Take y=1/x^2. Stretch it by a factor of 5, shift it 4 units to the right and 7 units down. What is the new function?

The dimensions of the poster with the smallest area are 48 cm by 16 cm.

Let the width of the printed material be x cm and the height be y cm. Then the total width of the poster including the margins is (x + 16) cm, and the total height is (y + 24) cm.

The total area of the poster is the area of the printed material plus the area of the margins:

(x + 16)(y + 24) = 1536

Expanding the left side, we get:

xy + 16y + 24x + 384 = 1536

Rearranging terms, we get:

xy = 1152 - 16y - 24x

To find the dimensions of the poster with the smallest area, we want to minimize the product xy subject to the constraint given by the equation above.

One way to do this is to use the method of Lagrange multipliers. Let L = xy + λ[(x + 16)(y + 24) - 1536] be the Lagrangian, where λ is a Lagrange multiplier. Setting the partial derivatives of L with respect to x, y, and λ equal to zero, we get:

y + 16λ = 0

x + 24λ = 0

(x + 16)(y + 24) = 1536

From the first two equations, we get:

x = -24λ

y = -16λ

Substituting these into the third equation, we get:

(-24λ + 16)(-16λ + 24) = 1536

Simplifying, we get:

-6λ + 4 = 0

Therefore, λ = 2/3. Substituting this into the expressions for x and y, we get:

x = -16

y = -32

These values give the dimensions of the printed material. To find the dimensions of the poster, we add the margins:

width = x + 16 + 16 = 48 cm

height = y + 24 + 24 = 16 cm

Therefore, the dimensions of the poster with the smallest area are 48 cm by 16 cm.

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the inverse function of f(x) is f⁻¹(x) = 1-√(x-1).

Given f(x) = (x - 2)^2 + 1 for x ≤ 2, we have to find f^-1(x).The given function is f(x) = (x - 2)^2 + 1.  

Here, we can see that x ≤ 2 implies that x - 2 ≤ 0.

The given function can be written as y = (x - 2)^2 + 1.  

Interchange x and y. Therefore, x = (y - 2)^2 + 1.

Solve the above equation for y to find the inverse of the given function.(x - 1)² + 1 = y ⇒ (x - 1)² = y - 1    ------ (1)So, x - 1 = √(y - 1) or x - 1 = - √(y - 1)Hence, x = √(y - 1) + 1 or x = - √(y - 1) + 1

It can be observed that the domain of the given function is x ≤ 2 and the range of the inverse function is y ≤ 1, so we choose the negative square root expression.Thus, f^-1(x) = - √(x - 1) + 1.

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The function is an exponential growth since it is increasing with time and k is positive

Given that at t =6, P = 167075

Then;

167075 =110.8e^6k

167075/110.8 = e^6k

1507.9 = e^6k

ln(1507.9) = 6k

k = ln(1507.9)/6

k = 1.2

Thus in the year 2020;

P = 110.8e^20(1.2)

P = 2.9 * 10^12

In the year 2025;

P = 110.8e^25(1.2)

P = 1.18 * 10^15

To reach 290,000

290,000 = 110.8e^1.2t

290000/110.8 = e^1.2t

2617.3 = e^1.2t

t = ln(2617.3 )/1.2

t = 7 years

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The correct option is:

c. Action research

What type of research is conducted by professionals in any type of school to investigate a problem, with findings that may have limited generalizability?

The type of research conducted by professionals in any type of school to investigate a problem, with findings that may have limited generalizability, is known as action research.

c. Action research.

Action research is a type of research that is intended to be carried out by professionals in any type of school setting to investigate a specific problem or issue. The focus of action research is on practical solutions and making improvements within a particular context.

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Answer:

2÷ 1/3 =6

3 ÷1/2=6

4÷2/3=6

4 ÷1/2=8

12÷3/2=8

Step-by-step explanation:

Hope this helps!

Therefore, the equivalent effective rate per year, rounded to 4 decimal places, is 0.6892.

To find the equivalent effective rate per year, we need to convert the given interest rate per two months to an annual rate.

Let's denote the interest rate per two months as r. From the given information, r = 29%.

To find the equivalent annual rate, we can use the formula:

\((1 + r)^6 - 1\)

where r is the interest rate per two months, and we raise it to the power of the number of two-month periods in a year, which is 6 since there are 12 months in a year and each two-month period is counted as one.

Let's calculate the equivalent effective rate per year:

\((1 + 0.29)^6 - 1 = 0.6892\)

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Answer: 3.6

Step-by-step explanation:

x=# of hours

Lisa's (L) rate = 1/6 per hour

Vicky's (V) rate = 1/9 per hour

L's work + V's work = 1

1/6x+1/9x=1

3/18x+2/18x=1

5/18x=1

18/5*5/18x=18/5*1

x=18/5

x=3.6

3.6 hours

Lisa and Vicky can paint the bedroom together in 3.6 hours. This is achieved by adding their individual rates of work (1/6 and 1/9 of the room per hour, respectively) to get 5/18 of the room per hour. Hence, the entire room can be painted in 18/5 hours.

The subject of this question is mathematics and concerns the time taken to paint a bedroom. Lisa can complete the job in 6 hours, meaning she can paint 1/6 of the room per hour. Vicky, who is slightly slower, can complete the job in 9 hours which implies she can paint 1/9 of the room per hour. When they work together, we simply need to add their rates together to determine how much of the room they can paint in one hour.

So, Lisa paints 1/6 of the bedroom per hour, and Vicky paints 1/9 of the bedroom per hour. Working together, they paint (1/6 + 1/9) of the bedroom per hour, which equals 5/18. Hence, they can paint the room in 18/5 (3.6) hours.

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Answer:

18:10 is equivalent to 9:5

Step-by-step explanation:

half of 18 is 9 and half of 10 is 5

Answer:

9:5

Step-by-step explanation:

18:10 is equivalent to 9:5 because 10 divided by 2 is 5 so you can do the same for 18. You will get 9 which makes it 9:5.

Answer:

8a³b

Step-by-step explanation:

Answer:

I think it's c

Step-by-step explanation:

Well I believe that would mean that one coordinate would shift by five, c looks the most likely in this case.

I was actually surprised to see that statement A is correct

graphed around with desmos until I reconstructed f(x), then graphed f(x+4)

see screenshot

Probability that 5 of 6 stolen cars will be recovered with insurance records a car with a certain protection system will be recovered 91% of the time is equal to P(x=5)=0.3369 (approximately).

As given,

Insurance protection system recovered of a car=91%

p=0.91

q=1-p

 =1-0.91

 =0.09

n=6

x=5

Using Binomial theorem ,probability of 5 of 6 stolen cars will be recovered is:

ⁿCₓ(p)ˣ(q)ⁿ⁻ˣ

=⁶C₅(0.91)⁵(0.09)⁶⁻⁵

=[6!/(6-5)!5!] × (0.91)⁵× (0.09)

=6×(0.91)⁵×0.09

=0.3369

Therefore, probability that 5 of 6 stolen cars will be recovered with insurance records a car with a certain protection system will be recovered 91% of the time is equal to P(x=5)=0.3369 (approximately).

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The probability of obtaining five tails in a row assuming the coin is​ fair is 1/32.

A person will have to do 5 coin tosses which means,

No. of total observations  = 25

Required outcome → 5 Heads { T , T , T , T , T }

This outcome  can occur only once so required outcome will be 1

Thus, required outcome  =1

Probability (5 Tails) = 1 / 2⁵ = 1 / 32

Hence , the probability of obtaining five tails in a row assuming the coin is​ fair is 1/32.

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The solution of the inequality are n  ≤ -7 and n ≥ -12.

A compound inequality is an inequality that combines two simple inequalities.

Therefore, let's solve the compound inequality individually.

n + 2 ≤ −5 and  n + 6 ≥ −6

Hence,

n + 2 ≤ − 5

subtract 2 from both sides of the inequality

n + 2 - 2 ≤ − 5 - 2

n  ≤ -7

n + 6 ≥ −6

subtract 6 from both sides of the inequality

n + 6 ≥ −6

n + 6 - 6 ≥ −6 - 6

n ≥ -12

Therefore, n  ≤ -7 and n ≥ -12

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The lines (x, y, z) = (t +5, 4t +5, t − 4) and (x, y, z) = (5s +4, s +1, 8s − 5) do not intersect.

To determine if the lines (x, y, z) = (t +5, 4t +5, t − 4) and (x, y, z) = (5s +4, s +1, 8s − 5) intersect, we need to set the equations equal to each other and solve for t and s.

(t +5, 4t +5, t − 4) = (5s +4, s +1, 8s − 5)

This gives us a system of three equations:

t + 5 = 5s + 4
4t + 5 = s + 1
t − 4 = 8s − 5

We can solve this system by using substitution or elimination. Here, we'll use substitution.

From the first equation, we can solve for t in terms of s:

t = 5s − 1

Substituting this into the second equation, we get:

4(5s − 1) + 5 = s + 1

Simplifying, we get:

20s − 4 + 5 = s + 1

19s = 0

s = 0

Substituting s = 0 into the first equation, we get:

t + 5 = 4

t = −1

Substituting s = 0 into the third equation, we get:

t − 4 = −5

Since t = −1 and not t = 3, the lines do not intersect.

The Question was Incomplete, Find the full content below :

Do the lines (x, y, z) = (t +5, 4t +5, t − 4) and (x, y, z) = (5s +4, s +1, 8s − 5) intersect?

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Answer:

Step-by-step explanation:

Given:

The equation for the nth term of the GP:

Substitute the values to get:

Correct choice is C

Step-by-step explanation:

We know that

\( \sf a_{n} = a \times r {}^{n - 1} \)

\( \sf \: a = 9(given)\)

\( \sf \: a_{n} = \frac{2}{3} ( a_{n} - 1)\)

Putting = 9

\(\sf a_n=9•\bigg(\dfrac{2}{3}\bigg)^{n-1}\)

Esi would receive 36 and Kwasi 24 from the 60 oranges

Ratio of their ages :

12 : 8

express to lowest term by dividing both sides by 4

3 : 2

Given the amount of oranges = 60

Esi = 3/5(60) = 36

Kwasi = 2/5(60) = 24

Therefore, Esi would receive 36 and Kwasi 24.

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If these conditions/assumptions are met, then the two-sample test for means with independent samples can be used to determine if there is a statistically significant difference between the means of two independent groups.

In order for the two-sample test for means with independent samples to be appropriate, the following conditions/assumptions must be met:

Independent samples: The samples for each group should be selected independently of each other.

Normality: The population distributions should be approximately normal, or the sample sizes should be large enough (n > 30) for the central limit theorem to apply.

Equal variances: The variances of the two populations should be approximately equal. This assumption is important for calculating the pooled variance estimate, which is used in the t-test formula.

Random sampling: The samples should be randomly selected from the populations of interest.

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Answer:

Area = 91 square inches

Step-by-step explanation:

Let

L = length of the rectangle in inches

W = width of rectangle in inches

We are given:
The length of a rectangle is one inch less than twice the width

In math terms this is equivalent to:
L = 2W - 1

he perimeter of the rectangle is 40 in.
The perimeter of the rectangle = 2(L+ W)

So in math terms;
2(L + W) = 40

L + W = 40/2

L + W = 20

Since L = 2W - 1 we can substitute for L in terms of W in the above equation:
L + W = 2W - 1 + W = 3W - 1

Equating it to 20 gives
3W - 1 = 20

Add 1 both sides:
3W = 21

W = 7

Which gives

L = 2W - 1 = 2(7) - 1 = 14 - 1 = 13

So L = 13

The area of the rectangle = L x W

= 13 x 7

= 91 square inches

Answer:

Step-by-step explanation:

Just as the “stop sign” uses its 8 sides to communicate about “sharing the stop in all directions”, the yield sign’s 3 sides communicate as well. That triangle communicates that things’ll get tighter and tighter for you, as you move up. It’s sort of implicit - your space is going away. You need to stop and yield to others whose space hasn’t gone away.

-lukelaws

please brainiest in almost another level up!

I may utilize the Cp Criterion, AICp, and SBCp to aid in choosing the optimal model. All of them impose sanctions for introducing predictions.

What is subset regression model?

Best subsets regression is a model-building regression analysis that is exploratory. It compares every model that might be built using a specified set of predictors.

There are Cp Criterion, AICp and SBCp that I can use to help select the best model. They all place penalties for adding predictors.

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Answer:

32

Step-by-step explanation:

Calculation for how much birdseed does she have left over

First step

(3*8*6*12) - 4-2*30

Second step

=[24+6*(10+2)] - 4-60

Third step

Let remove the bracket of (10+2)

=[24+6*10+6*2] - 4-60

Fourth step

=(24+60+12) - 4-60

Fifth step

=(84+12)-4-60

Sixth step

=96-4-60

Seventh step

=92-60

=32

Therefore the amount of birdseed that she have left over will be 32

Using the concept of similarity ratio, the values of x and y in the similar polygons are 24 and 7 respectively.

It is given that the two triangles given are similar, therefore, their corresponding sides will be in ratio.

Thus;

25/50 = y/14 = x/48

We will use the same ratio of the similar triangles we have already found out to get x and y;

25/50 = x/48

x = (48 * 25)/50

x = 24

Similarly;

25/50 = y/14

y = (14 * 25)/50

y = 7

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The inequality is given by 20x + 25y ≤ 1100 and x + y > 50

An inequality is an expression that shows the non equal comparison of two or more numbers and variables.

Let y represent the number of soccer balls and x represent the number of volleyballs.

The coach can spend a maximum of $1,100, hence:

20x + 25y ≤ 1100

Also, The coach plans to order at least 50, hence:

x + y > 50

The inequality is given by 20x + 25y ≤ 1100 and x + y > 50

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The values of a and b that make the function both continuous and differentiable everywhere are a = -3 and b = 19.

A function is a mathematical concept that assigns a unique output value for each input value. It is a rule that takes in an input or set of inputs and maps it to a specific output. Functions are represented by symbols, usually denoted by a letter, such as "f".

In mathematical notation, a function is usually expressed as "f(x)" where "x" is the input and "f(x)" is the corresponding output. For example, a function could be defined as f(x) = x^2, which means that for any value of x, the function will calculate and return the square of that value.

Functions play a central role in mathematics and are used to model real-world phenomena and to study the relationships between variables. They are also used in computer programming to perform specific tasks, such as converting temperatures from Celsius to Fahrenheit or calculating the square root of a number.

To make the function continuous at x = -3, the value of f(-3) must be equal for both the first and second parts of the definition. That is, 3 * -3 + 4 = -3 * -3 + a * -3 + b. Solving for a and b gives us:

a = -3

b = 19

To make the function differentiable at x = -3, the limits of the first and second parts of the definition must be equal, and their derivatives must also be equal.

The limit from the left of f(-3) is:

\(\lim_{x \to \ -3}\)f(x) = 3 * -3 + 4 = 5

The limit from the right of f(-3) is:

\(\lim_{x \to \ -3}\) + f(x) = -3 × -3 + a × -3 + b = -3 × -3  + 19 = 19

So the function is continuous at x = -3. To check for differentiability, we find the derivative of the first part:

f'(x) = 3

And the derivative of the second part:

f'(x) = -6x + a

The derivative of the two parts must be equal at x = -3, so we have:

3 = -6 × -3 + a

3 = 18 - a

a = -15

This value of a is different from the value we found in the first step, so the function is not differentiable at x = -3. To make it differentiable, we must choose the value of a that makes the function continuous, which is a = -3.

So the values of a and b that make the function both continuous and differentiable everywhere are a = -3 and b = 19.

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Answer:

y = x + 1

Step-by-step explanation:

x + y = 6

y = -x + 6

Perpendicular slope to -1 is 1

(0,1)

y - y1 = m(x - x1)

y - 1 = 1(x - 0)

y - 1 = x

y = x + 1

Standard form:

y = x + 1

-x + y = 1

The mass of NaF that is required to make a standard 1 solution of 250 ml 0.1 M F- solution is 5.45 g of NaF. The number of moles in a solution is the concentration in moles per litre multiplied by the volume in litres.

To calculate the mass of a solute required, we need to first calculate the number of moles required. We can then use the molar mass of the solute to calculate its mass.To calculate the number of moles required in this question, we can use the formula:n = c × V where n is the number of moles, c is the concentration in moles per litre and V is the volume in litres. We have:c = 0.1 M

and V = 0.25 L

Substituting these values into the formula gives:n = 0.1 mol/L × 0.25 L

= 0.025 mol

Now we can use the molar mass of NaF to calculate its mass. The molar mass of NaF is 41.99 g/mol (22.99 g/mol for Na and 19.00 g/mol for F).

We have:n = 0.025 mol

solving for mass:m = n × M

where M is the molar mass of NaF.

Substituting gives:m = 0.025 mol × 41.99 g/mol ≈ 1.05 g

However, this is the mass required to make 0.25 L of solution. To make 1 L of solution, we would need to multiply the mass by 4. Therefore, the mass of NaF required to make a standard 1 solution of 250 ml 0.1 M F- solution is:1.05 g × 4 = 4.20 g Rounding this to two significant figures gives:4.2 g NaF.

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Answer:

2/5

Step-by-step explanation:

Total=4+5+1=9+1=10

4/10=2/5

2/5 is the correct answer

Respuesta:

(segundo + 3) (segundo + 2) = 0

Explicación paso a paso:

Dada la expresión cuadrática b² + 5b + 6, debemos factorizarla;

b² + 5b + 6 = 0

b² + 2b + 3b + 6 = 0

b (segundo + 2) +3 (segundo + 2) = 0

(segundo + 3) (segundo + 2) = 0

Por tanto, el factor requerido es (b + 3) (b + 2) = 0

Answer:

The area base of the cylinder is 32 pi square meters which is correct option(A).

Step-by-step explanation:

The volume of a cylinder is equal to the product of area of circular base and height of a cylinder. The volume of a cylinder is defined as the space occupied by the cylinder as the volume of any three-dimensional shape is the space occupied by it

V = A × h, where

A = area of the base

h = height

The base of a  circular cylinder is a circle and the area of a circle of radius 'r' is πr². Thus, the volume (V) of a circular cylinder, using the formula, is, V = πr²h

where , 'r' is the radius of the base (circle) of the cylinder

'h' is the height of the cylinder

π is a constant whose value is either 22/7 (or) 3.142.

Given data,

The volume of cylinder = 288π cubic meters

V = πr²h

Substitute the value of V in the formula

288π = π(r²)(9)

Divided by π both the sides,

288 = 9 r²

288/9 = r²

32 = r²

r² = 32

r ≈ 5.65 meters

The area base (circle) of the cylinder = πr²

Substitute the value of r in the formula,

The area base  of the cylinder = π(5.65)²

The area base  of the cylinder = π(32)

The area base of the cylinder = 32π

Hence, the area base of the cylinder is 32π square meters.

hope this helps gangy

Answer:

32π square meters

Step-by-step explanation:

Use the volume of cylinder formula: V = πr²h:

288π = πr² x 9

Make r² the subject of the formula:

r² = 288π divided by 9π = 32

Now we know r² = 32, we use the circle area formula as the base of the cylinder is a circle:

πr² = formula to find area of circle

π x 32 (which is r²) = 32π m² (square meters)

Hope this answers your question!

Answer:

-5/-3

Step-by-step explanation:

first y intercept=

-5/-3