A local council is concerned that there are too many students for staff to look after in schools. There are 18 staff and 225 students in school A. a Write the staff : student ratio in the form 1 : n.

The system of equation can be used to find the root of the equation is y= x³-4x² +2x and y=0 , y=4x² and y= x³+2x

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

y=-4x²

y= x³+2x

By equating the above equation we have

-4x²=x³+2x

Now, y= x³-4x² +2x

and y=0

By equating the above equation we have

x³-4x² +2x=0

y=4x²

y= -x³-2x

By equating the above equation we have

4x²=-x³-2x

Lastly,

y=4x²

y= x³+2x

By equating the above equation we have

4x²=x³+2x

Hence, the equation can be used is y= x³-4x² +2x and y=0 ,

y=4x² and y= x³+2x

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The man's journey took 43 minutes.

The distance traveled divided by the motion's duration gives the average speed, or vavg. Time is calculated as distance divided by average speed. Time is calculated as distance divided by average speed. distance = v avg 150 kilometers in time 3.2 h = 47 km/h.

Take the start time and subtract the end time.

The man was supposed to arrive at 12:25, but he was 15 minutes late, thus his actual arrival time was 12:40 (12:25 plus 15).

The man's journey began at 11:57, therefore we can calculate how long it took by deducting the start time from the end time.

End time - Start time = Journey time

12:40 - 11:57 = 43 minutes

So, The man's journey took 43 minutes.

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Answer:

-5 or 5

Step-by-step explanation:

the absolute value of -5 is 5. The absolute value of 5 is also 5.

Hope this helps :)

Answer:9342

Step-by-step explanation:

I am smart UwU

Answer:

2

Step-by-step explanation:

Answer:

2) y ≥ 2x - 3

Step-by-step explanation:

3 and 4 would be eliminated because the line does not intersect at (0, 2), but rather (0, -3).

Answer:

Step-by-step explanation:

l = (wh)/a(w+p)

wh = la(w+p)

w = (la(w+p))/h

61mm has to be converted to cm.

Simply divide by 10 [ 10mm = 1cm ]

61 mm = (61/10) = 6.1 cm

5.5 + 6.1 = 11.6cm

OR...

Convert 5.5cm to mm by multiplying by 10

5.5cm = (5.5×10) = 55mm

55+61 = 116mm

116mm = (116/10) = 11.6cm

The answer for this question is 11.6 cm or 116 mm.

You need to convert either millimeter to centimeter or vice versa

1 cm = 10 mm

converting 5.5 cm to mm :

5.5 X 10 = 55 mm

Now, add both the values of millimeter:

55 + 61 = 116 mm

If we need answer in centimeter

we can convert 116 mm into cm

116/10 = 11.6 cm

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The correct question is :

Add 5.5 cm to 61mm

Answer:

1.87 tonnes

Step-by-step explanation:

A ton is 2,000 lb.

A kg is 2.2 lb

1700 kg x 2.2 lb/kg = 3740 lb

3740 lb x (1 ton/2000 lb) = 1.87 tons

The Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

To solve the ODE using the Euler method, we divide the interval into smaller steps and approximate the derivative with a difference quotient. Given that the step size is h = 0.5, we will perform three steps to obtain the numerical solution.

we calculate the initial condition: y(0) = -2.

1. we evaluate the derivative at t = 0 and y = -2:

y' = 3(0) - 10(-2)² = -40

Next, we update the values using the Euler method:

t₁ = 0 + 0.5 = 0.5

y₁ = -2 + (-40) * 0.5 = -22

2. y' = 3(0.5) - 10(-22)² = -14,860

Updating the values:

t₂ = 0.5 + 0.5 = 1

y₂ = -22 + (-14,860) * 0.5 = -7492

3. y' = 3(1) - 10(-7492)² ≈ -2.2395 x 10^9

Updating the values:

t₃ = 1 + 0.5 = 1.5

y₃ = -7492 + (-2.2395 x 10^9) * 0.5 = -1.1198 x 10^9

Therefore, after performing three steps of the Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

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The simplified expression is 9j¹⁴k⁹ + 9j¹¹k⁶ - 72j⁶k².

When you use operations like addition, subtraction, multiplication, division, exponentiation, and other operations to combine numbers and variables.

Expressiοns in math are mathematical statements that have a minimum οf twο terms cοntaining numbers οr variables, οr bοth, cοnnected by an οperatοr in between. The mathematical οperatοrs can be οf additiοn, subtractiοn, multiplicatiοn, οr divisiοn. Fοr example, x + y is an expressiοn, where x and y are terms having an additiοn οperatοr in between. In math, there are twο types οf expressiοns, numerical expressiοns - that cοntain οnly numbers; and algebraic expressiοns- that cοntain bοth numbers and variables.

To simplify the expression 9j⁶k²(j⁸k⁷ + j⁵k⁴ - 8j²k), we need to distribute the factors and simplify the resulting terms:

9j⁶k²(j⁸k⁷ + j⁵k⁴ - 8j²k)

= 9j⁶k²j⁸k⁷ + 9j⁶k²j⁵k⁴ - 72j⁸k³

= \(9j^{(6+8)}k^{(2+7)} + 9j^{(6+5)}k^{(2+4)} - 72j^{(8-2)}k^{(3-1)\)

= \(9j^{14}k^9 + 9j^{11}k^6 - 72j^6k^2\)

Therefore, the simplified expression is 9j¹⁴k⁹ + 9j¹¹k⁶ - 72j⁶k².

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The loan amount for this extension is approximately $32,631. The correct option is (A) $32,631.

To find the loan amount for the extension Liam built onto his home, we can use the loan formula:

Loan formula:

PV = PMT * [{1 - (1 / (1 + r)^n)} / r]

Where,

PV = Present value (Loan amount)

PMT = Monthly payment

r = rate per month

n = total number of months

PMT = $750

r = 4.9% per annum / 12 months = 0.407% per month

n = 48 months

Putting the given values in the loan formula, we get:

PV = $750 * [{1 - (1 / (1 + 0.00407)^48)} / 0.00407]

PV ≈ $32,631 (rounded off to the nearest dollar)

Therefore, This extension's loan amount is roughly $32,631. The correct answer is option (A) $32,631.

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Answer:

36 I think, also to fintd the are of an object you count how many shapes its in the object:).

The projection of u onto v is (3,9) and the vector component of u orthogonal to v is (6,-2).

To find the projection of u onto v, we use the formula:

proj_v(u) = (u.v/||v||²) × v

where u.v is the dot product of u and v, and ||v||² is the magnitude of v squared.

First, we calculate u.v:

u.v = (9)(1) + (7)(3) = 30

Next, we calculate ||v||²:

||v||² = (1)² + (3)² = 10

Now we can plug these values into the formula to get the projection of u onto v:

proj_v(u) = (30/10) × (1,3) = (3,9)

To find the vector component of u orthogonal to v, we use the formula:

comp_v(u) = u - proj_v(u)

We already calculated proj_v(u) to be (3,9), so we can subtract that from u:

comp_v(u) = (9,7) - (3,9) = (6,-2)

Therefore, the projection of u onto v is (3,9) and the vector component of u orthogonal to v is (6,-2).

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Calculation of market rate of interest at the time of purchasing the bondThe information given in the problem is as follows:FV = $1000PMT = (7% of 1000)/2 = $35 (semiannual)N = 10 * 2 = 20 (semiannual)Semi-annual yield = 7% (coupon rate)/2 = 3.5%

Using the above-given information, the value of the bond can be calculated as follows: The price of the bond at the time of purchase = $1000 = PV= $832.67This implies that the market rate of interest at the time of purchasing the bond was 8.5%.b)

Calculation of selling the bond todayThe market rate of interest is now 8%. Using the given formula, the value of the bond can be calculated as follows: 
PMT = (7% of 1000)/2 = $35 (semiannual)N = 10 * 2 = 20 (semiannual)The price of the bond today = $881.57
Quoted price of bond = 88.16% = 0.8816 x $1000 = $881.6Current yield on bond = (70/881.6) x 100 = 7.94%Annual holding period return on bond = [(881.57-832.67) / 832.67] / 6.5 = 0.59%Suppose the bond is offered at $950, the holding period return will be calculated as follows: 
Holding period return = [(950-832.67) / 832.67] / 6.5 = 1.42%As per the given scenario, the annual holding period return on the bond is 0.59%. So, it can be concluded that the friend's offer is better than the current return. So, it is recommended to sell the bond to the friend.

The market rate of interest at the time of purchasing the bond was 8.5%.The price of the bond today = $881.57.The quoted price of the bond is $881.6.The current yield on bond is 7.94%.The annual holding period return on bond is 0.59%.The holding period return if bond is sold to a friend for $950 is 1.42%.

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Bob continues his research because even though there is no linear equation relationship between the number of bedrooms and selling price, there could be another type of relationship.

Bob continues his research because even though the correlation value he calculated between the number of bedrooms and the selling price was only 0.05, this does not necessarily mean that there is no relationship of any kind between these two variables. It simply means that there is no linear relationship between the two. There could still be other types of relationships between the two variables, such as an exponential or quadratic relationship. It is possible that further analysis and exploration of the data set would reveal such a relationship and allow Bob to uncover the relationship between the two variables. Additionally, even if the correlation value is low, it does not necessarily mean that there is no relationship between the two variables. It simply means that the relationship is weak. Therefore, Bob should continue his research in order to uncover any potential relationships between the number of bedrooms and selling price.

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Answer: Parallel lines have equal slopes

If the slope of line s is -32 or -3/2, then the same applies to line t

Parallel lines have equal slopes but different y intercepts. These lines do not cross or intersect.

Answer:  -32

Step-by-step explanation:

The two lines are parallel which means these two lines have the same slope. Therefore, the slope of line t is -32.

Answer:

perez has 28 student . and , according to this questions ,5 / 7 of those student participants in school sports.Thus 20 students participate in school sport .

The qualities of the given set are that it is closed and its interior is open.

The given set is the region between two concentric circles centered at the origin with radii of 3 and 4. To determine the qualities of this set, we can consider its boundaries, interior, and exterior. The boundaries of the set are the two circles of radius 3 and 4. These boundaries are included in the set, so the set is closed. The interior of the set consists of all points whose distance from the origin is between 3 and 4. Since the set contains no points on the boundaries, it is open. The exterior of the set consists of all points whose distance from the origin is either less than 3 or greater than 4. Since the complement of the set is the union of two open disks, the exterior of the set is also open. Therefore, the qualities of the given set are that it is closed and its interior is open.

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Answer:

Question 1: A. Replace one equation with a multiple of the other equation

Question 2: B. No

Step-by-step explanation:

1) How can we get System B from System A?

Choose 1 answer:

A. Replace one equation with a multiple of the other equation

B. Replace one equation with a multiple of itself

C. Swap the left-hand sides of both equations

D. Swap the order of the equations

2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?

Choose 1 answer:

A. Yes

B. No

The answer to both questions is in bold and in the "Answer" section.

Hope this helps!

If not, I am sorry.

Answer:

Answer:

\({ \rm{ \hookrightarrow{ \blue{ {x}^{2} + 6x + 9 }}}} \\ { \rm{ \hookrightarrow{ \red{ {x}^{2} - 9 }}}}\)

Step-by-step explanation:

» General Quadratic expression:

\( { \rm{y = {x}^{2} - (sum \: of \: roots)x + (product \: of \: roots)}}\)

» For (-3, -3), roots are -3 and -3

• Sum of roots:

\({ \tt{sum = - 3 + - 3}} \\ { \tt{sum = - 6}}\)

• Product of roots:

\({ \tt{product = - 3 \times - 3}} \\ { \tt{product = 9}}\)

• Equation:

\({ \underline{ \underline{ \tt{ \: y = {x}^{2} + 6x + 9 \: }}}}\)

» For (3, -3), roots are 3 and -3

• Sum of roots:

\({ \tt{sum = - 3 + 3}} \\ { \tt{sum = 0}}\)

• Product of roots:

\({ \tt{product = - 3 \times 3}} \\ { \tt{product = - 9}}\)

• Equation:

\({ \underline{ \underline{ \tt{ \: y = {x}^{2} - 9 \: }}}}\)

The system of two quadratic equation is

x² + 6x + 9 = 0

x² - 9 = 0

"A quadratic equation is an algebraic equation of the second degree in 'x'. The quadratic equation in its standard form is ax² + bx + c = 0, where 'a'(a ≠ 0) and 'b' are the coefficients, 'x' is the variable, and 'c' is the constant term."

The solution of the first equation in the system is (- 3, - 3).

Therefore, the equation will be

[x - (- 3)] [x - (- 3)] = 0

⇒ (x + 3)(x + 3) = 0

⇒ (x + 3)² = 0

⇒ x² + 6x + 9 = 0

The solution of the second equation in the system is (3, - 3).

Therefore, the equation will be

[x - 3] [x - (- 3)] = 0

⇒ (x - 3)(x + 3) = 0

⇒ (x)² - (3)² = 0

⇒ x² - 9 = 0

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Answer:

vertical angles

Step-by-step explanation:

A and b are vertical angles, since they are formed by the same lines and share a vertex

Answer:

\(option \: a \: is \: correct \\ and \: vertically \: opp \: angels \: are \: equal.\)

The y-intercept of the equation y = 2x + 3 is 3.

To find the y-intercept in an equation of slope, you need to understand the slope-intercept form of a linear equation, which is written as y = mx + b.

In this equation, 'm' represents the slope, and 'b' represents the y-intercept.

The y-intercept is the value of y when x is equal to zero, meaning it is the point where the line intersects the y-axis. To determine the y-intercept, set x = 0 in the equation and solve for y.

This will give you the y-coordinate of the point where the line crosses the y-axis.

For example, let's say you have the equation y = 2x + 3. To find the y-intercept, substitute x = 0 into the equation:

y = 2(0) + 3

y = 0 + 3

y = 3

Therefore, the y-intercept of the equation y = 2x + 3 is 3.

In summary, to find the y-intercept in an equation of slope, substitute x = 0 into the equation and solve for y. This will give you the y-coordinate where the line intersects the y-axis.

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a). To maximize production within the budget, 600 units of labor and 100 units of capital should be purchased. b). The maximum production under the budgetary constraint is approximately 8,366 units.

a). To maximize production, we need to allocate the budget efficiently between labor and capital. We can calculate the number of units of labor and capital by dividing the budgeted amount by the cost per unit. The budget of $576,000 divided by the cost of labor per unit ($400) gives us 1,440 units of labor. Similarly, dividing the budget by the cost of capital per unit ($2,400) gives us 240 units of capital. However, this allocation does not maximize production within the budgetary constraint.

b). To find the optimal allocation, we can use the partial derivatives of the production function with respect to L and K. Taking the partial derivative of the production function with respect to L, we get 37.5L^(-0.25)K^0.25. Equating this to the budgeted amount of labor (600 units), we can solve for K, which comes out to be 100 units. Similarly, by taking the partial derivative of the production function with respect to K, we get 12.5L^0.75K^(-0.75). Equating this to the budgeted amount of capital (100 units), we can solve for L, which comes out to be 600 units.

By substituting these values into the production function, we can calculate the maximum number of units of production, which is approximately 8,366 units.

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To find the distinct possibilities for the values in the diagonal going from the top left to the bottom right of a BINGO card, we need to consider the ranges of numbers that can appear in each column.

The first column can have any 5 numbers from the set 1-15. There are 15 numbers in this range, so there are "15 choose 5" possibilities for the numbers in the first column.

The second column can have any 5 numbers from the set 16-30. Again, there are 15 numbers in this range, so there are "15 choose 5" possibilities for the numbers in the second column.

The third column has a Wild square in the middle, so we need to skip it and consider the remaining 4 squares. The numbers in the third column can come from the set 31-45, which has 15 numbers. Therefore, there are "15 choose 4" possibilities for the numbers in the third column.

The fourth column can have any 5 numbers from the set 46-60, which has 15 numbers. So there are "15 choose 5" possibilities for the numbers in the fourth column.

The last column can have any 5 numbers from the set 61-75, which again has 15 numbers. So there are "15 choose 5" possibilities for the numbers in the last column.

To find the total number of distinct possibilities for the diagonal, we multiply the number of possibilities for each column together:

"15 choose 5" "15 choose 5"  "15 choose 4"  "15 choose 5"  "15 choose 5".

Evaluating this expression, we find:

(3003)  (3003)  (1365)  (3003)  (3003) = 13,601,464,112,541,695.

Therefore, there are 13,601,464,112,541,695 distinct possibilities for the values in the diagonal going from the top left to the bottom right of a BINGO card, in order.

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A relation as mapping between A and B, two non-empty sets. Ronnie's data represent a relation.

Relation is simply defined as mapping between A and B, two non-empty sets.

In conclusion, The connection in which each input value has just one output is known as a function.

Therefore, relations are functions, but not all functions are relations.

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The number of regular sodas served is 12.

Percentage is the fraction of an amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %. Percentage is a measure of frequency.

Number of regular sodas served = percentage of regular sodas served x number of sodas served

= 25% x 48

= 25/100 x 48 = 12

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Answer:

x=5

Step-by-step explanation:

\(2 {x}^{2} = 50\)

\( {x}^{2} = \frac{50}{2} \)

\( {x}^{2} = 25\)

\(x = \sqrt{25} \)

\(x = 5\)

Answer: Perry

Step-by-step explanation:

Perry pays 29 dollars per ticket and Jackie pays 28 dollars per ticket