You want to buy some noodles. An 8-ounce package costs $2.88. A 14-ounce package costs
$5.18. A 20-ounce package costs $6.80. Which package is the best buy?
The
-ounce package of noodles is the best buy.
Click to select your answer(s).

Answer:

w = \(\frac{p -2l}{2}\)

Step-by-step explanation:

p = 2l + 2w  Subtract 2l from both sides of the equation

p - 2l = 2p  Divide both sides by 2

\(\frac{p -2l}{2}\) = w

Answer:

The equation would be x ÷ 4 ≤ 5

The median number of newspapers sold over seven weeks is 223.

The median is the middle score for a data set arranged in order of magnitude. The median is less affected by outliers and skewed data.

The formula for the median is as follows:

Find the median number of newspapers sold. (87, 87, 215, 154, 288, 235, 231)

We'll first arrange the data in ascending order.87, 87, 154, 215, 231, 235, 288

The median is the middle term or the average of the middle two terms. The middle two terms are 215 and 231.

Median = (215 + 231)/2

= 446/2

= 223

In statistics, the median measures the central tendency of a set of data. The median of a set of data is the middle score of that set. The value separates the upper 50% from the lower 50%.

Hence, the median number of newspapers sold over seven weeks is 223.

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Answer:

To get the answer for X we have to subtract 16 from 4 which gives us 12

X=12

Hope this helps.

Answer:

4+X= 16

X=16-4

X=12

*To find X , you need to minus 16 by four. That is because you have to move (+4) to the other side (change sides,change signs). So (+4) becomes (-4) so 16-4 =12

The radius is approximately 3.78 inches.

We can solve the question using the formula for the surface area of a sphere:

S=4πr^2

We are given that the surface area is 225 square inches, so we can substitute this value into the formula and solve for r:

\(225=4\pi r^2\frac{225}{4\pi}\)

      = r^2

r={{225}{4π}}

approx  3.78

A sphere does not have any edges or vertices, like other 3D shapes. The points on the surface of the sphere are equidistant from the center.

Hence, the distance between the center and the surface of the sphere are equal at any point. This distance is called the radius of the sphere.

The Radius of a circle or sphere is equal to the Diameter divided by 2.

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Answer:

420

Step-by-step explanation:

edge

The answer is E(Y) = E(X^2) + 3E(X).

To calculate the E(Y) with poisson distribution we first understand poisson distribution and then calculate:

Poisson distribution is one of many statistical distributions. It has a bell-shaped curve, which means that it’s equally likely to be any point on the distribution.

The expected value of Y can be found as:

E(Y) = E[(X+2)(X+1)]

= E(X^2 + 3X + 2)

= E(X^2) + 3E(X) + 2

Since X has a Poisson distribution with parameter kA, we know that:

E(X) = kA

E(X^2) = kA + (kA)^2

Substituting these values into the expression for E(Y), we get:

E(Y) = E(X^2) + 3E(X)

This can be interesting because it means that if you know where a random variable falls on the sample space, then you also know its probability of being anywhere in the corresponding tail of a normal distribution or other probability distribution.

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Answer:

The area will be:

\(A=18(1+\sqrt{3}) \: u^{2}\) or \(A=49.18 \: u^{2}\).

Step-by-step explanation:

Using the definition of tangent, we have:

\(tan(\alpha)=\frac{6}{\vec{AB}}\)

We know that tan(α) = 1, then we can find AB

\(1=\frac{6}{\vec{AB}}\)

\(\bar{AB}=6\: u\)

u means any unit.

Now, we need to find the distance BC. If the angle ∠D is 60°, then ∠C must be 30°. Using the tangent definition in the triangle BCD we have:

\(tan(30)=\frac{6}{\bar{BC}}\)

\(\bar{BC}=\frac{6}{tan(30)}\)

\(\bar{BC}=\frac{6}{1/\sqrt{3}}\)

\(\bar{BC}=6\sqrt{3} \: u\)

So, the base of the triangle will be:

\(b=\bar{AB}+\bar{BC}=6+6\sqrt{3}=6(1+\sqrt{3}) \: u\)

The area of a triangle is given by the following equation:

\(A=\frac{b*h}{2}\)

\(A=\frac{6(1+\sqrt{3})*6}{2}\)

\(A=18(1+\sqrt{3})\)

Therefore, the area will be \(A=49.18 \: u^{2}\).

I hope it helps you!

According to the question For ( a ) the amount and concentration of salt at any time \(\(t\)\) can be \(\[S(t) = 10 + 11 - 44 \times C(t) \text{ kg}\]\)\(\[C(t) = \frac{S(t)}{100}\text{ kg/L}\]\) . For ( b ) the limiting concentration of salt in the tank is 0.25 kg/L.

To determine the amount and concentration of salt at any time in the tank, we need to consider the inflow of saltwater, outflow of water, and evaporation. Let's denote the time as \(\(t\)\) in hours.

a. Amount and Concentration of Salt at any time:

Let's denote the amount of salt in the tank at time \(\(t\) as \(S(t)\)\) in kg and the concentration of salt in the tank at time \(\(t\) as \(C(t)\) in kg/L.\)

Initially, the tank contains 100 L of water with a salt concentration of 0.1 kg/L. Therefore, at \(\(t = 0\)\), we have:

\(\[S(0) = 100 \times 0.1 = 10 \text{ kg}\]\)

\(\[C(0) = 0.1 \text{ kg/L}\]\)

Considering the inflow, outflow, and evaporation rates, the amount of salt in the tank at any time \(\(t\)\) can be calculated as:

\(\[S(t) = S(0) + \text{Inflow} - \text{Outflow} - \text{Evaporation}\]\)

The inflow rate of saltwater is 55 L/h with a concentration of 0.2 kg/L. Thus, the amount of salt entering the tank per hour is:

\(\[\text{Inflow} = \text{Inflow rate} \times \text{Concentration} = 55 \times 0.2 = 11 \text{ kg/h}\]\)

The outflow rate is 44 L/h, so the amount of salt leaving the tank per hour is:

\(\[\text{Outflow} = \text{Outflow rate} \times C(t) = 44 \times C(t) \text{ kg/h}\]\)

The evaporation rate is 11 L/h, and as only water evaporates, it does not affect the salt concentration in the tank.

Therefore, the amount and concentration of salt at any time \(\(t\)\) can be expressed as follows:

\(\[S(t) = 10 + 11 - 44 \times C(t) \text{ kg}\]\)

\(\[C(t) = \frac{S(t)}{100}\text{ kg/L}\]\)

b. Limiting Concentration:

The limiting concentration refers to the concentration reached when the inflow and outflow rates balance each other, resulting in a stable concentration. In this case, the inflow rate of saltwater is 55 L/h with a concentration of 0.2 kg/L, and the outflow rate is 44 L/h. To find the limiting concentration, we equate the inflow and outflow rates:

\(\[\text{Inflow rate} \times \text{Concentration} = \text{Outflow rate} \times C_{\text{limiting}}\]\)

\(\[55 \times 0.2 = 44 \times C_{\text{limiting}}\]\)

\(\[C_{\text{limiting}} = \frac{55 \times 0.2}{44} = 0.25 \text{ kg/L}\]\)

Therefore, the limiting concentration of salt in the tank is 0.25 kg/L.

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Answer:

3a + 2r + 7b = 21

2a + 6r + b = 29

a + 4r + 5b = 23

Step-by-step explanation:

a = price of apples

r = price of oranges (I used r instead of letter o since o can be confused with zero)

b = price of bananas

Sally went to the grocery store and bought 3 lbs. of apples, 2 lbs. of oranges, and 7 lbs. of bananas for $21.

3a + 2r + 7b = 21

Kevin bought 2 lbs. of apples, 6 lbs. of oranges and 1 lb. of bananas for $29.

2a + 6r + b = 29

Heather bought 1 lb. of apples, 4 lbs. of oranges and 5 lbs. of bananas for $23.

a + 4r + 5b = 23

The system of equations is:

3a + 2r + 7b = 21

2a + 6r + b = 29

a + 4r + 5b = 23

Answer:

2xsquare +12x+12=0. i think thats the ryt answer

8*22 = 22*8

Hope this helps!

Answer:

Whatever has the answer of 80.

Step-by-step explanation:

Since the algae grow exponentially with doubling time of 4 days, then the population will be quadruple in size in 8 days and will be triple in size in  6.34 days.

The easiest way is to consider the situation as a geometric sequence. If the population doubles its size in 4 days, then it will be quadruple in:

2 x 4 days = 8 days.

In general, we can use the growth formula:

P(t) = Po . 2^(t/Td)

Where:

P(t) = population at time t

Po = initial population

Td = doubling time

Parameters given:

Td = 4 days

P(t) = 3Po

Plug those parameters into the formula:

3 Po = Po . 2^(t/4)

3 = 2^(t/4)

log 3 = (t/4) log 2

t = 4 . log 3 / log 2 = 6.34 days.

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The given matrix 'a' can be diagonalized. To diagonalize 'a', we need to find a matrix 'P' and a diagonal matrix 'D' such that 'D' is equal to the inverse of 'P' multiplied by 'a' multiplied by 'P'.

A square matrix 'a' is diagonalizable if there exists an invertible matrix 'P' such that 'P^(-1) * a * P' is a diagonal matrix. To determine whether 'a' is diagonalizable, we need to check if 'a' satisfies certain conditions.

Firstly, we check if 'a' has 'n' linearly independent eigenvectors, where 'n' is the size of the matrix. If 'a' has 'n' linearly independent eigenvectors, it is diagonalizable.

Secondly, we need to verify if the geometric multiplicity of each eigenvalue of 'a' matches its algebraic multiplicity. The geometric multiplicity represents the number of linearly independent eigenvectors corresponding to an eigenvalue, while the algebraic multiplicity denotes the number of times an eigenvalue appears in the characteristic equation.

If 'a' satisfies both conditions, it is diagonalizable. To find the diagonal matrix 'D', we place the eigenvalues of 'a' on the diagonal of 'D'. The matrix 'P' is formed by taking the eigenvectors of 'a' as its columns. Finally, 'D' is equal to the inverse of 'P' multiplied by 'a' multiplied by 'P', as stated earlier.

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Answer:

y=1/3x+0 or y=1/3x

Step-by-step explanation:

find the slope by taking two points and putting them in

y2 - y1/x2 - x1

so, (3,1) and (6,2) becomes 2-1/6-3 or 1/3 so, slope is 1/3

then to find y intercept you can put a point (6,2) and slope (1/3) into slope intercept form y - y1 = m(x - x1)

y - 2 = 1/3(x-6)

when you solve this you get y = 1/3x + 0, so y intercept is 0. you can also see. this on the graph given

The value of the side x is 7. 071

It is important to note that there are six different trigonometric identities with their ratios.

They are;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the information given, we have that;

The side ,'x' is the hypotenuse side

The side '5' is the opposite side

Using the sine identity, we have;

sin 45 = 5/x

cross multiply the values

x = 7. 071

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Cost for each pound of almonds is $1.5 and cost for each pound of jelly beans is $2.5.

Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.

System of linear equations involve two or more linear equations.

Let x be the cost of each pound of almond and y be the cost of each pound of jelly beans.

Then from the first purchase, we have the equation,

3x + 5y = 17

Similarly, from the second purchase, we have,

12x + 2y = 23

So the system of equations are

3x + 5y = 17 and 12x + 2y = 23

Solving these, we will get the values of x and y which is the cost of each pound of almond and jelly beans.

3x + 5y = 17

12x + 2y = 23

Multiplying the first equation with 4, we get,

12x + 20y = 68

Subtracting 12x + 2y = 23 from 12x + 20y = 68,

18y = 45

y = $2.5

Substituting y = 2.5 in any of the equation above, we get,

x = $1.5

Hence the cost for each pound of almond and jelly beans are $1.5 and $2.5 respectively.

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The value of the angle will be C. 20°

From the information given, it was stated that the protractor showed an angle going through the tenth tick mark after ten degrees.

This means the value of the angle will be:

= 10° + 10°

= 20°

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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In a Cartesian coordinate system for a three-dimensional space, let the sphere S be represented by the equation:

(x - a)^2 + (y - b)^2 + (z - c)^2 = r^2

where (a, b, c) are the coordinates of the center of the sphere, and r is the radius.

Let the plane P be represented by the equation:

Ax + By + Cz + D = 0

where (A, B, C) is the normal vector to the plane.

Since the line d is parallel to P and passes through the origin, it can be represented by the equation:

lx + my + nz = 0

where (l, m, n) is a vector parallel to the plane P.

To find the intersection points of the sphere S and the line d, we can substitute the equation of the line into the equation of the sphere, which gives us a quadratic equation in t:

(lt - a)^2 + (mt - b)^2 + (nt - c)^2 = r^2

Expanding this equation and collecting terms, we get:

(l^2 + m^2 + n^2) t^2 - 2(al + bm + cn) t + (a^2 + b^2 + c^2 - r^2) = 0

Since the line d passes through the origin, we have:

l(0 - a) + m(0 - b) + n(0 - c) = 0

which simplifies to:

al + bm + cn = 0

Therefore, the quadratic equation reduces to:

(l^2 + m^2 + n^2) t^2 + (a^2 + b^2 + c^2 - r^2) = 0

This equation has two solutions for t, which correspond to the two intersection points of the line d and the sphere S:

t1 = -(a^2 + b^2 + c^2 - r^2) / (l^2 + m^2 + n^2)

t2 = -t1

The coordinates of the intersection points can be obtained by substituting these values of t into the equation of the line d:

A = lt1, B = mt1, C = nt1

and

D = lt2, E = mt2, F = nt2

To find the distance between A and B, we can use the distance formula:

AB = sqrt((A - D)^2 + (B - E)^2 + (C - F)^2)

To maximize this distance, we can differentiate the distance formula with respect to t1 and set the derivative equal to zero:

d/dt1 (AB)^2 = 2(A - D)l + 2(B - E)m + 2(C - F)n = 0

This equation represents the condition that the direction vector (A - D, B - E, C - F) is orthogonal to the line d. Therefore, the vector (A - D, B - E, C - F) is parallel to the normal vector (l, m, n) of the plane P.

Using this condition, we can find the values of t1 and t2 that correspond to the maximum distance AB. Then we can substitute these values into the distance formula to find the maximum length of AB.

Answer:

28-7x

Step-by-step explanation:

Distribute the 7 outside the parentheses to give:

7(4) = 28

7(-x) = -7x

Hope this helped!

Answer:

28-7x

Step-by-step explanation:

7(4-x)

expand:

=7*4 + 7*-x

= 28-7x

Step-by-step explanation:

slope of the given line=2/3

since the required line is parallel to the given line, it's slope will be same.

hence slope of required line:2/3

The required line passes through the point(9,1),

hence the equation of the required line,

y-1=(2/3)(x-9)

3y-3=2x-18

2x-3y-15=0

There the equation of the required line is 2x-3y-15=0

it have manny solution it depand on a method u are using

Given the function `f(x, y) = x² - 2xy + 2y`.To find the critical point of the given function, we need to take partial derivatives with respect to x and y and set them equal to zero.

Partial derivative with respect to x `f_x(x,y) = 2x - 2y`Partial derivative with respect to y `f_y(x,y) = -2x + 2`Now, we need to solve these equations for x and y:`f_x(x,y) = 2x - 2y = 0` `=> 2x = 2y` `=> x = y` -------------(1)`f_y(x,y) = -2x + 2 = 0` `=> -2x = -2` `=> x = 1` -------------(2)

Using equations (1) and (2)`y = x = 1`Hence, the critical point of f(x, y) = x² - 2xy + 2y is `(1, 1)`The correct option is a) (1,1).

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The exercise involves finding the product C = AB, where matrix A is given by [2 9] and matrix B is given by [3 6 1]. We need to perform the matrix multiplication to obtain the resulting matrix C.

Let's calculate the matrix product C = AB step by step:

Matrix A has dimensions 2x1, and matrix B has dimensions 1x3. To perform the multiplication, the number of columns in A must match the number of rows in B.

In this case, both matrices satisfy this condition, so the product C = AB is defined.

Calculating AB:

AB = [23 + 912 26 + 94 21 + 95]

[103 + 612 106 + 64 101 + 65]

Simplifying the calculations:

AB = [6 + 108 12 + 36 2 + 45]

[30 + 72 60 + 24 10 + 30]

AB = [114 48 47]

[102 84 40]

Therefore, the product C = AB is:

C = [114 48 47]

[102 84 40]

In summary, the matrix product C = AB, where A = [2 9] and B = [3 6 1], is given by:

C = [114 48 47]

[102 84 40]

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Answer:

False

Step-by-step explanation:

Dividing integers is opposite operation of multiplication. But the rules for division of integers are same as multiplication rules. Though, it is not always necessary that the quotient will always be an integer.

wording credits goes to BYJUS

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The largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9 has dimensions x = 1.5, y = 1, and z = 2.25, with a maximum volume of 3.375 cubic units.

To find the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9, we can use the method of Lagrange multipliers.

Let the sides of the rectangular box be represented by the variables x, y, and z. We want to maximize the volume V = xyz subject to the constraint x + 3y + 4z = 9.

The Lagrangian function is then given by L = xyz + λ(x + 3y + 4z - 9).

Taking the partial derivatives of L with respect to x, y, z, and λ, and setting them equal to zero, we get:

yz + λ = 0

xz + 3λ = 0

x*y + 4λ = 0

x + 3y + 4z - 9 = 0

Solving these equations simultaneously, we get:

x = 1.5, y = 1, z = 2.25, and λ = -0.5625

Therefore, the maximum volume of the rectangular box is V = 1.512.25 = 3.375 cubic units.

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