what is the amplitude of y = 3[6(x-4)] - 5

The values of p1, p2, p3 that minimize Var(X) are p1 = 0, p2 = 1/3, and p3 = 2/3.

We can use the following formulas to find the variance of X:

Var(X) = E[X^2] - (E[X])^2

E[X] = p1 + 2p2 + 3p3

E[X^2] = p1 + 4p2 + 9p3

Substituting these expressions into the formula for the variance, we get:

Var(X) = p1 + 4p2 + 9p3 - (p1 + 2p2 + 3p3)^2

Simplifying this expression, we get:

Var(X) = -\((p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3\)

To maximize Var(X), we want to maximize this expression subject to the constraint p1 + p2 + p3 = 1. We can use Lagrange multipliers to find the maximum. Let:

L(p1, p2, p3, λ) = -\((p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3 + λ(1 - p1 - p2 - p3)\)

Taking partial derivatives and setting them equal to zero, we get:

-2p1 + 2p2 + 6p3 - λ = 0

4p1 - 4p2 + 4p3 - λ = 0

6p1 + 8p2 - 6p3 - λ = 0

p1 + p2 + p3 = 1

Solving these equations, we get:

p1 = 2/7, p2 = 3/7, p3 = 2/7, λ = 4/7

Therefore, the values of p1, p2, p3 that maximize Var(X) are p1 = 2/7, p2 = 3/7, and p3 = 2/7.

To minimize Var(X), we want to minimize the expression \(-(p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3\) subject to the constraint p1 + p2 + p3 = 1. We can use the same Lagrange multiplier method to find the minimum. Taking partial derivatives and setting them equal to zero, we get:

-2p1 + 2p2 + 6p3 - λ = 0

4p1 - 4p2 + 4p3 - λ = 0

6p1 + 8p2 - 6p3 - λ = 0

p1 + p2 + p3 = 1

Solving these equations, we get:

p1 = 0, p2 = 1/3, p3 = 2/3, λ = 2/3

Therefore, the values of p1, p2, p3 that minimize Var(X) are p1 = 0, p2 = 1/3, and p3 = 2/3.

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\(\stackrel{\textit{2nd equation }\times 2}{\begin{array}{rrrrr} -8x&+&2y&=&8\\ 2(4x&+&8y)&=&2(-4) \end{array}}\qquad \implies \qquad \begin{array}{rrrrr} -8x&+&2y&=&8\\ 8x&+&16y&=&-8\\\cline{1-5} 0&+&18y&=&0 \end{array} \\\\\\ 18y=0\implies y=\cfrac{0}{18}\implies \boxed{y=0} \\\\\\ \stackrel{\textit{we know that}}{4x+8y=-4}\implies 4x+8(0)=-4\implies 4x=-4\implies x\cfrac{4}{-4}\implies \boxed{x=-1} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{one solution}}{(-1~~,~~0)}~\hfill\)

you'd want to often enough check their slopes first, if the slopes differ, they meet, if equal, they're parallel and either never meet or meet everywhere.

 The 32 ways to get a five-card combination containing two jacks and three aces.

(a) A full house consists of three of one kind and two of another kind. Therefore, there are 13 different choices for the rank of the triplet and 4 cards of the same rank. Once the triplet has been chosen, there are 12 choices for the rank of the pair and 4 cards of the same rank. Therefore, the number of ways to get a full house is as follows:$${13}{\times}{4}{\times}{12}{\times}{4}={7488}$$Therefore, there are 7488 ways to get a full house.(b) In this case, the two jacks and three aces must be chosen out of the 4 jacks and 4 aces in the deck. Therefore, the number of ways to get a five-card combination with two jacks and three aces is as follows:$$\frac{{4\choose2}{4\choose3}{44\choose0}}{5!}={32}$$Therefore, there are 32 ways to get a five-card combination containing two jacks and three aces.

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Answer:

t = 3

Step-by-step explanation:

................................

Step-by-step explanation:

1.3t+3(t+8.2)=37.5

1.3t+3t+24.6=37.5

4.3t=12.9

t=12.9/4.3

ans: t= 3

Answer:

13.85$

Step-by-step explanation:

105$-8$=97$

97$/7$=13.85$

Answer: About $13.86

Step-by-step explanation: To find how much the cost of the forks is, we need to subtract the value of the lunch box from the total cost, because we don't need to find the value of the lunch box. So:

105 - 8 = 97

So, now since he bought 7 forks, we need to divide 7 by 97. So:

97 / 7 = 13.857142857142858

So, we need to round to the nearest cent. So, the 7 is greater than 5, so we round up. So, we have $13.86 each. So, check, we do:

13.86(7) + 8

97.02 + 8

= 105.02

This is the closest he can buy for each fork is ABOUT $13.86. I hope this helps ;)

The degree of a polynomial is the highest power of the variable in the equation. In this case, the equation 2x² 5x³ 7 has the highest power of x being 3, so the degree of the polynomial is 5.

Step 1: Identify the highest power of the variable (x).

Step 2: Count the number of terms in the equation.

Step 3: The degree of the polynomial is the highest power of the variable plus the number of terms minus one.

Step 4: In this case, the highest power of x is 3 and the number of terms is 3, so the degree of the polynomial is 3 + 3 - 1 = 5.

The degree of the polynomial 2x² 5x³ 7 is 5. This can be calculated by taking the highest power of the variable (x) and adding it to the number of terms in the equation (3), and then subtracting 1.

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The slope can be found with two sets of points

The points can be any points, but in this case I choose the point (-1,10) and (1,2)

Slope = \(\frac{y2-y1}{x2-x1} =\frac{10-2}{-1-1} =\frac{8}{-2} =-4\)

The slope of the line that contains these points is -4.

Hope that helps!

Answer:

89m

Step-by-step explanation

area of the triangle 15

area of the rectangle 104

104-15=89m

Answer:

\(89\) \(m^{2}\)

Step-by-step explanation:

area of a triangle  = \(\frac{bh}{2}\)

so \(\frac{(5)(6)}{2}\) = 15 \(m^{2}\)

area of a rectangle = \(\\ bh\)

so \(\\ 8\)×\(\\ 13\) \(\\ = 104\) \(m^{2}\)

so the area of the figure is

\(\\ 104\) \(m^{2}\) -  15 \(m^{2}\) = \(89\) \(m^{2}\)

Answer:

-17°C at sunset

15°C at sunrise

Answer: See explanation

Step-by-step explanation:

A pizza is in the shape of a circle.

Since the perimeter is 10 inches, we have to find the radius. This will be:

2πr = 10

πr = 10/2

πr = 5

3.14r = 5

r = 5/3.14

r = 1.5924

Area = πr²

= 3.14 × 1.5924²

= 7.96 inches

= 8 inches approximately

Answer:

102 cm

Step-by-step explanation:

45 + 45 = 90

6 + 6 = 12

90 + 12 = 102

Answer:

Step-by-step explanation:

Left sides of both equations are the same sum (8x+2y), so the right sides also has to be the same. They are not so  there is no solutions.

{If they are the same then system has infinitely many solutions.}

The periodic solutions of the system are:

(0, 0),

(±√2, ±√2).

These points represent periodic orbits in the phase space of the system.

To determine the periodic solutions, if any, of the system:

ẋ = yx^p(x^2y^2 - 2),

ẏ = -xy^p(x^2y^2 - 2),

we need to find values of x and y for which the derivatives ẋ and ẏ are equal to zero simultaneously. These points represent potential periodic solutions.Setting ẋ = 0 and ẏ = 0, we have:

0 = yx^p(x^2y^2 - 2),

0 = -xy^p(x^2y^2 - 2).

From the first equation, we can see that either y = 0 or x^2y^2 - 2 = 0.

If y = 0, then the second equation implies that x = 0. Therefore, (0, 0) is a solution.

If x^2y^2 - 2 = 0, then x^2y^2 = 2.

Taking the square root of both sides, we get xy = ±√2.Considering the second equation, we have -xy^p(x^2y^2 - 2) = 0.

Substituting xy = ±√2, we find that this equation holds true.

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The correct answer is option a) Descriptive statistics; inferential statistics

a. Statistics with descriptions; Inferential statistics is the branch of statistics that deals with organizing, summarizing, and presenting data in a meaningful manner. Descriptive statistics are examples of this. It includes graphs or charts that provide a comprehensive overview of the data as well as measures like the mean, median, mode, and standard deviation.

On the other hand, inferential statistics is a subfield of statistics that uses a sample to make inferences or conclusions about a population. It makes predictions or generalizations about the larger population by utilizing sampling methods and probability theory.

Therefore, a. descriptive statistics is the correct response; statistical inference.

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The second generator runs longer because it uses less fuel per hour than the first generator, meaning it will take longer for the two generators to use the same amount of fuel.

In this case, it will take 60 hours for the two generators to use the same amount of fuel, and the second generator will run for the entire 60 hours.

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Answer:

Second choice, 2/5

Step-by-step explanation:

12 + 9 + 10 + 11 + 8 = 50

12 red and 8 blue, the probability of getting either is 12 + 8 = 20/50 which simplified is 2/5

Reflection at point y = -6 will have coordinates as

preimage      image

Q(0, -9)          Q' (0, -6)

R(4, -9)           R' (4, -6)

S(6, -8)           S' (6, -5)

T(2, -8)           T' (2, -5)

The transformation involve is reflection and this is a type of transformation that produces the mirror image of the preimage

The transformation rule to get the mirror image is (x, y) → (x, y + 3)

The coordinates are applied as follows

Q(0, -9) → (0, -9 + 3) → Q' (0, -6)

R(4, -9) → (4, -9 + 3) → R' (4, 6)

S(6, -8) → (6, -8 + 3) → S' (6, -5)

T(2, -8) → (2, -8 + 3) → T' (2, -5)

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Answer:

B=28

Step-by-step explanation:

The length of the fabric which Brandon formed a rectangle, is 11 inches.

To find the length of the fabric, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the length of the fabric is one of the other two sides, and the diagonal cut is the hypotenuse. So, we can write the equation:

\(L^2 + 5^2 = 13^2\)

where L is the length of the fabric.

Solving for L, we get:

\(L^2 = 144 - 25 = 119, and L =\sqrt{119} = 11.\)

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Answer:

Step-by-step explanation: π = 3.142

r = 10 cm

Area of the circle = 3.142 × 10²

Area = 3.142 × 100

Area = 314.2 cm²

The area of the required circle would be 149.590 cm² which is a radius of 6.9 cm.

The area of the circle is equal to the product of the square of the radius of the circle and pi.

A = πr²

where 'r' is the radius of the circle

We have been given that the radius of a circle is 6.9 cm.

So here r = 6.9 cm

the area of a circle = πr²

the area of a circle = π(6.9)²     [take π = 3.142]

the area of a circle = (3.142)(47.61)

the area of a circle = 149.590 cm²

Hence, the area of the required circle would be 149.590 cm².

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The range of Box A is 31 grams which is smaller.

Given that, Jaxon bought two boxes of eggs at a market and recorded the mass of each egg in the stem-and-leaf diagram,

So, the ranges are ;

Box A = 76 - 45 = 31 grams

Box B = 78 - 43 = 35 grams

Therefore, we see that the range of the box A is smaller than the range of the box B.

Hence, the range of Box A is 31 grams which is smaller.

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Answer:

Step-by-step explanation:

Well the internet has some good videos on how to graph but I'll try to explain it.

That -3/5 which is beside your x is the slope. 3 is the rise and 5 is the run.

That -3 or your b value is the y-intercept. So when x=0

So put a dot on (0, -3)

Next try to plug in whole number values for x to find points on the graph. Then connect the dots and you're done.

If the population grows by 15 people. The original number of people was 50, hence the new share of each person was Rs. (which is refused).

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

Let no. of persons = x

Each person get

= 6500/x

If there 15 persons were added more

= 6500/(x + 15)

(6500/x) - 6500/(x + 15) = 30

\(\Rightarrow 6500\left[\frac{(\mathrm{x}+15)-(\mathrm{x})}{\mathrm{x}(\mathrm{x}+15)}\right]=30\)

\(\Rightarrow 6500\left[\frac{x+15-x}{x^2+15 x}\right]=30\)

\(& \Rightarrow 1625\left[\frac{15}{x^2+15 x}\right]=3 \\\)

Then,

\(& \Rightarrow \frac{24375}{x^2+15 x}=3 \\\)

Simplifying the above equation,

\(& \Rightarrow 3 x^2+45 x=24375 \\\)

\(& \Rightarrow 3 x^2+45 x-24375=0 \\\)

\(& \Rightarrow x^2+15 n-3250=0 \\\)

\(& \Rightarrow x^2+(65 n-50 n)-3250=0 \\\)

Then we get,

\(& \Rightarrow x^2+65 n-50 n-3250=0 \\\)

\(& \Rightarrow x+65)-50(x+65)=0\)

\(\Rightarrow(\mathrm{x}-50)(\mathrm{x}+64)=0\)

x = 50, x = -65

Since the number of people cannot be zero,

the number of people is 50.

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Answer:

a)1√2

b)4√11

.........

Answer:

23

Step-by-step explanation:

Sum of all angles is 180

So b + 36 + 4b - 16 + (180 -  (8b - 49)) = 180

Notice that 3rd angle is 180 - (8b - 49)

b + 36 + 4b - 16 + 180 - 8b + 49 = 180

3b = 69

b = 23

Answer:

The interest rate is 7.5%

Step-by-step explanation:

The winner’s prize was in 1893 = $230

Now the winner prize in 2015 = $1570000

Total time period = 2015 – 1893 = 122 years

We have given the initial prize and final price along with the time period of 122 years. Now interest rate is required to calculate.

Future value = present  value (1 + r)^n

1570000 = 230 (1 + r)^122

r = 0.075 or 7.5 %

The interest rate is 7.5%

Answer:

(x+4)(3x-2)(x+1)

Step-by-step explanation:

Answer:

2^3

Step-by-step explanation:

you subtract the exponents if they have the same coefficient when dividing them.

9-6=3

13) The best prediction is that the college will need about 480 cookies.

14) The correct answer is Bus 47, with a median of 16.

For Question 13:

The total number of students surveyed is 225. Out of these, 27 students prefer cookies. So, we can estimate that approximately (27/225) * 4000 = 480 students will prefer cookies.

Therefore, the best prediction is that the college will need about 480 cookies.

For Question 14:

The correct graph for displaying the data is a bar graph with the title "Favorite Sport" and the x-axis labeled "Sport" and the y-axis labeled "Number of Students". The first bar should be labeled "Basketball" and go to a value of 17, the second bar should be labeled "Baseball" and go to a value of 12, the third bar should be labeled "Soccer" and go to a value of 27, and the fourth bar should be labeled "Tennis" and go to a value of 44.

For Question 15:

We can see that the median for Bus 18 is (10+12)/2 = 11 and the median for Bus 47 is (16+16)/2 = 16. Therefore, Bus 47 typically has the faster travel time.

The correct answer is Bus 47, with a median of 16.

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