuous if they can take on any value within a range. In this case study, there are different elephants including small/young ones and big ones/old ones.
Thus, their heights will vary and can take on any value within a particular range.
WILL MARK AS BRAINLIEST 4. Suppose there is a card game where you are dealt a hand of three cards. You have already learned that the total number of three-card hands that can be dealt from a deck of 52 cards is: 52C3=52!/49!3! 52C3=22100 Calculate the probability of getting a hand that has exactly two aces in it (A A X). Do this by finding out the number of possible hands that have exactly two aces, and then dividing by the total possible number of three-card hands that is stated above. Part A: Use the multiplication principle to tell the total number of three-card hands (permutations) that can be made with two aces. (2 points) Part B: In the answer from Part I, each two-ace hand got counted twice. For example, A A X got counted as a separate hand from A A X. Since order should not matter in a card hand, these are really the same hand. What is the actual number of two-ace hands (combinations) you can get from a deck of 52 cards?(2 points) Part C: Find the probability of drawing a three-card hand that includes two aces from a deck of 52 cards. Write your answer as a fraction. (2 points)
Answer:
Part A- 6
Part B- 3
Part C- 3/22100
Step-by-step explanation:
Part A-
Use the permutation formula and plug in 3 for n and 2 for k.
nPr=n!/(n-k)!
3P2=3!/(3-2)!
Simplify.
3P2=3!/1!
3P2=6
Part B-
Use the combination formula and plug in 3 for n and 2 for k.
nCk=n!/k!(n-k)!
3C2=3!/2!(3-2)!
Simplify.
3C2=3!/2!(1!)
3C2=3
Part C-
It is given that the total number of three-card hands that can be dealt from a deck of 52 cards is 22100. Use the fact that the probability of something equals the total successful outcomes over the sample space. In this case the total successful outcomes is 3 and the sample space is 22100.
I believe the answer is 3/22100
I honestly suck at probability but I tried my best.
which values will only have one zero??
If it has a single zero that means it has to be just touching the x-axis with its tip.
We know that if it has only one zero, the discriminant equals 0.
So,
[tex]D=b^2-4ac=0\implies (-k)^2-4(1)(9)=0[/tex]
Solving for k,
[tex]k=\pm\sqrt{36}=\boxed{\pm{6}}[/tex].
Hope this helps.