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Answer:

The equation of the line with a slope of 3 that passes through (-4,-7) is;

Explanation:

We want find the equation of the line with;

Using the point slope form of linear equation;

substituting the given values into the equation above we have;

Above is a point slope form of the equation.

solving further we have;

The equation of the line with a slope of 3 that passes through (-4,-7) is;

The inverse demand function is P = 20 – QD, and the inverse supply function is P = QS + 40. The equilibrium price is 30, and the equilibrium quantity is -10. The graph illustrates these relationships.


a. To find the inverse demand and inverse supply functions, we need to solve the given demand and supply equations for the price (P).
Demand equation: QD = 20 – P
Inverse demand: P = 20 – QD
Supply equation: QS = -40 + P
Inverse supply: P = QS + 40

b. To determine the equilibrium price and quantity, we need to set the demand and supply equations equal to each other and solve for the price (P).
20 – QD = QS + 40
Since both QD and QS represent the same quantity, we can substitute QD with QS:
20 – QS = QS + 40
Rearranging the equation:
2QS = -20
Dividing by 2:
QS = -10
Substituting the value of QS back into either the demand or supply equation to find the equilibrium price:
P = QS + 40
P = -10 + 40
P = 30
So the equilibrium price is 30, and the equilibrium quantity is -10.

c. Let’s graph the demand and supply curves to illustrate this. We’ll use the price (P) on the vertical axis and the quantity (Q) on the horizontal axis.
Demand curve:
- Set P = 0 in the inverse demand equation to find the x-intercept:
0 = 20 – QD
QD = 20
- Set QD = 0 to find the y-intercept:
P = 20 – QD
P = 20 – 0
P = 20
Plot the points (0, 20) and (20, 0) on the graph and draw a straight line connecting them.
Supply curve:
- Set P = 0 in the inverse supply equation to find the x-intercept:
0 = QS + 40
QS = -40
- Set QS = 0 to find the y-intercept:
P = QS + 40
P = -40 + 40
P = 0
Plot the points (0, 0) and (-40, 0) on the graph and draw a straight line connecting them.
Finally, mark the equilibrium point where the demand and supply curves intersect. In this case, it’s (Q = -10, P = 30).
The graph should show the demand curve sloping downwards from the top left to the bottom right, the supply curve sloping upwards from the bottom left to the top right, and the equilibrium point (Q = -10, P = 30) where the curves intersect.

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Step-by-step explanation:

The cube is 2 x 2 x 2  inches

 so the cone has a height of 2 inches and a radius of 1 inch

volume of cone = 1/3 pi r^2 h

                           = 1/3 pi (1^2)(2) = 2/3 pi in^3   or  = 2.09 in^3

Answer: C. Is true 7/8>-0.78

using the euclidean model,  the sum of distances between qrs and its four vendors is g.14

What do you mean by the euclidean model?

A mathematical system known as Euclidean geometry is credited to the ancient Greek mathematician Euclid. It is detailed in his geometry textbook, the Elements. In Euclid's method, many more propositions (theorems) are derived from a small collection of axioms (postulates) that are intuitively attractive.

The distance of (0,0) is 0 ,similarly, distance from (2,0) is 2; (1,2) is 1 and (0,5) is 5 and (6,0) is 6.

the sum of all distances are (0+2+1+5+6) is 14.

Hence according to the euclidean model , the sum of all distances is 14.

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By using the concept of function, it can be concluded that (-2, -1) needs to be removed to make the given relation a function

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here, from the figure, it can be seen that -2 has  two images,

2 and -1

So from the options given, the point (-2, -1) needs to be removed to make the given relation a function

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Complete Question

Input Output Which ordered pair needs to be removed in order for the mapping to represent a function? O (-3, -4) O (-2, -1) O (1, -3) O (3,7)​

The length of the segment with the variable x is as follows:

EF = 9 units.

A trapezium is a quadrilateral. The midsegment of a trapezoid is a line that goes across from the middle of one leg to the middle of the other leg.

Therefore, the side EF is the mid segment of the trapezium.

Hence, let's find the variable x as follows:

Therefore,

EF = x - 5 + 2x - 4 / 2

combine like terms

EF = x + 2x - 5 -4 / 2

EF = 3x - 9 / 2

x = 3x - 9 / 2

cross multiply

2x = 3x - 9

2x - 3x = -9

-x = -9

x = 9

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The solution to the system of simultaneous equations is x = 34/7, y = -13/7, z = -9/7.

To solve the system of simultaneous equations:

i. x + 2y + 3z = -5

ii. 3x + y - 3z = 4

iii. -3x + 4y + 7z = -7

We can use the matrix method or the augmented matrix to solve the equations. Let's use the augmented matrix method:

1 2 3 | -5

3 1 -3 | 4

-3 4 7 | -7

We'll perform row operations to transform the matrix into row-echelon form:

R2 = R2 - 3R1

R3 = R3 + 3R1

1 2 3 | -5

0 -5 -12 | 19

0 10 16 | 4

R2 = -R2/5

R3 = R3 + 2R2

1 2 3 | -5

0 1 12/5 | -19/5

0 0 56/5 | -36/5

R3 = (5/56)R3

1 2 3 | -5

0 1 12/5 | -19/5

0 0 1 | -9/7

R2 = R2 - (12/5)R3

R1 = R1 - 3R3

1 2 0 | 8/7

0 1 0 | -13/7

0 0 1 | -9/7

R1 = R1 - 2R2

1 0 0 | 34/7

0 1 0 | -13/7

0 0 1 | -9/7

The row-echelon form of the augmented matrix is obtained. Now, we can read off the solution to the system of equations:

x = 34/7

y = -13/7

z = -9/7

Therefore, the solution to the system of simultaneous equations is x = 34/7, y = -13/7, z = -9/7.

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If u is a combination of v1, v2, v3, it implies that u can be expressed as a linear combination of those vectors. By setting the coefficient of v4 to 0, we can still represent u in the same form while including v4, thereby confirming that u is also a combination of v1, v2, v3, v4.

If u is a combination of v1, v2, v3, it means that we can express u as a linear combination of v1, v2, v3. In other words, we can find coefficients (scalars) such that:

u = c1 * v1 + c2 * v2 + c3 * v3,

where c1, c2, and c3 are scalars.

Now, let's consider the set of vectors v1, v2, v3, v4. We know that u is a combination of v1, v2, v3. So, we can express u as:

u = c1 * v1 + c2 * v2 + c3 * v3.

To show that u is also a combination of v1, v2, v3, v4, we need to demonstrate that we can express u using the same coefficients but also include v4 in the linear combination. In other words, we need to find a scalar c4 such that:

u = c1 * v1 + c2 * v2 + c3 * v3 + c4 * v4.

To do this, we can simply set c4 to 0, because multiplying v4 by 0 does not affect the sum. Therefore, we can express u as a combination of v1, v2, v3, v4 by setting c4 = 0:

u = c1 * v1 + c2 * v2 + c3 * v3 + 0 * v4.

By including v4 with a coefficient of 0, we have not changed the expression of u as a linear combination of v1, v2, v3. Thus, u is indeed a combination of v1, v2, v3, v4.

In summary, if u is a combination of v1, v2, v3, it implies that u can be expressed as a linear combination of those vectors. By setting the coefficient of v4 to 0, we can still represent u in the same form while including v4, thereby confirming that u is also a combination of v1, v2, v3, v4.

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If Joe wants to work for less than 4.54 years, he should choose the first position. If he wants to work more than 4.54 years, he needs to choose the second job.

We must figure out the value of f(x) for the number of years that Joe is considering working in order to evaluate which employment would be more lucrative after a few years. Let's say Joe is thinking about taking on x years of employment. Since he would be paid $500 per week for 52 weeks in a year for the first x years, his pay from the first job would be 500 × 52 × x = 26000x dollars.

On the other side, after x years, his compensation from the second job would be $20,800.

Compare 26000x against 20800 to find which of these two figures is greater.

By making the two expressions equal to one another and finding x, we can do this:

26000x = 20800\((1.03)^{x}\)

(26000/20800)) = \(1.03^{1/x}\)

x = log(1.03)/log(26000/20800)

This equation's solution has an x value of roughly 4.54 years. This indicates that the two jobs would pay the same amount after 4.54 years, on average.

The answer to this equation has an x value of around 4.54 years. This suggests that, on average, the two jobs would pay the same amount after 4.54 years.

If he intended to work for exactly 4.54 years, any job would be a perfect fit.

It's important to highlight that this study bases its conclusions on the supposition that the annual 2% raise for the first job is a given. The second job should be accepted if there is a chance that the raise won't be offered or that it will be less than 2%.

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Answer:

44.68 square cm

Step-by-step explanation:

To find the area of the whole circle you use the formula pie x r^2

then multiply that area by 40/360 because that is the area of the sector

Answer:

I think 32

I'm not sure

Answer:

=£75

Step-by-step explanation:

ratio=5(lottie):1(Ollie)

we do 15/1 which will stay the same as 15

15/1=15

Then we times 15 by 5( lotties share)=75

15*5=75

Therefore lottie got £75

=£75

Answer:

75 : 15

Step-by-step explanation:

The best approximation of vector u = (3,-7,2,3) as a linear combination of v₁=(2,-1,-3,1) and v₂=(1,1,0,-1) is -17/7 v₁ + 19/14 v₂.

To find the best approximation to u as a linear combination of v₁ and v₂, we need to find the coefficients x and y that minimize the distance between u and the linear combination x v₁ + y v₂. This distance is given by

d = ||u - (x v₁ + y v₂)||

where ||.|| denotes the Euclidean norm. Expanding this out gives

d^2 = ||u||^2 - 2x(u.v₁) - 2y(u.v₂) + x^2 ||v₁||^2 + y^2 ||v₂||^2 + 2xy (v₁.v₂)

where u.v₁ denotes the dot product of u and v1, and similarly for the other dot products.

To minimize d^2, we take the partial derivatives with respect to x and y and set them equal to zero

d^2/dx = -2(u.v₁) + 2x ||v₁||^2 + 2y (v₁.v₂) = 0

d^2/dy = -2(u.v₂) + 2y ||v₂||^2 + 2x (v₁.v₂) = 0

Solving these equations for x and y, we get

x = (u.v₁)(||v₂||^2) - (u.v₂)(v₁.v₂) / (||v₁||^2)(||v₂||^2) - (v₁.v₂)^2

y = (u.v₂)(||v₁||^2) - (u.v₁)(v₁.v₂) / (||v₁||^2)(||v₂||^2) - (v₁.v₂)^2

Plugging in the given values, we get

x = (32 + (-7)1 + 2(-3) + 31)(1^2) - (31 + (-7)1 + 20 + 3(-1))(21) / (2^21^2) - (1*1)^2

= -17/7

y = (31 + (-7)1 + 20 + 3(-1))(2^2) - (32 + (-7)1 + 2(-3) + 31)(12) / (1^22^2) - (1*2)^2

= 19/14

Therefore, the best approximation to u as a linear combination of v₁ and v₂ is

-17/7 v₁ + 19/14 v₂

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Answer:

To find the value of a5, we need to know the formula for the nth term of the sequence. We know that a1 = 2, so we can start by finding the common difference (d) between consecutive terms. an-1 + 5 = a1 + (n-2)d + 5 Simplifying this equation, we get: an-1 = a1 + (n-2)d Substituting a1 = 2, we get: an-1 = 2 + (n-2)d We also know that a5 is the 5th term of the sequence, so n = 5. Substituting n = 5, we get: a4 = 2 + (5-2)d a4 = 2 + 3d We don't have enough information

Answer:

-1/1

Step-by-step explanation:

go down 2

go right 2

-2/2

simplify

-1/1

a. The table value of z 0.99 is given as 2.58.

b. we use σ = 2.30 minutes.

c. The value of Z is given as 0.609.

d. The confidence interval is (23.391, 24.609) minutes.

a) To find the z-score for a 0.99 confidence interval, we need to find the z-score that leaves 0.5% (since it's two-tailed, we split the 1% or 0.01 of the data that's not within the confidence interval into two) in each tail. The z-score for 0.995 (0.5% in the upper tail) is approximately 2.58 in standard normal distribution tables. So, Z_0.99 is 2.58.

b) Therefore, we use σ = 2.30 minutes.

c) The standard error of the mean (SE) is given by σ/√n, where n is the sample size.

Here, σ = 2.30 minutes and n = 95.

Therefore, SE = σ/√n

= 2.30/√95

= 0.236 minutes.

Multiply this by the z-score to find Z * σ/√n.

Therefore, Z * σ/√n = 2.58 * 0.236 ≈ 0.609.

d) The 0.99 confidence interval for μ

Here, x is the sample mean which is 24 minutes.

So the confidence interval is approximately

= (24 - 0.609, 24 + 0.609)  

= (23.391, 24.609) minutes.

This is the range of values we are 99% confident that the true population mean (μ) falls in.

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The scatterplot of  the given data points are attached herewith.

A scatter plot uses dots to speak to values for two different numeric factors. The position of each dot on the level and vertical axis shows values for an individual information point. Scatter plots are utilized to watch connections between variables, Scatter plots’ essential uses are to observe and show connections between two numeric variables. The dots in a scatter plot do not as it were report the values of personal information points, but moreover designs when the information is taken as a whole.

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Answer:

It would be 10.

Step-by-step explanation:

10+8=18, so if 8 students signed up you would need 10 more.

hope this helps <33

Answer:the answer is 2

Step-by-step explanation:I did the quiz

The unknown number, n in the equation is 63.

Five less than the quotient of a number and 3 is 16. Therefore, let's find the number.

Quotient is the number we obtain when we divide one number by another.

Therefore, let's find the number.

let

n = number

n / 3 - 5 = 16

add 5 to both sides of the equation.

n / 3 - 5 = 16

n / 3 - 5 + 5 = 16 + 5

n / 3 = 21

cross multiply

n  = 21 × 3

n = 63

Therefore,

n = 63

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The relation is a function if every ordered pair has one value of x, which means x does not repeat

Let us study each relation

a) {(5, 1), (-2, 4), (1, 1), (5, 2)}

Since each ordered pair has a different value of x

There are 2 ordered pairs that have x = 5

This relation is not a function

b) {(1, 4), (-2, 2), (5, 1), (-6, 2)}

Since no repeated x in the ordered pairs

Then the relation is a function

c) There are 2 ordered pairs with x = -2

It is not a function

d) There are 2 ordered pairs with x = 1

It is not a function

The answer is b

We will investigate how to determine the y-intercept of an equation of a line.

A general equation of a line is given in a slope-intercept form as follows:

Where,

The slope of the line is already determined and expressed as follows:

To determine the y-intercept of an equation of a line we need a coordinate pair. We are given a table of values through which the line passes. We can use any of the coordinate pair. We will pick the first pair:

We will plug in the respective coordinate values in the given equation and solve for y-intercept ( c ) as follows:

Therefore, the value of the y-intercept when plugged in the general equation we have:

If I were required to survey Fresno City College students regarding their employment status, I would use a stratified random sampling technique.

Stratified random sampling involves dividing the population into subgroups, or strata, based on certain characteristics that are relevant to the survey. In this case, the relevant characteristic is employment status. The population consists of all Fresno City College students, and the two strata are employed and unemployed students.

Once the population has been divided into strata, a random sample is taken from each stratum. The sample size for each stratum is proportional to the size of the stratum in the population. For example, if 60% of Fresno City College students are employed, then 60% of the sample should consist of employed students.

Using a stratified random sampling technique ensures that the sample is representative of the population and that each subgroup is represented in the sample. It also reduces sampling error and increases the precision of the estimates.

Answer:

Step-by-step explanation:

You want to know the price per bushel for wheat, corn, and rye, given the sales ...

Using x, y, and z for price per bushel of wheat, corn, and rye, respectively, the given sales tell us ...

The easiest way to solve a system of equations like this is to make use of the matrix manipulation capabilities of a calculator. The attached calculator display shows the reduction of the augmented matrix of coefficients to "reduced row-echelon form". That puts the solution in the last column:

  x = y = 3.61, z = 1.91

The price per bushel for wheat and corn is the same: $3.61; the price per bushel for rye is $1.91.

__

Additional comment

The second attachment shows a solution using a graphing calculator. In this solution, an expression for z based on the first equation is used in the remaining two equations, which then tell us the values of x and y.

If you add all of the equations, you get 10x +10y +10z = 91.30, which gives you ...

  x + y + z = 9.13

This can be solved for any variable you may want to substitute into any pair of the equations. This approach avoids any messy fractions.

<95141404393>

a. the marginal profit at x = 500 is $28.3.

b. the marginal profit at x = 1000 is $62.3.

c. the marginal profit at x = 6000 is $358.3.

d. the marginal profit at x = 12,000 is $718.3.

The profit in dollars from the sale of x expensive watches is P(x)=0.03x2−2x+7x0.3−5400. Let's find the marginal profit in each of the given values of x, namely, 500, 1000, 6000, and 12,000.  

Marginal Profit:

The marginal profit is the extra profit earned by selling one additional product. The marginal profit is found by taking the derivative of the profit function with respect to x and then substituting the given values of x. Then, we will evaluate the derivatives and substitute the given values of x.

(a) x = 500

To calculate the marginal profit at x = 500, we need to find the derivative of P(x).

P'(x) = 0.06x - 2 + 7/3 P'(500)

= 0.06(500) - 2 + 7/3

= 28.3

Therefore, the marginal profit at x = 500 is $28.3.

(b) x = 1000P'(x)

= 0.06x - 2 + 7/3P'(1000)

= 0.06(1000) - 2 + 7/3

= 62.3

Therefore, the marginal profit at x = 1000 is $62.3.

(c) x = 6000P'(x)

= 0.06x - 2 + 7/3P'(6000)

= 0.06(6000) - 2 + 7/3

= 358.3

Therefore, the marginal profit at x = 6000 is $358.3.

(d) x = 12,000P'(x)

= 0.06x - 2 + 7/3P'(12000)

= 0.06(12000) - 2 + 7/3

= 718.3

Therefore, the marginal profit at x = 12,000 is $718.3.

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The value for x is 7π/6 and 11π/6.

sin2xsecx+2cosx=0

(2sinxcosx)(1/cosx)+2cosx=0

sinxcosx/cosx+2cosx=0

So,

2sinx+2cosx=0

2(sinx+cosx)=0

(2(sinx+cosx))²=0

4(sin²x+cos²x+2sinxcosx)=0

hence,

(sin²x+cos²x+2sinxcosx)/4=0/4

sin2x+cos2x+2sinxcosx=0

1+sin2x=0

sinx=−1/2

=7π/6 and 11π/6

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Answer:

- 2

Step-by-step explanation:

Using the rules of exponents

\(a^{m}\) ⇔ \(\frac{1}{a^{m} }\)

0.25 = \(\frac{1}{4}\) = \(\frac{1}{2^{2} }\) = \(2^{-2}\)

Answer:

  about 6995

Step-by-step explanation:

The second catch indicates about 15/251 of the fish were tagged. Then the population can be estimated to be 251/15 times the number that were tagged:

  (251/15)(418) ≈ 6995

The population can be estimated to be about 6995 trout.

Answer:

The other angle is also 45°

Step-by-step explanation:

They are corresponding angles.

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