At two years of age, sardines inhabiting Japanese waters have a
length distribution that is
approximately normal with mean 20.2 cm and standard deviation 0.65
cm. Draw a bell curve
for each problem.
a

Answer:

C. strong negative

Step-by-step explanation:

The reason why is because, the student's grade is falling dramatically while they watch TV. So therefore, we can erase A and D. B maybe however, it isn't "weak" but it is a heavy decrease. Therefore, your answer would be C.

Answer:

\((x - \frac{ - 9 + \sqrt{161} }{2} )(x - \frac{ - 9 - \sqrt{161} }{2} ) \)

Step-by-step explanation:

\(1. \: a(x - \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} ) \: (x - \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a}) \\ 2. \: (x - \frac{ - 9 + \sqrt{ {9}^{2} - 4 \times - 20 } }{2} ) \: (x - \frac{ - 9 - \sqrt{ {9}^{2} - 4 \times - 20 } }{2} )\)

Answer:

here are four main types of transformations: translation, rotation, reflection and dilation. These transformations fall into two categories: rigid transformations that do not change the shape or size of the preimage and non-rigid transformations that change the size but not the shape of the preimage

Step-by-step explanation:

pls make me brainiest

\(\left\lceil\begin{matrix}1 & 0 & 0 & 1 \\-2 & 0 & 0 & 2 \\5 & -2 & 3 & -2 \end{matrix}\right\rceil\)

These three vectors are linearly independent and can span the space generated by the original set of vectors.

The vectors given are:
v₁ = (1, 0, 0, 1)
v₂ = (-2, 0, 0, 2)
v₃ = (5, -2, 3, -2)
v₄ = (15, -8, 12, -6)
v₅ = (14, -6, 9, -5)

To find a basis for the space spanned by these vectors, we need to determine which vectors are linearly independent.

A set of vectors is linearly independent if none of the vectors can be expressed as a linear combination of the others.

We can start by setting up an augmented matrix using these vectors:

\(\left\lceil\begin{matrix}1 & -2 & 5 & 15 & 14\\0 & 0 & -2 & -8 & -6\\0 & 0 & 3 & 12 & 9\\1 & 2 & -2 & -6 & -5\end{matrix}\right\rceil\)

We can then perform row operations to reduce the matrix to row-echelon form:

\(\left\lceil\begin{matrix}1 & -2 & 5 & 15 & 14\\0 & 0 & 3 & 12 & 9\\0 & 0 & 0 & -2 & -1\\0 & 0 & 0 & 0 & 0\end{matrix}\right\rceil\)

From the row-echelon form, we can see that the first three columns form a linearly independent set.

Therefore, a basis for the space spanned by the given vectors is:

\(\left\lceil\begin{matrix}1 & 0 & 0 & 1 \\-2 & 0 & 0 & 2 \\5 & -2 & 3 & -2 \end{matrix}\right\rceil\)

These three vectors are linearly independent and can span the space generated by the original set of vectors.

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From the row-echelon form for the space spanned by the given vectors the basis is \(\[\begin{bmatrix}1 & 0 & 0 \\1 & -2 & 0 \\0 & 2 & 5 \\\end{bmatrix}\]\).

The basis for the space spanned by the given vectors can be determined by finding a set of linearly independent vectors that span the same space. The given vectors are: \(\[ \begin{bmatrix}1 & 0 & 0 \\1 & -2 & 0 \\0 & 2 & 5 \\-2 & 3 & -2 \\15 & -8 & 12 \\-6 & 14 & -6 \\9 & -5 & 0 \\\end{bmatrix}\].\)

To find a basis, we can perform row operations on the given matrix to obtain its row-echelon form. After performing the row operations, we get:

\(\[ \begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \\0 & 0 & 0 \\0 & 0 & 0 \\0 & 0 & 0 \\0 & 0 & 0 \\\end{bmatrix}\]\)

From the row-echelon form, we can observe that the first three rows are linearly independent, while the remaining rows are all zeros. Therefore, a basis for the space spanned by the given vectors is the set of three vectors corresponding to the first three rows of the row-echelon form:

\(\[\begin{bmatrix}1 & 0 & 0 \\1 & -2 & 0 \\0 & 2 & 5 \\\end{bmatrix}\]\).

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Fabio traveled approximately 5.1 + 5.1 = 10.2 miles.

To calculate the total distance traveled, you need to add up the distances for both the forward and return trip.

Fabio rode 2.3 miles to his friend's house, then 0.7 mile to the grocery store, and finally 2.1 miles to the library.

For the forward trip, the total distance is 2.3 + 0.7 + 2.1 = 5.1 miles.

Since Fabio rode the same route back home, the total distance for the return trip would be the same.

Therefore, in total, Fabio traveled approximately 5.1 + 5.1 = 10.2 miles.

COMPLETE QUESTION:

The distance travelled by Fabio on his scooter was 2.3 miles to the home of his first friend, 0.7 miles to the grocery shop, and 2.1 miles to the library. How far did he travel overall if he took the same route home?

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Given that, the function s(t) describes the motion of a particle along a line. s(t) = t³ − 13t² + 35t − 220

We need to find the time intervals in which the particle moves in the positive direction and the negative direction.

The given equation is s(t) = t³ − 13t² + 35t − 220

Taking the derivative,

v(t) = s'(t) = 3t² -26t + 35 = velocity at time t

s'(t) = 3t² -26t + 35 = 0

(3t -5)(t-7) = 0

t = 5/3 and 7 seconds

Therefore, the velocity > 0 when s'(t) > 0, when t>7 or t < 5/3 seconds

velocity <0 when 5/3 < t < 7 seconds

When moving in a positive direction, the intervals :-

(-∞, 5/3) ∪ (7, ∞)

When moving in a negative direction, the interval :-

(5/3, 7)

Hence, the time intervals are; positive direction (-∞, 5/3) ∪ (7, ∞) and negative direction (5/3, 7)

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The question was incomplete, so I solved for the question;

The function s(t) describes the motion of a particle along a line.

s(t) = t³ − 13t² + 35t − 220

(a) Find the velocity function v(t) of the particle at any time t ≥ 0.

(b) Identify the time interval(s) on which the particle is moving in a positive direction. (Enter your answer using interval notation.)

(c) Identify the time interval(s) on which the particle is moving in a negative direction. (Enter your answer using interval notation.)

Answer:

-6

Step-by-step explanation:

-30÷5=-6

this is the ans

The first-order Adams-Moulton formula derived as: y(t+h) ≈ y(t) + h/2 * [f(t, y(t)) + f(t+h, y(t+h))].

The first-order Adams-Moulton formula is equivalent to the trapezoid rule for approximating the integral in ordinary differential equations.

The first-order Adams-Moulton formula is derived by approximating the integral in the ordinary differential equation (ODE) using the trapezoid rule.

To derive the formula, we start with the integral form of the ODE:

∫[t, t+h] y'(t) dt = ∫[t, t+h] f(t, y(t)) dt

Approximating the integral using the trapezoid rule, we have:

h/2 * [f(t, y(t)) + f(t+h, y(t+h))] ≈ ∫[t, t+h] f(t, y(t)) dt

Rearranging the equation, we get:

y(t+h) ≈ y(t) + h/2 * [f(t, y(t)) + f(t+h, y(t+h))]

This is the first-order Adams-Moulton formula.

To verify its equivalence to the trapezoid rule, we can substitute the derivative approximation from the trapezoid rule into the Adams-Moulton formula. Doing so yields:

y(t+h) ≈ y(t) + h/2 * [y'(t) + y'(t+h)]

Since y'(t) = f(t, y(t)), we can replace it in the equation:

y(t+h) ≈ y(t) + h/2 * [f(t, y(t)) + f(t+h, y(t+h))]

This is equivalent to the trapezoid rule for approximating the integral. Therefore, the first-order Adams-Moulton formula is indeed equivalent to the trapezoid rule.

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the series converges for all x in the interval (-1/6, 1/6) in interval notation.

The given series is a geometric series with first term a=1 and common ratio r=6x. The series converges if and only if |r|<1.

So, |6x|<1

Solving this inequality, we get:

-1/6 < x < 1/6

To find all values of x for which the series converges, we need to analyze the given series:
∑(6x)^n

This is a geometric series with a common ratio of 6x. For a geometric series to converge, the absolute value of the common ratio must be less than 1:

|6x| < 1

Now, we can solve for the interval of x:

|-1/6| < |x| < |1/6|

Using interval notation, the range of values for which the series converges is:

(-1/6, 1/6)

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As asked in the question the value of xz and y will be even ,

xz is even and y is also even

given

X = factor of Y

Y = factor of Z

Therefore,

z= mnz = mnx  , xz = even

because

either z even, so the answer is directly yes or x is even (or both) but if x is even and as then  z= mnz = mnx must be even too (one of the multiples of z is even, so z is even too).

(2) y=  even

because

as z=ny then as one of the multiples of z even then only  z  will be even

Integers are the collection of whole numbers and negative numbers. Similar to whole numbers, integers also does not include the fractional part. Thus, we can say, integers are numbers that can be positive, negative or zero, but cannot be a fraction. We can perform all the arithmetic operations, like addition, subtraction, multiplication and division, on integers.

The examples of integers are, 1, 2, 5,8, -9, -12, etc. The symbol of integers is “Z“.

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Answer:

The length is 6.5

and the area is 6.5⁴

Using proportions, it is found that:

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

A test of a new car results in 360 miles on 20 gallons of gas, hence the mileage is given by:

360/20 = 18 miles per gallon.

Hence the distance on 60 gallons is:

18 x 60 = 1080 miles.

You could drive 1080 miles on 60 gallons of gas.

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The sum of given series is infinity ∑(n = 1) sin(nx)/(2n - 1).

What is sum of series?

A series' sum is the sum of the words or list of numbers that make up the series. If a series has a sum, it will be one integer (or fraction), such as 0, 1/2, or 99.

As given series is,

f(x) = sinx + sin(2x)/3 + sin(3x)/5+.....

The series function is trigonometric function such as sinx, sin(2x), sin(3x).

The nth term of series is sin(nx).

The coefficient of series is 1, 1/3, 1/5.

The coefficient of nth terms is 1/(2n - 1).

Sum of series is,

= infinity ∑(n = 1) sin(nx)/(2n - 1).

Hence, the sum of given series is infinity ∑(n = 1) sin(nx)/(2n - 1).

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In linear equation,3 whole pizzas should they order .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

total people = 4

Each person always eats 3/4 of a cheese pizza.

   3/4 + 3/4 + 3/4 + 3/4  

= 3 + 3 + 3 + 3 /4

= 12/4

= 3

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Since rectangles ABCD and EFGH are similar, we can take the ratios of the corresponding sides of the rectangles

cross multiplying

8 x 6 = 4 x k

48 = 4k

4k = 48

Divide both sides by 4

k = 48/4

k = 12

The total probability of winning is 0.75, which is not equal to 1, indicating that the game is not fair.

To decide in case this is a fair game, we ought to calculate the likelihood of each player winning.

Let H speak to the result of flipping a head and Tail speak to the result of flipping a tail. At that point, the conceivable results of three coin flips are:

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

The likelihood of getting each result is 1/8, accepting the coin flips are reasonable and autonomous.

Xenia wins on the off chance that there are 2 heads and 1 tail. Three conceivable results fulfill this condition:

HHT, HTH, and THH. Hence, the likelihood of Xenia winning is 3/8.

Yolanda wins in case there are 2 tails and 1 head. There are moreover three conceivable outcomes that fulfill this condition:

TTH, THT, and HTT. Subsequently, the likelihood of Yolanda winning is additionally 3/8.

Zoe wins if there are 3 heads or 3 tails. Two conceivable results fulfill this condition:

HHH and TTT. In this manner, the likelihood of Zoe winning is 2/8 = 1/4.

To check in case the diversion is reasonable, we include the probabilities of each player winning:

3/8 + 3/8 + 1/4 = 0.75

The full probability of winning is 0.75, which isn't break even with 1, indicating that the game is not fair.

One way to form it a fair diversion would be to alter the payouts or the rules of the amusement to guarantee that the full likelihood of winning includes up to 1.

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Answer:

Step-by-step explanation:

Even though the options to choose from are not given in this question we can try and lay our hand on the most likely equation for the number of minutes Jack reads his book.

firstly on a daily Jack reads a total of = 8+10 = 18 mins

He attends school from Mon- fri = 5 days

Now on a weekly basis jack reads = 5*18

in other words, the equation is simply the number of days times the time spent to read his book per day

hence this is  = 90 min or 1hr 30 mins

Number of terms of sequence N

Difference D = -1

Then there are here

In negative part, 70 numbers

In positive x line, 40 numbers

And add also zero

Then, ANSWER IS

N= 70 + 40 + 1

. = 111

There are 111 numbers

Answer:$2.97

Step-by-step explanation: 35 divided by 12 = 2.97

Given, Jada walks at a speed of 3 mph and Elena walks at a speed of 2.8 mph.Both Jada and Elena start walking along a walking trail at the same time.

Let us determine the distance covered by both of them.Distance travelled by Jada in 3 hours is:Distance = Speed × Time= 3 mph × 3 hours= 9 miles Distance travelled by Elena in 3 hours is:Distance = Speed × Time= 2.8 mph × 3 hours= 8.4 miles Thus, Jada will walk 0.6 miles farther than Elena after 3 hours.

To determine how far Jada will walk after 3 hours, we need to calculate the distance traveled based on her speed.

Jada walks at a speed of 3 miles per hour (mph), so we can calculate her distance using the formula:

Distance = Speed × Time

Plugging in the values, we have:

Distance = 3 mph × 3 hours

Distance = 9 miles

Therefore, Jada will walk a distance of 9 miles after 3 hours.

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The given information is as follows:

Jada walks at a speed of 3 mph and Elena walks at a speed of 2.8 mph. If they both begin walking along a walking trail at the same time.

Therefore, Jada will walk 9 miles after 3 hours.

The distance covered by Jada after 3 hours can be calculated as follows:

Distance = Speed x Time

Since Jada walks at a speed of 3 mph, the distance covered by her in 3 hours can be calculated as:

Distance covered by Jada = 3 mph x 3 hours

= 9 miles.

Therefore, Jada will walk 9 miles after 3 hours.

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The equation's value for y is 2

In mathematics, an equation is a statement that two expressions are equivalent. There are usually one or more variables present, which stand for unknown values that must be determined. Numbers, variables, and mathematical operations like addition, subtraction, multiplication, division, and exponentiation can all be found in an equation. The variables' values that determine whether an equation is true are its solutions.

Given equation;

3x-y=23........Equation1

2x+5y=4.........Equation2

Multiplying equation 1 by 2 and Equation2 by 3 and subtract both, we get

-2y-15y=46-12

Simplifying the terms;

-17y=34

Dividing both side by -17, we get

y=-2

hence, value of y in the equation is -2.

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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:

T~final is 150.11 C

Step-by-step explanation:

To solve this we need this specific heat equation:

Q=mc(T~final - T~initial) that is the difference of final temperature minus initial temperature.

We are given:

Q = 294 J

m = 10 g

c = 0.235 J/gC

T~initial = 25 C

Plug the values in to the equation

294 J = 10 g * 0.235 J/gC * T(difference)

294 J = 2.35 J/C * T(difference)

Divide both sides by 2.35 J/C

294 J / 2.35 J/C = T(difference)

T(difference) = 125.11 C

If the initial temperature was 25 C then then

T~final = 25 C + 125.11 C or 150.11 C

Paulie's opportunity cost of producing a cup of ice cream is 4 T-shirts while Vinny's opportunity cost (C) of producing a t-shirt is 0.53

The table entries are given as:

          Ice Cream (cups) T-shirts (quantity)

Paulie 5.00                          20.00

Vinny 8.00                              15.00

Paulie's opportunity cost of producing a cup of ice cream is calculated by dividing the number of T-shirts by the cups of ice cream.

So, we have:

\(C = \frac{20.00}{5.00}\)

\(C =4.00\)

Similarly, Vinny's opportunity cost (C) of producing a t-shirt is calculated by dividing the cups of ice cream by the number of T-shirts

So, we have:

\(C = \frac{8.00}{15.00}\)

\(C = 0.53\)

Hence, Vinny's opportunity cost (C) of producing a t-shirt is 0.53

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Step-by-step explanation:

5×2=10

2x-2y=2y

2y+3=5x

Answer:

p=0.78837351631052428187102047390789

n=5

Therefore, the directional derivative of f at P=(1,-1,-2) in the direction of A=3i+2j-6k is -2.

To find the directional derivative of f(x,y,z) at P=(1,-1,-2) in the direction of A=3i+2j-6k, we first need to find the gradient of f at P, which is given by:

grad(f) = ∇f = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k

Here, f(x,y,z) = xy + yz + zx, so we have:

∂f/∂x = y + z

∂f/∂y = x + z

∂f/∂z = x + y

Thus, at P=(1,-1,-2), we have:

∇f(P) = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k

= (y+z)i + (x+z)j + (x+y)k

= (0+(-2))i + (1+(-2))j + (1+0)k

= -2i - 1j + 1k

Next, we need to find the unit vector in the direction of A:

|A| = sqrt(3^2 + 2^2 + (-6)^2) = 7

u = A/|A| = (3/7)i + (2/7)j - (6/7)k

Finally, we can compute the directional derivative of f at P in the direction of A as:

(DAf) | 1(1,-1,-2) = ∇f(P) · u

= (-2i - 1j + 1k) · (3/7)i + (2/7)j - (6/7)k

= -6/7 - 2/7 - 6/7

= -2

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Yes, the statement is true. This is a restatement of the definition of the limit of a function of two variables.

Formally, we say that the limit of f(x,y) as (x,y) approaches (a,b) is L if and only if for every number ε > 0, there exists a number δ > 0 such that if the distance between (x,y) and (a,b) is less than δ, then the distance between f(x,y) and L is less than ε. In symbols:

For every ε > 0, there exists a δ > 0 such that if 0 < sqrt((x-a)^2 + (y-b)^2) < δ, then |f(x,y) - L| < ε.

The condition that f(x,y) approaches L along every straight line through (a,b) is equivalent to saying that the limit of f(x,y) as (x,y) approaches (a,b) along any path is also L. This is a stronger condition than the usual definition of the limit, and implies that the limit exists and is equal to L.

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