Find the dimensions of the rectangle of maximum area, with sides parallel to the coordinate axes, that can be inscribed in the ellipse given by
.
144* 13

A point on the graph is (30, 4) and the meaning is that the cost of 30 units of electricity is £4

From the question, we have the graph that can be used in our computation:

From the graph, we have the following ordered pairs

(0, 0) and (30, 4)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (0, 0) and (30, 4)

The gradient of the line is then calculated using the following slope equation

gradient = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (0, 0) and (30, 4)

Substitute the known values in the above equation

So, we have the following equation

gradient  = (4 - 0)/(30 - 0)

Evaluate

gradient  = 4/30

So, the gradient of the line is 4/30

As a general rule:

Generally, slope or gradient means rate

This means that the gradient of this line represent the rate

i.e. the amount for each unit is 4/30

So, we can conclude that the point (30, 4) on the graph means that the cost of 30 units is £4

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Complete question

An electricity company charges the same fixed amount for each unit of electricity used. David uses this graph to work out the total cost of the electricity he has used.

See attachment for graph

As per the concept of probability, If L is invited to speak on Friday, then the science fiction writer be invited on Monday and Wednesday

Probability:

In statistics, probability refers the possible and favorable outcome of the particular event.

Given,

Here we need to find if L is invited to speak on Friday, then on what days MUST a science fiction writer be invited.

Here we know that the writers of the same genre may not speak on consecutive nights.

And here we have the only five slots to fill, two of the three science fiction writers must speak on Monday and Friday

So, If both X and J are invited, then at least one will be forced to speak on Monday or Friday, which is not allowed.

Then, modification of the rules is actually just a bit of a red herring, since all of the answer choices except for the one regarding science fiction writers is true regardless.

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If to approximate the length of a marsh, a surveyor walks x = 420 meters. The Approximate the length AC of the marsh is 420.7m.

Using this formula to find the length of Ac of the march

b² = a²+c² -2ac Cos B

Where:

a²=220

c²= 420

Cos B = 180°  - 75° = 105°

Let plug in the formula

b² = 220² + 420² - 2(220)( 420) Cos  105°

b² = 220² + 420² - 2(220)( 420) (-0.258819045)

b² = 48,400 + 176,400 - 47,829.76

b² = 224,800 -  47,829.76

b = √176,970.24

b = 420.7m

Therefore the length is 420.7m

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Answer:

40

Step-by-step explanation:

40

The total surface area of the figure is 1208cm². Option A

You should understand that the total surface area of the figure is the sum of all the face areas of the various parts of the figure. There are front and back faces of the prism

Area of bases of the prisms

1. Area = a*c*2

= 20*12*2

Area = 480cm²

2. Area = a*c*2

= 20*8*2

Area = 320cm²

3. Area = (d*c)/2 * 4

Area = (5*12)/2 *4 = 30*4

Area = 120 cm²

4) Area = c*b*2= *12*2

Area = 208cm²

5) Area = a*c*2 = 5*8*2Area = 80cm²

Therefore, the total surface area of the figure is

Total surface area= (480+320+120+208+80)cm²

= 1208cm²

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Correct question:

Two same-sized triangular prisms are attached to a rectangular prism as shown below.If a = 20 cm, b = 13 cm, c = 12 cm, d = 5 cm, and e = 8 cm, what is the surface area of the figure?a 1,208 square centimetersb 1,592 square centimetersc 1,004 square centimetersd 1,400 square centimeters

Answer:

--------------------------

The linear functions will have same or equivalent equations in order to have infinitely many solutions.

Convert the given to slope-intercept form, y = mx + b, to make it equivalent:

Answer:

Before you get into classifying polynomials, let’s define what polynomials are!

Polynomials are a specific type of mathematical expression that has all of the following:

One or more terms

Variables with only positive whole-number exponents

No variables in the denominators of any term

So, let's discuss the questions:

A)1/x+1 is not a polynomial

B)1/√x+1 is not a polynomial

C)1/x²+x+1 is not a polynomial

D) x^3+1 is a polynomial bc it has positive whole number exponent, their no variables in the denominators and its more than 1 terms

Step-by-step explanation:

hope this helps <3

[tex]\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} ~\hspace{7em} \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\log(x)=2\hspace{5em}\log(y)=3\hspace{4em}\log(2)\approx 0.3\hspace{4em}\log(3)\approx 0.48 \\\\[-0.35em] ~\dotfill\\\\ \log\left(\sqrt[3]{x^4\cdot y^2} \right)\implies \log\left(\left( x^4\cdot y^2 \right)^{\frac{1}{3}} \right)\implies \cfrac{1}{3}\log(x^4 y^2) \\\\\\ \cfrac{1}{3}[\log(x^4)~~ + ~~\log(y^2)]\implies \cfrac{1}{3}[4\log(x)~~ + ~~2\log(y)]\implies \cfrac{1}{3}[4(2)~~ + ~~2(3)] \\\\\\ \cfrac{1}{3}[8~~ + ~~6]\implies {\Large \begin{array}{llll} \cfrac{14}{3} \end{array}}[/tex]

The probability that at least one client will have a food allergy is 0.6323 and the percentage of customers who will have a food allergy is 0.08.

What is probability?

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not.

As given in the question,

The percentage of customers who will have a food allergy is 0.08

At Ying Ying's bakery,

121 people place orders on a single day.

We can utilize the binomial distribution if we believe that each of the 12 clients has an equal probability of reporting a food allergy.

Formula for Binomial probability distribution:

P(X=x)=ⁿCₓ pˣ (1-p)ⁿ⁻ˣ

Here, P(x) = probability of getting success in x trials, n= sample size ,p = represents the probability that each event will succeed.

As given, we have

n = 12

p=0.08

Let x is the client will have a food allergy.

Following that, the probability that at least one client will have a food allergy will be:

P(x≥1) = 1 - P(x<1)

= 1 - P(x=0)

= 1 - ¹²C₀(0.08)⁰(1 - 0.08)¹²⁻⁰

= 1 - (1)(0.12)¹²

= 1 - 0.3677

= 0.6323

Hence , the probability that at least one client will have a food allergy will be 0.6323 when the percentage of customers who will have a food allergy is 0.08.

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Complete Question

When a customer places an order at Ying Ying's bakery, there is an 8\%8%8, percent probability that the customer will report a food allergy. One day, 121212 customers place orders at Ying Ying's bakery.

Assuming that each of the 121212 customers is equally likely to report a food allergy, what is the probability that at least one customer will report a food allergy?

Answer:

the portion of the x-axis that the straight line cuts is the interval [5r, -5r].

Step-by-step explanation:

To find the portion of the x-axis that the straight line cuts, we first need to solve the equation for θ. The sine function has a range of [-1, 1], so the value of r must be greater than or equal to 5 in order for the equation to have a solution.

To solve the equation, we can use the fact that sin(π/4 - θ) = cos(θ). Therefore, the equation can be rewritten as:

cos(θ) = 5

We can then use the fact that cos(θ) = x/r to solve for x:

x = 5r

Therefore, the portion of the x-axis that the straight line cuts is the interval [5r, -5r].

Note that this is only valid if r is greater than or equal to 5. If r is less than 5, there are no solutions to the equation and the straight line does not cut the x-axis.

Answer:

6418698

-3485835

2932863

Step-by-step explanation:

In the given diagram, the length of arc AB is 10.05.

From the question, we are to determine the length of arc AB.

From the formula for calculating the length of an arc, we have that

Length of an arc = θ/360° × 2πr

Where θ is the angle subtended by arc at the center of the circle

and r is the radius of the circle

In the given diagram,

Angle subtended by the arc = 48°

Radius, r = 12

Therefore,

The length of the arc = 48/360 × 2×3.14×12

Length of the arc = 2/15 × 1884/25

Length of the arc = 10.05

Hence, the length of AB is 10.05

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The statement -7 < y < 12 meant y is greater than -7 and less than 12.

{-7 < y < 12}

This is a compound inequality.

A compound inequality is a type of inequality which combones two or more simple inequality.

-7 < y < 12

This can be broken down into two parts;

This can also be written together as y is greater than -7 and less than 12.

This means y is between the values that are greater than -7 but less than 12

So,

y could be -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11

Therefore, y can be said to be within the range of values between -6 and 11

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Answer:

The correct answer is (1, -3).

Step-by-step explanation:

To solve this question, we should use substitution. This means we can substitute the value given for y (as indicated by the second equation) into the first equation. This is shown below:

4x + y = 1

4x + (x - 4) = 1

We simplify the left side of the equation and then solve for x.

5x - 4 = 1

5x = 5

x = 1

We must also solve for y. To do this, we can plug in x = 1 into either of the given equations.

y = x - 4

y = 1 - 4

y = -3

Therefore, x = 1 and y = -3. The question asks us to express the answer as an ordered pair (x,y), so the answer is (1, -3).

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Based on the combination technique,

1. The position of wire 3

2. The magnitude and direction of current in wire 3

Combination method:

In statistics, the mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter is know a combination method.

Given,

Here we have the three long wires hang vertically. The distance between wire 1 and wire 2 is 23.0 cm On the left, wire 1 carries an upward current of 1.50 A. To the right, wire 2 carries a downward current of 3.60 A. Wire 3 is to be located such that when it carries a certain current, each wire experiences no net force.

And now we need to find the position of wire 3 and the magnitude and direction of the current in wire 3.

As per the given question, we know that the

=> Current in wire 1, i1 =1.2A upward

=> Current in wire 2, i2=5A downward

And the distance between wire 1 and 2 is calculated is

=> 20cm = 0.2m

Here the current is calculated as

=> F/l = μo•i1•i3/2πx

So,

=> F/l=6×10⁻⁶N/m

=> 6×10⁻⁶ = μo•i1•i3/2πx

=> 6×10⁻⁶ =4π×10⁻⁷×1.2×i3/(2π×0.0632)

When we do Cross multiply,

=> 6×10⁻⁶×2π0.0632=4π×10⁻⁷×1.2×i3

=> 2.383×10⁻⁶=4π×10⁻⁷×1.2×i3

=> i3= (2.383×10⁻⁶)/(4π×10⁻⁷×1.2)

Therefore, i3= 1.58A and it's direction is downward.

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Answer:

[tex]\frac{-8}{9}[/tex]

Step-by-step explanation:

Substitute in 7 for x

[tex]\frac{7^{2}-5(7) -6 }{7^{2}-6(7) - 16 }[/tex]

[tex]\frac{49-35-6}{49-42-16}[/tex]

[tex]\frac{-8}{9}[/tex]

Simplifying an exponential equation can be done by using different laws of exponents.

In this case, we can use the power rule and negative exponent rule

Power rule:

[tex](a^x)^y=a^x^y[/tex]

Negative exponent rule:

[tex]a^-^y=\frac{1}{a^y}[/tex]

1. Use the negative exponent rule

[tex](10x^2)^-^3=\frac{1}{(10x^2)^3}[/tex]

2. Use the power rule and simplify

[tex]10^3=1000[/tex] and [tex](x^2)^3=x^6[/tex]

∴[tex]\frac{1}{1000x^6}[/tex]

Answer:

= 10x⁻⁶

Step-by-step explanation:

2*-3 = -6

then:

[tex]10x^{2^{-3}} = 10x^{-6}[/tex]

= 10x⁻⁶

0.477 ft/min, the water level is rising when the water is 2 feet deep in the tank.

The derivative of a function of a real variable in mathematics quantifies the sensitivity of the function's value (output value) to changes in its argument (input value).

Calculus's core tool is the derivative. The velocity of an item, for instance, is the derivative of its position with respect to time; it quantifies how quickly the object's position varies as time passes.

When it occurs, the slope of the tangent line to the function's graph at a given input value is the derivative of a function of a single variable.

The function closest to that input value is best approximated linearly by the tangent line. Because of this, the derivative is

According to our question-

The tank's water volume, V, is as follows:

V=πr2h

When the height, h, of the water rising from the tank's bottom increases with time, t, and the radius, r=4ft, is constant.

Using the volume's first derivative, we obtain:

dVdt=πr2dhdt

How to solve for the height change over time:

dhdt=1πr2dVdt

dhdt=1π(4ft)2(24ft3min)

dhdt≈0.477ftmin

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The value of the surd when simplified is 1/6

We should recall that surd is the square root of all irrational numbers, simplification involves making it more simpler.

The given question is [tex]\frac{1}{(1-\sqrt{5 })^{2} } + \frac{1}{(1+\sqrt{5} )^{2} }[/tex]

We shall be simplifying the expression in parts

From difference of two squares

(1)/[(1-√5)(1+√5) = 1+5 = 1/6

The second part is 1/[(1+√5)(1+√5) = 1/(1+√10+5)

= 1/(6+√10)

Joining the two parts to get

1/6 + 1/(6+√10

Simplifying the fractions

(√10+1)/(6+√10)

= 1/6

Therefore the value of the expression is 1/6

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A₂ₓ₃ matrix and B₃ₓ₄ matrix, The dimension of the matrix AB obtained by multiplying A and B will be AB₂ₓ₄.

Matrices represent data in the form of rows and columns in an array form.

Suppose we have two matrices and their multiplication is possible only when the no. of columns in the first matrix is equal to the no. of rows in the second matrix.

Let A₂ₓ₃ matrix and B₃ₓ₄ matrix, Then the dimension of the matrix AB obtained by multiplying A and B will be AB₂ₓ₄.

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.

Answer:

Left shift, 6 units

Step-by-step explanation:

In the equation:

f(x)=3 |x+6| +9

the " +6 " in close to the x represents the horizontal shift. X always tells us about horizontal or right/left moves. So an adjustment to the x is a horizontal adjustment.

But Caution! It is the opposite of what you might think. A PLUS6 is a LEFT shift. (While a MINUS6 would be a right shift, not the case here).

The parent function is:

f(x) = |x|

So our equation:

f(x)=3 |x+6| +9

has two changes made to it. LEFT6 because of the

" +6 " by the x. And the +9 tacked onto the end of the equation is a vertical shift UP9.

He will spend 5 minutes bicycling at 11mph and 40 minutes bicycling at 15mph.

From the information, the person is planning to ride his bicycle for 45 minutes every day. He burns 6 calories per minute bicycling at 11 mph and 9.25 calories per minute bicycling at 15 mph

This will be illustrated as:

x + y = 45 ..... i

6x + 9.25y = 400 ..... ii

From equation i, x = 45 - y ..... iii

x = number of minutes cycling at 11mph

y = number of minutes cycling at 15mph

Put equation iii into ii

6x + 9.25y = 400

6(45 - y) + 9.25y = 400

270 - 6y + 9.25y = 400

3.25y = 130

Divide

y = 40

Since x + y = 45.

x = 45 - 50

x = 5

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A single statement that declares and initializes an array named a that has 10 elements of type int. is as:

int [] denominations = {10,20,30,40,50,60,70,80,90,100};

We know that there are two ways you can declare and initialize as array in Java.

The first with the new keyword, where you have to initialize the values one by one.

The second is by putting he values in curly brackets.

An Array is a collection of data of the same type. Arrays are an important part of the fundamental data structures in Java.

An Array is usually declared so you can have multiple values in the same memory.

The syntax for declaring an array is: datatype[] arrayName;

Datatype means the type of objects that will be stored in the array ed. int, char,etc.

You can declare an array of arrays by following the array declarator with a list of bracketed constant expressions.

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Angle θ in radians is 12/5 or 2.4 radians.

Define Arc Length

Arc length is more accurately described as the length along the perimeter of any circle or curve (arc). The arc length is the measurement of any distance along the curved path that forms the arc. Arc refers to a segment of a curve or the circumference of a circle. Each of them is shaped like a curve. An arc's length is more than the distance in a straight line between its endpoints (a chord).

Given,

radius = 5 cm

length of arc = 12 cm

We know that,

θ = length of arc / radius

Now, plug in the values

θ = 12 / 5 or 2.4 radians

Hence,angle θ in radians is 12/5 or 2.4 radians.

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Answer: 2.4

Step-by-step explanation:

radius = 5 cm

length of arc = 12 cm

θ = length of arc / radius

θ = 12 / 5 or 2.4 radians

2.4 radians

By "standard deviation", 30.62% the percentage of takeoff distances .

How to interpret a standard deviation?

The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.

                          Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

X ~ N ( µ = 628 , σ = 80 )

P ( 464 < X < 592 ) = ?

Standardizing the value

Z = ( X - µ ) / σ

Z = ( 464 - 628 ) / 80

Z = -2.05

Z = ( 592 - 628 ) / 80

Z = -0.45

P ( -2.05 < Z < -0.45 )

P ( 464 < X < 592 ) = P ( Z < -0.45 ) - P ( Z < -2.05 )

P ( 464 < X < 592 ) = 0.3264 - 0.0202

P ( 464 < X < 592 ) = 0.3062

               = 30.62%

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Answer:

$5.25 C

Step-by-step explanation:

17 student = $89.25

per student(1) = x

cross multiply

17x = $89.25

x = $89.25/17

x = $5.25

RATE AS BRAINLIEST

Answer:

5.25

Step-by-step explanation:

the person above is right

The Alternating Series Estimation Theorem to estimate the range of values of x for which the given approximation is ( -0.0654 , 0.0654 ) .

Given :

Use the Alternating Series Estimation Theorem to estimate the range of values of x for which the given approximation is accurate to within the stated error.sin x = x − x^3 / 6 ( | error | < 0.01 )

The next nonzero term in the Taylor series for sine is x^5 / 120 .

x^5 / 120 < .00000001

-0.00000001 < x^5 / 120 < .00000001

-0.0000012 < x^5 < .0000012

( -0.0000012 )^1/5 < x < ( .0000012 )^1/5

we have ( .0000012 )^1/5 ≈ .0654

= ( -0.0654 , 0.0654 )

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When a mass of 3 kg is hanged to it, the string will stretch 7.5 cm.

Given,

The length of the spring attached to the ceiling = 10 cm

The quantity of the mass hanged in the spring = 2 kg

The amount of stretching happened in the spring = 15 cm

We have to find the stretching of string when a mass of 3 kg is hanged to it;

Here,

Given that the force applied to the spring by the 2.0 kg is equal to the mass's weight:

F = mg = 2 kg × 9.8 m/s² = 19.6 N

Additionally, the stretching of:

Δx = 15 cm - 10 cm = 5 cm

So, applying Hooke's law:

F = kΔx

To determine the spring constant, k;

k = F/Δx = 19.6/5 = 3.92  N/ cm

The spring is now coupled to a new mass of m = 3.0 kg; the force this mass exerts on the spring equals

F = mg = 3 kg × 9.8 m/s² = 29.4 N

Thus, we may apply Hooke's law once more to determine the new stretching:

Δx = F/k = 29.4/3.92 = 7.5 cm

Therefore,

The string will be stretched 7.5 cm when a mass of 3 kg is hanged to it.

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The values of v for the electric impulse model in the Fitzhugh-Nagumo model are 0, 1, and a.

The strength of the field is shown by the distance between the lines; the closer they are to one another, the stronger the field.

In this scenario, the field weakens as we travel away from the charge because the distance between the lines widens (it actually obeys an inverse square law,

The electric field, which is pointed away from the core charge, is indicated by the direction of the lines.

This is due to the fact that a positive test charge would be repelled away from the electric field if it were placed there because the direction of the electric field corresponds to the direction of the force that a positive test charge would experience when immersed in the electric field.

Hence, The values of v for the electric impulse model in the Fitzhugh-Nagumo model are 0, 1, and a.

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Answer:

In this problem, we are looking for an equation in the form of y = mx + b that describes the situation where a bank puts $50 into a savings account when it is opened and 12 weeks later, the account has a total of $275.

To find the equation, we need to find the slope (m) and the y-intercept (b). The y-intercept is the point at which the line crosses the y-axis, which in this case is the initial amount of money in the account ($50). The slope is the rate at which the amount of money in the account is changing over time.

To find the slope, we can use the following formula:

slope = (y2 - y1) / (x2 - x1)

In this case, y2 is the total amount of money in the account after 12 weeks ($275), y1 is the initial amount of money in the account ($50), x2 is the number of weeks after the account is opened (12 weeks), and x1 is the number of weeks before the account is opened (0 weeks).

Plugging these values into the formula, we get:

slope = (275 - 50) / (12 - 0) = 225 / 12 = 18.75

Now that we have the slope, we can plug it into the equation y = mx + b, along with the y-intercept (b = 50), to get the final equation:

y = 18.75x + 50

This equation represents the situation described in the problem, where the bank puts $50 into a savings account when it is opened and 12 weeks later, the account has a total of $275.