(3) The table shows some values of the linear
function f(n). Find the linear equation of f(n)
n f(n)
6-1
4 2
2 5

Answer:

2 hours and 30 mins

Step-by-step explanation:

is 12 cookies made = 30 mins

then times both sides by 5

then,60 cookies made= 150 mins or 2 hours and 30 mins.

Answer:

150 min = 2,5 hours

Step-by-step explanation:

12 cookies ....... 30 min

1 cookie ........ 30/12 = 2,5 min

60 cookies ...... 2,5 * 60 = 150 min

The roots of the equations are as follow :

a. x = 6 , roots are not extraneous.

b. x = 2 , no extraneous roots.

Roots of the equations are:

a) 4 x- 1 = 5 + 3x

⇒ 4x - 3x = 5 + 1

⇒ x = 6

x = 6 is not an extraneous roots.

b)  log₂ x + log₂ (x ²) = 3

⇒ log₂ x + 2log₂ (x ) = 3

⇒log₂ x ( 1 + 2 ) = 3

⇒ log₂ x ( 3) = 3

⇒ log₂ x = 3/3

⇒ log₂ x = 1

⇒ x = 2¹

⇒ x = 2

x = 2 is not an extraneous root.

Therefore, the equations a) 4 x- 1 = 5 + 3x  and b)  log₂ x + log₂ (x ²) = 3 have the roots x = 6 and x = 2 respectively and are not extraneous.

The above question is not complete , the complete question is:

solve the following equations and identify any extraneous roots where applicable:

a) 4 x- 1 = 5 + 3x

b) log₂ x + log₂ (x ²) = 3

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Answer:

To calculate the length of the metal band, you need to first calculate the circumference of each pipe. The circumference of a pipe is equal to the diameter of the pipe multiplied by π (3.14). Therefore, the circumference of each pipe is 10 cm x 3.14 = 31.4 cm. Since there are 16 pipes, the total circumference of all the pipes is 16 x 31.4 cm = 500.64 cm. The length of the metal band will be the same as the total circumference, so it will be 500.64 cm.

Answer: x=7[tex]\sqrt{3}[/tex] and y = 14

Step-by-step explanation:

Ram obtained 680 marks in his examination.

We have to use the concept of percent-to-decimal conversion to solve this problem.

Ram scored 85% of the total marks, which was 800 of the total. To find the number of marks he obtained, we have to multiply 800 by 85% (0.85).

85% is equivalent to 0.85 when expressed as a decimal. To find the number of marks Ram obtained, we have to multiply the total marks (800) by 0.85,

After multiplying 800 * 0.85 = 680 marks.

So the marks obtained by Ram in his examination are 680.

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The concept of instantaneous rate of change, also known as derivative, gives us the rate at which a quantity changes with respect to time at a specific instant. To find the instantaneous rate of change, we can take the derivative of the function that describes the position of the ball.

In this case, the position of the ball is given by the function f(x) = 2Vx, where V is the initial velocity of the ball. Taking the derivative of the function, we get the derivative as f'(x) = 2V, which represents the instantaneous rate of change of the ball's position with respect to time at any instant x.

When x = 9 seconds, the instantaneous rate of change of the ball's position is given by f'(9) = 2V. Therefore, the correct answer is d. 2/3V ft/sec.

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The volume of the solid that is enclosed by the cone is 1.74 cube/unit

What is Volume?

A measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected.

What is Dimension?

The minimal set of coordinates required to specify any point within a mathematical space is the dimension of that space. In light of the fact that only one coordinate is required to specify a line, it has a dimension of one.

Given,

cone z = px2 y2

sphere x2 y2 z2 = 2

r = [tex]\sqrt{2}[/tex]

z = [tex]\sqrt{x^{2} +y^{2} }[/tex]

[tex]z^{2} = x^{2} +y^{2}[/tex]

[tex]x^{2} +y^{2} -z^{2}=0[/tex]

using spherical cordinate system

[tex]x^{2} +y^{2} +^{2} =r^{2} \\tan θ =\frac{y}{x} \\cos θ = \frac{z}{\sqrt{x^{2} +y^{2} } }[/tex]

volume of shaded region between cone and sphere

v = [tex]\frac{3^{\sqrt{2^{2} } } }{3} (\frac{-1}{\sqrt{2}+1 } 2(x)[/tex]

v= 1.74 cube units

consecutive cone and sphere

[tex]x^{2} +y^{2}+x^{2} y^{2} =2\\x^{2} +y^{2} =1 at\\from cone equation\\z^{2} =x^{2} +y^{2} \\z=1\\so θ = 45 degree \\=\frac{x}{y}[/tex]

The solid that the cone encloses has a volume of 1.74 cubes per unit.

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From the advertisement, Company B's plan is $7.50 lower per month than Company A's plan.

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Answer: 7

Step-by-step explanation:

When solving the equation remember to follow pemdas (parentheses, multiplication, division, addition and finally subtraction.)

1. Distribute the two. Two times 1 is two and two times two is 4.

6÷2+4

2. 6 divided by 2 is 3.

3+4

3. 3 plus 4 equals 7.

:)

We traveled to our grandparents for vacation. We drove 234.7 miles before lunch. We got back in the car and drove 37.93 miles before

The equation of the line passing through the points (1,-5) and (3, -17) is y = -6x + 1.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,

Points are  (1,-5) and (3, -17)

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

m = -17 + 5 / 3 - 1

m  = -6

The equation of the line is given as

y - y₁ = m (x - x₁)

y + 5 = -6 (x -1)
y = -6x + 1

Thus, the equation of the line passing through the points (1,-5) and (3, -17) is y = -6x + 1.

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The region that minimizes the value of ∫∫R(x² + y² - 9)dA is the unit circle centered at (0, 0) with radius 3.

To see why this is the case, consider that x² + y² is the equation of a circle with center at the origin. The value of the integrand, x² + y² - 9, is minimized when x² + y² = 9, which is a circle with radius 3 centered at the origin.

The double integral ∫∫R(x² + y² - 9)dA represents the total area under the graph of x² + y² - 9 over the region R. The minimum value of this integral would be achieved when the region R is the smallest possible region that covers the minimum value of the integrand.

In this case, the smallest region that covers the minimum value of the integrand is the unit circle centered at (0, 0) with radius 3.

Therefore, the region that minimizes the value of ∫∫R(x² + y² - 9)dA is the unit circle centered at (0, 0) with radius 3.

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Using ratios, There are total 4 green marbles.

If b is not equal to 0, an ordered pair of numbers, a and b, expressed as a / b, is a ratio. A proportion is an equation that balances two ratios. As an illustration, the ratio could be expressed as follows: The ratio is 1:3 if there is 1 boy and 3 girls. (There are three girls for every one boy) Only one in four men are male, with three out of four being female.

In mathematics, a ratio shows how frequently one number appears in another. For instance, the ratio of oranges to lemons on a fruit platter would be eight to six if there were eight oranges and six lemons.

Given,

The ratio of blue to orange to green is 4:2:1 ,

bag contains 8 blue marbles,

green marbles = 2x = 8

x = 4

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Answer:

Step-by-step explanation:

8+2*3-5*2+(82+4+4):(12+6+12)+3=
Firstly, we should use the BODMAS rule.
B: Brackets
O: Off
D: Division
M:Multiplication
A:Additioin
S:Subtraction
by this format we should start our problem.
Now, we solve the brackets
=8+2*3-5*2+(90):(28)+3
Now, we solve the multiplication
=8+6-7+(90):(28)+3

Now, we solve the addition part
=108-7:31
Now, the subtraction
=101:31 is the answer

Answer:

i) x ≈ -0.2 or x ≈ 1.2

ii) x ≈ -0.5 or x ≈ 1.5

Step-by-step explanation:

y = 4x^2-4x-1

that means 4x^2-2-4x-1 can be also considered as y

so 4x^2-2-4x-1 = 0 can be considered as y = 0

same goes to 4x^2-2-4x-1 = 2  which is considered as y = 2

since y = 0 and y = 2

we draw a horizontal like at y = 0 and y = 2

then you can determine which points the blue drawn parabola touches the horizontal line drawn

the co-ordinates would be written in (x,y)

i) (-0.2,0) and (1.2,0)

ii) (-0.5,2) and (1.5,2)

Answer:

(4,0) and (6,0)

Step-by-step explanation:

X intercepts lie on the x-axis, and has a y value of 0. Remember it as a coordinate intercepts x on the x axis. The 2 points with a y value of 0 is (4,0) and (6,0).

The sine function graphed is defined as follows:

y = sin(2x) + 2.

The sine function for this problem is defined as follows:

y = Asin(Bx) + C.

For which the parameters are given as follows:

The difference between the highest and the lowest value of the function is of 3 - 1 = 2, hence the amplitude is obtained as follows:

2A = 3 - 1

2A = 2.

2A = 1.

The period is of π, hence the coefficient B is given as follows:

2π/B = π

B = 2.

A function with amplitude 1, with no vertical shift, would oscillate between -1 and 1, while this function oscillates between 1 and 3, hence the vertical shift C is given as follows:

C = 2.

Hence the function is defined as follows:

y = sin(2x) + 2.

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Answer:

1. Answer is A 43 degrees

2. Answer is c 65 degrees

Step-by-step explanation: Hope this helps! :))

The number of the solutions for each system of equation is;

a) Two solutions

b) Two solutions

c) Two solutions

d) Two solutions

An equation is a mathematical statement that asserts the equality of two expressions, usually represented by a symbol such as "=". The expressions on either side of the equation can include numbers, variables, and operations, and the goal is to find the values of the variables that make the equation true.

The number of the solutions that the equation would have would depend on the type of equation that we have to deal with in the problem that have been give.

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The least square regression line equation is y = a + bx, where y is the response variable (sepal width), x is the independent or predictor variable (sepal length), a is the intercept, and b is the slope of the line.

The equation for the least square regression line is y = a + bx, where y is the dependent or response variable, x is the independent or predictor variable, a is the intercept, and b is the slope of the line. To calculate the equation for the least square regression line when the independent or predictor variable is sepal length and the dependent or response variable is sepal width for iris versicolor, the following steps should be taken: First, calculate the mean of the sepal lengths and the sepal widths. Then, calculate the variance of the sepal lengths, and the variance of the sepal widths. Next, calculate the covariance of the sepal length and sepal width. Finally, calculate the slope (b) of the regression line using the formula b = covariance/(variance of x). Once the slope is calculated, substitute it into the regression line equation to calculate the intercept (a). Using the mean of the sepal lengths and the slope and intercept, the equation for the least square regression line for the given data set can be calculated.

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The initial value problem for the concentration of salt in the tank over time will be: dc/dt = [(1 g/L * 2 L/min) - (c * 2 L/min)] / 2000 L

An initial value problem (IVP) in multivariable calculus is an ordinary differential equation with an initial condition that determines the value of the unknown function at a specific location in the domain. In physics or other sciences, modelling a system typically entails addressing an initial value issue.

Let's call the concentration of salt in the tank "c" (in grams/liter).

The initial concentration of salt in the tank is: c(0) = 400 / 2000 = 0.2 g/L

The rate of change of concentration with time "t" (in minutes) can be represented as:

dc/dt = (inflow rate of saltwater - outflow rate of saltwater) / volume of tank

dc/dt = [(1 g/L * 2 L/min) - (c * 2 L/min)] / 2000 L

This is the initial value problem for the concentration of salt in the tank over time.

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If the sum of $5000 is invested at rate of 5% per annum simple interest for 2 years then the amount of interest is $500  .

The amount of interest earned for a sum invested at a rate of 5% per annum simple interest for 2 years can be calculated using the formula:

Interest  = (P × R × T)/100 ;

Where:  I = interest  ,  P = principal (initial sum invested) = $5000

r = interest rate = 5%  ;  t = time = 2 years

Substituting the values into the interest  formula, we get:

Interest  = (5000 × 5 × 2)/100

On simplifying , we get Interest is = $500 .

Therefore, the amount of interest earned is $500.

The given question is incomplete , the complete question is

Find the amount of interest earned for time = 2 years , when the sum of $5000 is invested at rate of 5% per annum simple interest ?

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Answer:

Answer below

Step-by-step explanation:

length of the arc of the circle formed by this central angle is 12.56 units.

The formula for calculating arc length is used to determine the length of the arc's curved line (a segment of a circle). The arc length is, to put it simply, the distance that passes across the curved line of the circle that forms the arc. Arc stability, weld current, and part concentricity are all factors that affect arc length. Arc stability, weld current, and part concentricity are all factors that affect arc length. The commercial welder's job in this situation is to maintain the electrode at a specific distance from the surface so that there is adequate room to prevent stubbing out.

Since, the length of an arc on a circle is:

l = r × θ

Where, r is the radius of the circle and  is the central angle ( in radian ) made by the arc,

Here,

r = 8 unit,

θ = 90° = 90 × (π/180) = π/2

( π radian = 180°)

Hence, the length of the given arc is,

l = 8 × (π/2)

l = 4π

l = 12.56 units

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The set of ordered pairs of A and C represents a linear function.

The graph of a linear function is a straight line. The following is the form of a linear function.

a + bx = y = f(x).

One independent variable and one dependent variable make up a linear function. x and y are the independent and dependent variables, respectively.

Given ordered pairs:

A (-2,8) (0,4) (2,3) (4,2)

B (1,2) (1,3) (1,4) (1,5)

C (-2,7) (0,12) (2,17) (4,22)

D (3,5) (4,7) (3,9) (5,11)​

The definition of a linear function is the relationship between input and output values.

Range refers to the set of output values, and domain refers to the set of input values.

The fact that an input value cannot have two different output values is the most significant attribute of functions (which defines them). Having stated so, observe how sets B and D include pairings that defy this rule.

Therefore, since each input value only produces one output value, the correct solutions are A and C.

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The complete question:

Which set of ordered pairs X Y could represent a linear function of x

A (-2,8) (0,4) (2,3) (4,2)

B (1,2) (1,3) (1,4) (1,5)

C (-2,7) (0,12) (2,17) (4,22)

D (3,5) (4,7) (3,9) (5,11)​

The percent markup is 66.67%.

The markup is the difference between the cost price and the selling price of a product, expressed as a percentage of the cost price.

Let's call the cost price of each shirt "cp". Then, the total cost price of 200 shirts would be 200 * cp.

The selling price of each shirt is $20, so the total revenue from selling 200 shirts would be 200 * $20 = $4000.

From the information given, we know that the total cost price of 200 shirts is $2400.

Therefore, we can set up the following equation to find the cost price of each shirt:

200 * cp = $2400

Dividing both sides by 200, we get:

cp = $12

The markup is the percentage increase from the cost price to the selling price, so it can be calculated as follows:

Markup = (Selling Price - Cost Price) / Cost Price * 100%

= ($20 - $12) / $12 * 100%

= 66.67%

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The correct answer is d. 1/x².

The integrating factor for the given equation is 1/x².

To solve a linear differential equation, we must first find an integrating factor so that the equation can be integrated. The integrating factor for the given equation is 1/x². To calculate it, we must multiply both sides of the equation by the integrating factor.

Let's start by rearranging the equation: y' - y/x = x

We multiply both sides of the equation by the integrating factor, 1/x²:

(1/x²) (y' - y/x) = (1/x²) x

We can simplify the left side of the equation by factoring out the y': y'/x² + (y/x³) = (1/x²) x

We can then solve for the integrating factor: 1/x² + (y/x³) = x/x²

We can then solve for the integrating factor: 1/x². Therefore, the integrating factor for the given equation is 1/x².

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