I need help with number 6

Answer:

Number of students

5

8

Step-by-step explanation:

Edg 2020

Answer:

number of students,5,8

Step-by-step explanation:

Answer:

0.125

Step-by-step explanation:

It could be a lot of things, but if you mean the decimal form then it would be 0.125. Just divide 1 by 8.

When the price increases from $2 to $2.58 per six-pack, the average Berkeley resident is predicted to consume approximately 38.7597 six-packs per year.

To predict the new consumption of six-packs per year, we can use the concept of price elasticity of demand. Price elasticity measures the responsiveness of demand to changes in price. In this case, we need to determine the percentage change in price and use it to estimate the percentage change in quantity consumed.

The price increase is from $2 to $2.58, which is an increase of $0.58 or 29% (0.58/2 * 100) compared to the original price. Assuming that the demand for six-packs follows a linear relationship with price, we can estimate the change in quantity consumed by applying the same percentage change to the original consumption.

The original consumption is 50 six-packs per year. Applying a 29% increase, the predicted change in consumption is 14.5 six-packs (50 * 0.29). Subtracting this change from the original consumption, we get the estimated new consumption of approximately 35.5 six-packs per year (50 - 14.5).

Therefore, when the price increases to $2.58 per six-pack, the average Berkeley resident is predicted to consume approximately 38.7597 six-packs per year.

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Simplified answers, including any radicals.

1. The length of u x v

|u x v| = 8√(17)

2. Direction of u x v

u x v = (2/√(17))i + (8/√(17))j + (9/√(17))k
3. Length of v x u

|v x u| = 8√(17)

4. The direction of v x u

v x u = (2/√(17))i + (9/√(17))j - (8/√(17))k

5. u x v x v times u is equal to 0.

To find u x v, we can use the formula:
u x v = |i j k|
|9 -2 -8|
|8  0 -8|

Expanding the determinant, we get:
u x v = (16)i + (64)j + (72)k

To find the length of u x v, we can use the formula:
|u x v| = √((16)² + (64)² + (72)²) = 8√(17)

To find the direction of u x v, we can normalize the vector by dividing it by its length:
u x v = (2/√(17))i + (8/√(17))j + (9/√(17))k

Now, to find v x u, we can use the formula:
v x u = |i j k|
|8  0 -8|
|9 -2 -8|

Expanding the determinant, we get:
v x u = (16)i + (72)j - (64)k

To find the length of v x u, we can use the formula:
|v x u| = √((16)² + (72)² + (-64)²) = 8√(17)

To find the direction of v x u, we can normalize the vector by dividing it by its length:
v x u = (2/√(17))i + (9/√(17))j - (8/√(17))k

Now, we need to find u x v x v times u. First, we need to find u x v x v:
u x v x v = u x (v x v) = u x 0 = 0

Therefore, u x v x v times u is equal to 0.

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Brass is an alloy of copper and zinc with a density of approximately 8.5 g/cm³. In addition, brass is a malleable and ductile metal that can be bent, stretched, and compressed without breaking. The sphere's volume can be reduced using a minimum pressure of 12,750 Pa.
First, let us comprehend the formula used in this case: Percentage decrease in volume = (change in volume/original volume) x 100. Now, we will obtain the change in volume.
Change in volume = (percentage decrease in volume/100) x Original volume
Here, percentage decrease in volume = 0.00003 %

Original volume can be derived from the formula of the volume of a sphere, which is:
V = 4/3πr³
As a result, the following is the equation for the original volume:
V = 4/3 π (d/2)³ = πd³/6
Where d is the diameter of the brass sphere.
Now we can find the change in volume:
Change in volume = (0.00003/100) x πd³/6
The change in volume is calculated to be 0.00000157πd³.
According to the formula of pressure, pressure = force/area, we can find the force necessary to decrease the volume by the required percentage using the Young’s modulus of brass, which is approximately 91 GPa (gigapascals) or 91 × 10⁹ Pa (pascals).
So, we can write:
Force = Young's modulus x (Change in volume/Original volume) x (Original diameter)²/4
Thus, the force needed to decrease the volume of the sphere is as follows:
F = 91 × 10⁹ x (0.00000157πd³) / (πd³/6) x (d/2)²
F = 3.53 × 10⁷ d² N
Finally, we can find the minimum pressure required to reduce the volume by dividing the force by the surface area of the sphere.
Minimum pressure = F/ Surface area of the sphere
= F/(4πr²)
= 3.53 × 10⁷ d²/ (4π (d/2)²)
= 12,750 Pa approximately
Therefore, the sphere's volume can be reduced using a minimum pressure of 12,750 Pa.

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There is no error, Jacob did everything correctly

Answer:

71,474

Step-by-step explanation:

Took the test

Answer:

The answer is 71,474

Step-by-step explanation: First you must subtract 34,180 from 200,000

200,000 - 34,180 = 165,820.

After that, you divide the answer by N(2.32)

165,820 ÷ 2.32 = 71,474

The amount of money that Suzie will make over the four weeks is; $1856

Suzie will make a profit of:

The first week =  $300

The second week =  (300 * 30%) + 300 = $390

The third week = 390 * (1430%) = $507

The fourth week: 507 × (1430%) = $659.1

Thus, Sum of profit = $300 + $390 + $507 + $659.1

Sum of Profit = $1856.1 ≈ $1856

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Answer:

D. 50.

Step-by-step explanation:

50 trials . The greater the number of trials the closer will the experimental probability be to the theoretical.

The characteristics of the given linear functions are as follows:

Function f(x): Rate of Change = 103, Initial Value = Not provided, Behavior = Increases at a constant rate of 103 units per change in x.

Function V(t): Rate of Change = 25, Initial Value = Not provided, Behavior = Increases at a constant rate of 25 units per change in t.

Function r(a): Rate of Change = 4, Initial Value = Not provided, Behavior = Increases at a constant rate of 4 units per change in a.

Function C(w): Rate of Change = Not provided, Initial Value = -7, Behavior = Not provided.

A linear function can be represented by the equation f(x) = mx + b, where m is the rate of change (slope) and b is the initial value or y-intercept. Based on the given information, we can determine the characteristics of the provided functions.

For the function f(x), the rate of change is given as 103. This means that for every unit increase in x, the function f(x) increases by 103 units. The initial value is not provided, so we cannot determine the y-intercept or starting point of the function. The behavior of the function f(x) is that it increases at a constant rate of 103 units per change in x.

Similarly, for the function V(t), the rate of change is given as 25, indicating that for every unit increase in t, the function V(t) increases by 25 units. The initial value is not provided, so we cannot determine the starting point of the function. The behavior of V(t) is that it increases at a constant rate of 25 units per change in t.

For the function r(a), the rate of change is given as 4, indicating that for every unit increase in a, the function r(a) increases by 4 units. The initial value is not provided, so we cannot determine the starting point of the function. The behavior of r(a) is that it increases at a constant rate of 4 units per change in a.

As for the function C(w), the rate of change is not provided, so we cannot determine the slope or rate of change of the function. However, the initial value is given as -7, indicating that the function C(w) starts at -7. The behavior of C(w) is not specified, so we cannot determine how it changes with respect to w without additional information.

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Therefore, the general solution of the given second-order differential equation is: y = c1 e^(0t) + c2 e^(-1/2 t).

To find the general solution of the given second-order differential equation 2y'' + y' = 0, we can assume that the solution is of the form y = e^(rt), where r is a constant to be determined.

First, we find the first and second derivatives of y with respect to t:

y' = re^(rt)

y'' = r^2 e^(rt)

Substituting these expressions into the differential equation, we get:

2r^2 e^(rt) + r e^(rt) = 0

Factoring out e^(rt), we get:

e^(rt) (2r^2 + r) = 0

This equation will be satisfied if either e^(rt) = 0 or 2r^2 + r = 0.

Since e^(rt) is never zero, we must have:

2r^2 + r = 0

Factoring out r, we get:

r(2r + 1) = 0

So, either r = 0 or r = -1/2.

Therefore, the general solution of the given second-order differential equation is:

y = c1 e^(0t) + c2 e^(-1/2 t)

Simplifying this expression, we get:

y = c1 + c2 e^(-1/2 t)

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Answer:

Step-by-step explanatB Convection caused hot air to rise to the top of your house is the best explanation for why you may feel very hot when you go up to your attic on a summer day.

Convection is the transfer of heat by the movement of a fluid, such as air. On a hot summer day, the air inside your attic can become very hot, and because hot air rises, it will accumulate at the top of your house. When you go up to your attic, you will feel the heat from this accumulated hot air.

Conduction, on the other hand, is the transfer of heat through a material, such as the roof or walls of your house. While some heat may be conducted through the roof, it is unlikely to be the primary cause of the heat in your attic.

Insulation (option C) can help to keep the heat from the attic from escaping into the cooler temperatures below, but it is not the primary cause of the heat in the attic.

ion:

Answer:

its 30

Step-by-step explanation:

1) a) The symmetric equations for the line is (x - 4) / -1 = (y + 4) / 4 = (z - 8) / -3

b) XY-plane is (4/3, 20/3, 0), YZ-plane is (0, 12, -4) and XZ-plane is (3, 0, 5).

2) The equation of the plane is 16x + 4y + 8z - 42 = 0.

3) The equation of the plane is -2x - 9y - 5z = 0.

1) Symmetric Equations for the Line:

a) To find the symmetric equations for the line that passes through the point (4, -4, 8) and is parallel to the vector (-1, 4, -3), we can use the parametric form of the line and then convert it into symmetric form.

Parametric Equations:

x = 4 - t

y = -4 + 4t

z = 8 - 3t

To convert these parametric equations into symmetric form, we eliminate the parameter 't' by setting up equations involving the ratios of differences of coordinates:

(x - 4) / -1 = (y + 4) / 4 = (z - 8) / -3

This gives us the symmetric equations for the line.

(b) Points of Intersection with Coordinate Planes:

To find the points in which the line intersects the coordinate planes, we substitute the appropriate values of coordinates into the equations of the line.

i) Intersection with XY-plane (z = 0):

Substituting z = 0 into the parametric equations, we get:

x = 4 - t

y = -4 + 4t

z = 8 - 3t

Setting z = 0, we have:

8 - 3t = 0

t = 8/3

Substituting t = 8/3 into the equations for x and y:

x = 4 - (8/3) = 4/3

y = -4 + 4(8/3) = 20/3

Therefore, the point of intersection with the XY-plane is (4/3, 20/3, 0).

ii) Intersection with YZ-plane (x = 0):

Substituting x = 0 into the parametric equations, we get:

x = 4 - t

y = -4 + 4t

z = 8 - 3t

Setting x = 0, we have:

4 - t = 0

t = 4

Substituting t = 4 into the equations for y and z:

y = -4 + 4(4) = 12

z = 8 - 3(4) = -4

Therefore, the point of intersection with the YZ-plane is (0, 12, -4).

iii) Intersection with XZ-plane (y = 0):

Substituting y = 0 into the parametric equations, we get:

x = 4 - t

y = -4 + 4t

z = 8 - 3t

Setting y = 0, we have:

-4 + 4t = 0

t = 1

Substituting t = 1 into the equations for x and z:

x = 4 - 1 = 3

z = 8 - 3(1) = 5

Therefore, the point of intersection with the XZ-plane is (3, 0, 5).

2) Equation for the Plane:

To find an equation for the plane consisting of all points equidistant from the points (-6, 4, 1) and (2, 6, 5), we can use the distance formula to set up an equation.

Let P(x, y, z) be a point on the plane.

The distance from P to (-6, 4, 1) should be equal to the distance from P to (2, 6, 5).

Using the distance formula, we have:

√[(x - (-6))² + (y - 4)² + (z - 1)²] = √[(x - 2)² + (y - 6)² + (z - 5)²]

Simplifying the equation gives:

(x + 6)² + (y - 4)² + (z - 1)² = (x - 2)² + (y - 6)² + (z - 5)²

Expanding and simplifying further:

x² + 12x + 36 + y² - 8y + 16 + z² - 2z + 1 = x² - 4x + 4 + y² - 12y + 36 + z² - 10z + 25

Rearranging the terms:

16x + 4y + 8z - 42 = 0

Therefore, the equation of the plane is 16x + 4y + 8z - 42 = 0.

3) Equation of the Plane:

To find the equation of the plane that passes through the point (-2, 1, 1) and contains the line of intersection of the planes x + y - z = 3 and 4x - y + 5z = 5, we can use the following steps:

Step 1: Find the direction vector of the line of intersection of the given planes.

To find the direction vector, we take the cross product of the normal vectors of the two planes.

The normal vector of the first plane, P1: (1, 1, -1)

The normal vector of the second plane, P2: (4, -1, 5)

The direction vector, D: P1 x P2

D = (1, 1, -1) x (4, -1, 5)

Using the cross product formula, we have:

D = ((1)(-1) - (-1)(1), (-1)(4) - (1)(5), (1)(-1) - (1)(4))

D = (-2, -9, -5)

So, the direction vector of the line of intersection is (-2, -9, -5).

Step 2: Use the point-direction form of the plane equation.

The equation of the plane passing through a given point (x0, y0, z0) with a direction vector (a, b, c) is given by:

a(x - x0) + b(y - y0) + c(z - z0) = 0

Substituting the values from the given information:

Point on the plane: (-2, 1, 1)

Direction vector: (-2, -9, -5)

The equation becomes:

(-2)(x - (-2)) + (-9)(y - 1) + (-5)(z - 1) = 0

(-2)(x + 2) - 9(y - 1) - 5(z - 1) = 0

-2x - 4 - 9y + 9 - 5z + 5 = 0

-2x - 9y - 5z = 0

Therefore, the equation of the plane is -2x - 9y - 5z = 0.

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The height of the quarter is given by the polynomial -16t^2 + 250 feet and the height of the dime is given by the polynomial -16t^2 - 10t + 100 feet.

To compare the height of the quarter and dime at any time t, we need to find the difference between their heights.

Let's first find the height of the dime when the quarter is released, which is at t=0:

Height of the quarter at t=0: 16(0)^2 + 250 = 250 feet

Height of the dime at t=0: -16(0)^2 - 10(0) + 100 = 100 feet

So, the initial height difference between the quarter and dime is 250 - 100 = 150 feet.

Now, let's find the height difference between the quarter and dime at any time t:

Height of the quarter at time t: 16t^2 + 250

Height of the dime at time t: -16t^2 - 10t + 100

So, the height difference at time t is:

(16t^2 + 250) - (-16t^2 - 10t + 100) = 32t^2 + 10t + 150

Therefore, the height difference between the quarter and dime at any time t is given by the polynomial 32t^2 + 10t + 150.

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After 12 days, 4.2 grams of curium-243 remains will be left in a sample with 5.6 grams after 12 days.

Given that,

The half-life of curium-243 is 28.5 days.

We have to find how many grams of curium-243 will be left in a sample with 5.6 grams after 12 days.

We know that,

The formula is

A(t) = A₀(1/2\()^{t/h}\)

Here,

t= 12 days, half life,

h =28.5 days .

And the initial value, A(0)=5.6 grams

So we will get

A(t) = 5.6(1/2\()^{12/28.5}\)

A(t) = 5.6×0.747 = 4.2 grams

Therefore, After 12 days, 4.2 grams of curium-243 remains will be left in a sample with 5.6 grams after 12 days.

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The given equation, 16x² - y² + 16z² = 4, represents a quadric surface known as an elliptic paraboloid.

To determine the classification, we can examine the coefficients of the squared terms. In this case, the coefficients of x², y², and z² are positive, indicating that the surface is bowl-shaped. Additionally, the signs of the coefficients are the same for x² and z², indicating that the bowl opens upward along the x and z directions.

The negative coefficient of y², on the other hand, means that the surface opens downward along the y direction. This creates a cross-section in the shape of an elliptical parabola.

Considering these characteristics, the given equation represents an elliptic paraboloid.

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Answer:

3 minutes 6 gallons of water is gone so therefor it would take 6 complete minutes but 3 more minutes

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x+3y=-4

-x+y=4  /*2

2x+3y=-4

-2x+2y=8

5y=4

y=4/5

x=y-4=4/5-4= - 3.2

If the function f(x) = |x-5| + 2, then the value of f(3) is 4

The function

f(x) = |x-5| + 2

The function is defined as the mathematical statement that shows the relationship between the independent variable and the dependent variable. The function consist of different variables, numbers and mathematical operators

Here the function consist of the absolute value symbol.

|-a| = a

The absolute value of the positive and the negative number will be always positive.

The function is f(x) = |x-5| + 2

Then,

f(3) = |3-5| + 2

= |-2| + 2

= 2 + 2

= 4

Therefore, the value of f(3) is 4

I have answered the question in general, as the given question is incomplete

The complete question is:

If f(x)=|x−5| + 2, find the value of f(3).

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Julie borrowed $12,000 from her aunt and $9000 from her uncle

Note the formula for simple interest = principal x time x interest rate

This question would be solved using simultaneous equation.

Two equations can be derived from the question

a - b = 3000 equation 1

(0.022 x 3 x a) + (0.045 x 3 x b) = 2007

0.066a + 0.135b = 2007 equation 2

where

a = amount borrowed from aunt

b = amount borrowed from uncle

Multiply equation 1 by 0.066

0.066a - 0.066b = 198 equation 3

subtract equation 3 from 2

0.201b = 1809

divide both sides of the equation by 0.201

b = 9000

Substitute for b in equation 1

a - 9000 = 3000

a = 9000 + 3000

a = 12,000

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No, the matrix [0 0 0 0] does not have an inverse. the matrix [0 0 0 0] fails to satisfy the criteria of being square and having a non-zero determinant, it does not have an inverse.

To have an inverse, a matrix must be square (i.e., have the same number of rows and columns) and be non-singular, meaning its determinant is not equal to zero. In this case, the given matrix is a 1x4 matrix, which is not square.

Additionally, the determinant of the given matrix is zero since all its elements are zero. The determinant of a matrix must be non-zero for it to have an inverse.

Therefore, because the matrix [0 0 0 0] fails to satisfy the criteria of being square and having a non-zero determinant, it does not have an inverse.

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The equation of the degree 6 polynomial with a root at 3, a double root at 2, and a triple root at -1, and y-intercept at y = 5 is given as follows:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

The zeros of the function, along with their multiplicities, are given as follows:

Then the linear factors of the function are given as follows:

The function is then defined as:

y = a(x - 3)(x - 2)²(x + 1)³.

In which a is the leading coefficient.

When x = 0, y = 5, due to the y-intercept, hence the leading coefficient a is obtained as follows:

5 = -12a

a = -5/12

Hence the polynomial is:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

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Answer:

2.6

Step-by-step explanation:

used a calculator to find out the answer

-3.1 + 5.7 + 2.6

Answer:

2.6

Step-by-step explanation:

345.989554676 to 1 decimal place is 346.0

Decimals numbers are the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point.

Example of decimal numbers are as follows;

12.4, 18. 9455, 56.7999, 6.7789, 9.067 etc.

When you round to the one decimal place, or to the nearest tenth, the number in the hundredth point place will determine whether you round up or down.

If the hundredths digit or second decimal number is a number between 5 and 9, round up to the nearest whole number. If it's a number between 0 and 4, you would "round down" by keeping the tenths place the same.

Therefore,

345.989554676 to 1 decimal place is 346.0

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It take the auxiliary equipment to fill the order working alone x is 70/3

Formulate based on the conditions stated:

10 * x/(10+x) = 7

In a defined fraction, the denominator cannot be zero.

10+x is not equal 0

Equation from inequality:

10+x=0

Unknown terms should be moved to the left side of the equation:

x = -10

Equation to inequality conversion

x is not equal to 10

As the domain, append the inequality:x is not equal to 10

Divide the common denominator by both sides of the equation:

10x(10+x)/10+x = 7(10+x)

Cut the fractions in half:

10x = 7(10+x)

Use the law of multiplicative distribution

10x = 70 +7x

Unknown terms should be moved to the left side of the equation:

10x-7x=70

combining similar terms 3x =70

Subtract the coefficient of the variable from both sides of the equation:

x = 70/3

the intersection, then: 70/3

get the outcome:x = 70/3

It take the auxiliary equipment to fill the order working alone x is 70/3

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The number of songs and games Jenna bought is 9.5 and 2.5 respectively.

let

x + y = 12

1.99x + 3.99y = 18.88

From (1)

x = 12 - y

Substitute into (2)

1.99x + 3.99y = 18.88

1.99(12 - y) + 3.99y = 18.88

23.88 - 1.99y + 3.99y = 18.88

- 1.99y + 3.99y = 18.88 - 23.88

2y = -5

y = -5/2

y = 2.5

Substitute into (1)

x + y = 12

x + 2.5 = 12

x = 12 - 2.5

x = 9.5

Therefore, Jenna bought 9.5 songs and 2.5 games.

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Answer:

The answer is option B

Step-by-step explanation:

-7z - 2.5 + 3.5z + 4y - 1.5

- 3.5 z + 4y - 4 (B)

// in case you are wondering the reason i got -2.5 is + sign outside and the - sign inside = -2.5

// Basically I just combined the like terms and solved it

Answer:

(x+2)^2 - 6

Step-by-step explanation: