Answers
All answer choices show the boundary line going through (0,-2) and (2,2). This is because y = 2x-2 goes through these two points. We make the boundary line a dashed line to indicate that solution points are not found on the boundary (because there is no "or equal to" portion in the inequality sign).
The shading is below the boundary line because of the "less than" sign. Any solution point (x,y) will have its y coordinate smaller than the y coordinate of points on the boundary line. So if (a,b) is on the boundary, then (a,c) is a solution where c < b.
In summary, the graph has a dashed boundary line and the shading is below the boundary
Answer: Graph BRelated Questions
Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145 a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
Answers
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145
a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)
c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)
Answer:
a. Cumulative Probability Distribution
Grade P(X ≤ x)
F 0.145
D 0.310
C 0.670
B 0.910
A 1
b. P(at least B) = 0.330
c. P(pass) = 0.855
Step-by-step explanation:
Professor Sanchez has been teaching Principles of Economics for over 25 years.
He uses the following scale for grading.
Grade Numerical Score Probability
A 4 0.090
B 3 0.240
C 2 0.360
D 1 0.165
F 0 0.145
a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
The cumulative probability distribution is given by
Grade = F
P(X ≤ x) = 0.145
Grade = D
P(X ≤ x) = 0.145 + 0.165 = 0.310
Grade = C
P(X ≤ x) = 0.145 + 0.165 + 0.360 = 0.670
Grade = B
P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 = 0.910
Grade = A
P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 + 0.090 = 1
Cumulative Probability Distribution
Grade P(X ≤ x)
F 0.145
D 0.310
C 0.670
B 0.910
A 1
b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)
At least B means equal to B or greater than B grade.
P(at least B) = P(B) + P(A)
P(at least B) = 0.240 + 0.090
P(at least B) = 0.330
c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)
Passing the course means getting a grade of A, B, C or D
P(pass) = P(A) + P(B) + P(C) + P(D)
P(pass) = 0.090 + 0.240 + 0.360 + 0.165
P(pass) = 0.855
Alternatively,
P(pass) = 1 - P(F)
P(pass) = 1 - 0.145
P(pass) = 0.855
PLSSS PEOPLE I NEED HELP
Answers
Answer:C
Step-by-step explanation:
The vertical line test
An integer is 3 less than 5 times another. If the product of the two integers is 36, then find the integers.
Answers
Answer:
3, 12
Step-by-step explanation:
Et x and y be the required integers.
Case 1: x = 5y - 3...(1)
Case 2: xy = 36
Hence, (5y - 3)*y = 36
[tex]5 {y}^{2} - 3y = 36 \\ 5 {y}^{2} - 3y - 36 = 0 \\ 5 {y}^{2} - 15y + 12y - 36 = 0 \\ 5y(y - 3) + 12(y - 3) = 0 \\ (y - 3)(5y + 12) = 0 \\ y - 3 = 0 \: or \: 5y + 12 = 0 \\ y = 3 \: \: or \: \: y = - \frac{12}{5} \\ \because \: y \in \: I \implies \: y \neq - \frac{12}{5} \\ \huge \purple{ \boxed{ \therefore \: y = 3}} \\ \because \: x = 5y - 3..(equation \: 1) \\ \therefore \: x = 5 \times 3 - 3 = 15 - 3 = 12 \\ \huge \red{ \boxed{ x = 12}}[/tex]
Hence, the required integers are 3 and 12.
let
x = one integer
y = another integer
x = 5y - 3
If the product of the two integers is 36, then find the integers.
x * y = 36
(5y - 3) * y = 36
5y² - 3y = 36
5y² - 3y - 36 = 0
Solve the quadratic equation using factorization method
That is, find two numbers whose product will give -180 and sum will give -3
Note: coefficient of y² multiplied by -36 = -180
5y² - 3y - 36 = 0
The numbers are -15 and +12
5y² - 15y + 12y - 36 = 0
5y(y - 3) + 12 (y - 3) = 0
(5y + 12) (y - 3) = 0
5y + 12 = 0 y - 3 = 0
5y = - 12 y = 3
y = -12/5
The value of y can not be negative
Therefore,
y = 3
Substitute y = 3 into x = 5y - 3
x = 5y - 3
x = 5(3) - 3
= 15 - 3
= 12
x = 12
Therefore,
(x, y) = (12, 3)
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Betty tabulated the miles-per-gallon values for her car as 26.5, 28, 30.2, 29.6, 32.3, and 24.7. She wants to construct the 95% two-sided confidence interval. Which value should Betty use for the value of t* to construct the confidence interval?
Answers
Answer:
Betty should use T = 2.571 to construct the confidence interval
Step-by-step explanation:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 6 - 1 = 5
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.571
Betty should use T = 2.571 to construct the confidence interval
if my medical expenses are $30,000 per year for 35 years with inflation at 5.13% how much money would I have to put in an interest bearing account with a 5% return to cover all medical expenses and the account be $0 at the end of 35 years
Answers
Answer:
$1,021,337.13
Step-by-step explanation:
The sum of present values of medical expenses is ...
30,000/1.05 +30,000(1.0513)/1.05^2 +30,000(1.0513^2)/1.05^3 +...
So, the series has an initial value of 30,000/1.05 and a common ratio of 1.0513/1.05. Its sum is given by ...
S = a(r^n -1)/(r -1)
where a = 30,000/1.05, n = 35, r = 1.0513/1.05.
Filling in these values and doing the arithmetic, we get ...
S = $1,021,337.13
You need an initial deposit of $1,021,337.13 to cover rising expenses for 35 years.
Determine what type of study is described. Explain. Researchers wanted to determine whether there was an association between high blood pressure and the suppression of emotions. The researchers looked at 1800 adults enrolled in a Health Initiative Observational Study. Each person was interviewed and asked about their response to emotions. In particular they were asked whether their tendency was to express or to hold in anger and other emotions. The degree of suppression of emotions was rated on a scale of 1 to 10. Each person's blood pressure was also measured. The researchers analyzed the results to determine whether there was an association between high blood pressure and the suppression of emotions.
Answers
Answer:
Experimental Study
Step-by-step explanation:
In an experimental study, the researchers involve always produce and intervention (in this case they were asked whether their tendency was to express or to hold in anger and other emotions. The degree of suppression of emotions was rated on a scale of 1 to 10) and study the effects taking measurements.
These studies are usually randomized ie subjects are group by chance.
As opposed to observation studies, where the researchers only measures what was observed, seen or hear without any intervention on their parts.
The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is a. k – 1. b. A chi-square distribution is not used. c. number of rows minus 1 times number of columns minus 1. d. n – 1.
Answers
Answer:
Option C
Step-by-step explanation:
The chi square test of independence is used to determine if there is a significant association between two categorical variables from a population.
It tests the claim that the row and column variables are independent of each other.
The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1) (c-1) where r is the number of rows and c is the number of columns.
I NEED HELP PLEASE, THANKS! :)
Answers
Answer:
68
Step-by-step explanation:
The number of chips tested is the integral of the rate over the specified time interval: t = 2 to 6.
[tex]\displaysyle n=\int_2^6{-3t^2+16t+5}\,dt=\left.-3\dfrac{t^3}{3}+16\dfrac{t^2}{2}+5t\right|_2^6\\\\=-(6^3-2^3) +8(6^2-2^2)+5(6-2)=-(216-8)+8(32) +5(4)\\\\=-208+256+20=\boxed{68}[/tex]
The technician can test 68 chips in that time period.
Find the value of x and the value of y. A.x = 15, y = 10 B.x = 20, y = 50 C.x = 50, y = 10 D.x = 50, y = 20
Answers
Answer:
X = 50
Step-by-step explanation:
(5x - 100) + (x - 20) = 180 (sum of angle on a straight line is = 180)
5x + x -100 -120 = 180
6x - 120 = 180
6x = 180 + 120
6x = 300
x = 300/6
x = 50
For y
3y + y + 140 = 180
4y = 180 -140
4y = 40
y = 40/4
y = 10
The domain and range of T
Answers
Answer:
Step-by-step explanation:
The domain is {-1, 2} (the domain has only two values).
The range is {-4, -3, 2} (the range contains three values)
acccording to this diagram what is cos 28
Answers
Answer:
[tex] \frac{15}{17} [/tex]Option B is the correct option.
Here,
Adjacent=15
Hypotenuse=17
Now,
[tex]cos \: theta = \frac{adjacent}{hypotenuse} \\ cos \: 28 = \frac{15}{17} [/tex]
Hope this helps..
Good luck on your assignment..
Answer:
B. 15/17
Step-by-step explanation:
(see attached graphic for reference)
Because we have a right triangle (i.e one of the internal angles is 90 degrees), we can use trigonometry to solve
from the diagram, we can see that
cos 28° = adjacent length / hypotenuse
we can also see that the length adjacent to 28° = 15 units and the hypotenuse is 17 units,
hence, substituting these values into the equation:
cos 28° = 15 / 17 (answer)
edit: typo
For the triangle show, what are the values of x and y (urgent help needed)
Answers
we just have to use the Pythagoras theorem and then calculate the value of x and y.
For the following data at the near-ground level, which location will residents likely see dew on their lawns in the morning? Group of answer choices City C: Dew Point Temperature = 25°F, expected low Temperature = 20°F City A: Dew Point Temperature = 65°F, expected low Temperature = 60°F City B: Dew Point Temperature = 45°F, expected low Temperature = 50°F
Answers
Answer: CITY B: Dew Point Temperature = 45°F, expected low Temperature = 50°F
Step-by-step explanation:
CITY C: Dew Point Temperature = 25°F, expected low Temperature = 20°F
CITY A: Dew Point Temperature = 65°F, expected low Temperature = 60°F
CITY B: Dew Point Temperature = 45°F, expected low Temperature = 50°F
city B is going to have dew on their lawn in the morning as the dew point temperature is less than the lowest temperature.
When surface temperature drops, eventually reaching the dew point, atmospheric water vapor condenses to form small droplets on the surface. Thus dew will be formed as the conditions are suitable only for city B.
Hartman Motors has $15 million in assets, which were financed with $6 million of debt and $9 million in equity. Hartman's beta is currently 1.4, and its tax rate is 30%. Use the Hamada equation to find Hartman's unlevered beta, bU. Do not round intermediate calculations. Round your answer to two decimal places.
Answers
Answer:
Unlevered beta ≈ 1.09
Step-by-step explanation:
Unlevered beta is basically the unlevered weighted average cost as it shows the volatility of returns without financial leverage. Unlevered beta is also known as asset beta, while the levered beta is commonly known as equity beta. Unlevered beta is calculated from the hamada equation as:
Unlevered beta = Levered beta/[1 + ((1 - Tax rate) × (Debt / Equity))]
We are given;
Levered beta = 1.4
Tax rate = 30% = 0.3
Debt = $6 million
Equity = $15 million
Thus, plugging these into the hamada equation, we have;
Unlevered beta = 1.4/[1 + ((1 - 0.3) × (6/15))]
Unlevered beta = 1.4/(1 + (0.7 × 0.4)
Unlevered beta = 1.4/(1 + 0.28)
Unlevered beta = 1.4/1.28
Unlevered beta = 1.09375
To 2 decimal places;
Unlevered beta ≈ 1.09
If George is 33 1/3% richer than Pete, than Pete is what percent poorer than George?
Answers
Answer:
25%
Step-by-step explanation:
George is 33[tex]\frac{1}{3}[/tex]% ([tex]\frac{100}{3}[/tex]%) richer than Pete. Let Pete's percentage of wealth be 100%.
Thus George percentage of wealth = 100% + [tex]\frac{100}{3}[/tex]%
= [tex]\frac{400}{3}[/tex]%
= 133[tex]\frac{1}{3}[/tex]%
Pete's percent poorer than George can be determined by;
= [tex](\frac{100}{3})[/tex] ÷ [tex](\frac{400}{3} )[/tex] × 100
= [tex](\frac{100}{3})[/tex] × [tex]\frac{3}{400}[/tex] ×100
= 0.25 × 100
= 25%
Pete is 25% poorer than George.
Find the general formula for the following sequence.
300000, 480000, 768000, 1228800, 1966080, ....
Answers
Answer:
3,145,728
Step-by-step explanation:
x1.6
300000 x 1.6 = 4800000
480000 x 1.6 = 7680000
768000 x 1.6 = 1228800
122800 x 1.6 = 1966080
1966080 x 1.6 = 3145728
Find the slope of the line passing through (6,8) and (-10,3)
Answers
Answer:
5/16
Step-by-step explanation:
Use the formula to find slope when 2 points are given.
m = rise/run
m = y2 - y1 / x2 - x1
m = 3 - 8 / -10 - 6
m = -5 / -16
m = 5/16
The slope of the line is 5/16.
Answer: m=5/16
Step-by-step explanation:
a line pass through the point (4,-2) and has a slope of 1/2 what is the value of (-4,a)
Answers
Answer:
if you are trying to find the value of a then a= -6
Step-by-step explanation:
i used the information along with desmos graphing calculator and i graphed the line and got the second point (-4,-6)
Answer:
a=-6
Step-by-step explanation:
slope=(y2-y1)/x2-x1)
1/2=(a-(-2))/(-4-4)
1/2=(a+2)/-8
a+2=1/2×-8=-4
a=-4-2=-6
31
z – 40-12
2
Solution
Answers
Answer:
31z-162
Step-by-step explanation:
[tex]-40-122=-162[/tex]
[tex]=31z-162[/tex]
Evaluate. Write your answer as a fraction or whole number without exponents. 7^–1 =
Answers
Answer:
1/7 = 0.142857... repeating
Step-by-step explanation:
7^(-1) = 1/(7^1) =1/7 = 0.142857... repeating
Answer:
[tex] \frac{1}{7} [/tex]Solution,
[tex] {7}^{ - 1} \\ = \frac{1}{ {7}^{1} } \\ = \frac{1}{7} [/tex]
Laws of indices:Law of zero index:[tex] {x}^{0} = 1[/tex]
Product law of indices:[tex] {x}^{m} \times {x}^{n} = {x}^{m + n} [/tex]
( powers are added in multiplication of same base)
Power law of indices:[tex] {( {x}^{m} )}^{n} = {x}^{m \times n} [/tex]
law of negative index:[tex] {x}^{ - m} = \frac{1}{ {x}^{m} } [/tex]
Root law of indices:[tex] {x}^{ \frac{p}{q} } = \sqrt[q]{ {x}^{p} } [/tex]
[tex]( \frac{x}{y} ) ^{n} = \frac{ {x}^{n} }{ {y}^{n} } [/tex] [tex] {(xy)}^{m} = {x}^{m} {y}^{m} [/tex][tex] \sqrt[n]{x} = x \frac{1}{n} [/tex]Hope this helps ....
Good luck on your assignment...
graph y=8 sec1/5 Ø the answers are graphs I am just unsure of how to answer
Answers
Answer:
Use a graphing calc.
Step-by-step explanation:
Among 20 golden hamster litters recorded, there was a sample mean of =7.72 baby hamsters, with a sample standard deviation of s=2.5 hamsters per liter. Create a 98% confidence interval for the mean number of baby hamsters per liter.
Answers
Answer:
[tex] 7.72 -2.539 \frac{2.5}{\sqrt{20}} =6.30[/tex]
[tex] 7.72 +2.539 \frac{2.5}{\sqrt{20}} =9.14[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex]\bar X= 7.72[/tex] represent the sample mean
[tex]s= 2.5[/tex] represent the sample deviation
[tex] n=20[/tex] represent the sample size
The confidence interval is given by:
[tex] \bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]
The confidence interval is 98% and the significance level is [tex]\alpha=0.02[/tex] the degrees of freedom are given by:
[tex] df= n-1 = 20-1=19[/tex]
And the critical value would be:
[tex] t_{\alpha/2}= 2.539[/tex]
And replacing we got:
[tex] 7.72 -2.539 \frac{2.5}{\sqrt{20}} =6.30[/tex]
[tex] 7.72 +2.539 \frac{2.5}{\sqrt{20}} =9.14[/tex]
The 98% confidence interval is between 6.42 hamsters per liter to 9.02 hamsters per liter
Mean (μ) = 7.72, standard deviation (σ) = 2.5, sample size (n) = 20, Confidence (C) = 98% = 0.98
α = 1 - C = 0.02
α/2 = 0.01
The z score of α/2 is the same as the z score of 0.49 (0.5 - 0.01) which is equal to 2.326.
The margin of error E is:
[tex]E = Z_\frac{\alpha }{2} *\frac{\sigma}{\sqrt{n} } \\\\E=2.326*\frac{2.5}{\sqrt{20} } =1.3[/tex]
The confidence interval = (μ ± E) = (7.72 ± 1.3) = (6.42, 9.02)
Hence the 98% confidence interval is between 6.42 hamsters per liter to 9.02 hamsters per liter
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Who'd be better at speed answering? Datguy323 or some Helping Hand? (Not a serious question) Solve for the variables: [tex]x^3+y^7=28\\x^3=27[/tex]
Answers
Answer:
x = 3
y = 1
Step-by-step explanation:
The equations are:
[tex]x^3+y^7 = 28[/tex]
and
[tex]x^3 = 27[/tex]
Putting second equation in the first one:
=> [tex]27+y^7 = 28[/tex]
Subtracting 27 to both sides
=> [tex]y^7 = 28-27[/tex]
=> [tex]y^7 = 1[/tex]
Taking power 7 to both sides
=> y = 1
Now,
[tex]x^3 = 27[/tex]
Taking cube root on the both sides
x = 3
Answer: (3,1)
Step-by-step explanation:
First, to find x, simply take the cube root of 27, or 3. Thus, x = 3.
Then, simply plug it in:
[tex]27+y^7=28\\Subtract(27)\\y^7=1\\y=1[/tex]
Thus, y = 1
Hope it helps <3
p.s. for some reason, in a graphing calculator, it shows no solutions
Hope it helps <3
2 in a row!
Write the comparison below as a ratio in simplest form using a fraction, a colon, and the word to. 11 oz to 5 oz
Answers
Explanation:
11 oz / 5 oz, 11 oz : 5 oz, eleven ounces to five ounces
[10 points] A manufacturer wants to design an open box having a square base and a surface area of 108 square inches. What dimensions will produce a box with maximum volume?
Answers
Answer:
6 inches square by 3 inches high
Step-by-step explanation:
For a given surface area, the volume of an open-top box is maximized when it has the shape of half a cube. If the area were than of the whole cube, it would be 216 in² = 6×36 in².
That is, the bottom is 6 inches square, and the sides are 3 inches high.
_____
Let x and h represent the base edge length and box height, respectively. Then we have ...
x² +4xh = 108 . . . . box surface area
Solving for height, we get ...
h = (108 -x²)/(4x) = 27/x -x/4
The volume is the product of base area and height, so is ...
V = x²h = x²(27/x -x/4) = 27x -x³/4
We want to maximize the volume, so we want to set its derivative to zero.
dV/dx = 0 = 27 -(3/4)x²
x² = (4/3)(27) = 36
x = 6
h = 108/x² = 3
The box is 6 inches square and 3 inches high.
_____
Comment on maximum volume, minimum area
In the general case of an open-top box, the volume is maximized when the cost of the bottom and the cost of each pair of opposite sides is the same. Here, the "cost" is simply the area, so the area of the bottom is 1/3 the total area, 36 in².
If the box has a closed top, then each pair of opposite sides will have the same cost for a maximum-volume box. If costs are uniform, the box is a cube.
Identifico el nombre de la propiedad a la que hacen referencia las siguientes expresiones:
Answers
Hacen falta las expresiones para poder responder a tu pregunta, estuve investigando y adjuntaré una imagen que hace referencia a tus preguntas, espero no equivocarme.
Si este es el caso, son 9 expresiones y el nombre de cada propiedad es:
1. Inverso aditivo (Sumar un número por su opuesto el resultado es 0)
2. Ley conmutativa (El orden de los factores no altera el producto)
3. Ley asociativa (Agrupar los términos sin alterar el resultado)
4. Ley de la identidad, (Sumar un número con 0 se obtiene el mismo número)
5. Ley distributiva (La misma respuesta cuando multiplicas un conjunto de números por otro número que cuando se hace cada multiplicación por separado)
6. Ley distributiva
7. Ley distributiva
8. Ley asociativa
9. Ley conmutativa
Tommy has "n" friends and he wants to give each friend 5 pencils. Write an expression to show how many pencils pencils Tommy will share.
Answers
Answer:
5n
Step-by-step explanation:
Think about it:
If Tommy has 4 friends (n = 4), then he will have to give 5 pencils to each person. The total number of pencils is 5 * n or 5 * 4 = 20.
Similarly, if Tommy has 0 friends (I can relate), then he will have to give 5 pencils to each of his imaginary friends. The total number of pencils he has to give out to his real friends is 5 * n or 5 * 0 = 0.
Find the work (in ft-lb) required to pump all the water out of a cylinder that has a circular base of radius 7 ft and height 200 ft. Use the fact that the weight-density of water is 62.4 lb/ft3
Answers
Answer:
work done is equal to 384279168 lb-ft
Step-by-step explanation:
The cylinder has a circular base of 7 ft.
The height of the cylinder is 200 ft
The weight density of water in the cylinder is 62.4 lb/ft^3
First, we find the volume of the water in the cylinder by finding the volume of this cylinder occupied by the water.
The volume of a cylinder is given as [tex]\pi r^{2} h[/tex]
where, r is the radius,
and h is the height of the cylinder.
the volume of the cylinder = [tex]3.142* 7^{2}*200[/tex] = 30791.6 ft^3
Since the weight density of water is 62.4 lb/ft^3, then, the weight of the water within the cylinder will be...
weight of water = 62.4 x 30791.6 = 1921395.84 lb
We know that the whole weight of the water will have to be pumped out over the height of cylindrical container. Also, we know that the work that will be done in moving this weight of water over this height will be the product of the weight of water, and the height over which it is pumped. Therefore...
The work done in pumping the water out of the container will be
==> (weight of water) x (height of cylinder) = 1921395.84 x 200
==> work done is equal to 384279168 lb-ft
The required work done will be "384279168 lb-ft".
Work done:Whenever a force pushes anything across distances, work is performed. This same energy transmitted, as well as work done, maybe determined by calculating the force through the kilometers moved throughout the direction of the applied force.
According to the question,
Circular base of cylinder = 7 ft
Height of cylinder = 200 ft
Weight density of water = 62.4 lb/ft³
The Volume of cylinder be:
= πr²h
By substituting the values,
= [tex]3.142\times (7)^2\times 200[/tex]
= [tex]3.142\times 49\times 200[/tex]
= [tex]30791.6[/tex] ft³
Now,
The weight of water be:
= [tex]62.4\times 30791.6[/tex]
= [tex]1921395.84[/tex] lb
hence,
The work done be:
= Water's weight × Cylinder's height
= [tex]1921395.84\times 200[/tex]
= [tex]384279168[/tex] lb-ft
Thus the above answer is right.
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I need help plz someone help me solved this problem I need help ASAP! I will mark you as brainiest!
Answers
Answer: k = -9
Step-by-step explanation:
kx² - 12x - 4 = 0
In order to have exactly one solution, it must be a perfect square.
Assume k is negative and factor out a negative 1.
-1(kx² + 12x + 4) = 0
[tex]\bigg(\sqrt{kx^2}+\sqrt4\bigg)^2=0\\\\[/tex]
The middle term = 12x [tex]= 2(\sqrt{kx^2})(\sqrt4)[/tex]
12x = 4x√k
3 = √k
9 = k
-1(9x² + 12x + 4) = 0
-9x² - 12x - 4 = 0
k=-9
PLEASE HELP!!! You want to distribute 7 candies to 4 kids. If every kid must receive at least one candy, in how many ways can you do this? (it's not 15)
Answers
Answer: 20
Step-by-step explanation:
I guess that we want to distribute all the 7 candies between 4 kids
We have 3 options:
first 3, 2, 1 and 1. (the number of candies that each kid gets)
The possible permutations in this case:
if we leave the 3 fixed, the ones do are equal, so the permutations are only given by the change in the kid that gets 2 candies, we have 3 permutations for this.
And for the fixed 3, we have 4 possible places where we can fix it, so the total number of combinations is:
c = 3*4 = 12.
and the second option is (2, 2, 2, 1)
Here the only change is the kid that gets only one candy, we have 4 options in this case:
c = 4.
the third option is (4, 1, 1, 1)
Here the only change is the kid that gets 4 candies, and we have 4 options for this, so we have 4 combinations:
c = 4.
Then the total number of possible combinations is:
C = 12 + 4 + 4 = 20