If the length of one side of a square is increased by 20%, then the perimeter will increase by a) 5% b) 10% c) 20% d) 40% e) 80%

I think it is W(week)...........

Mean and Variance of the given table are 3.43672 and 7.837755 respectively.

What is probability ?

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

a)E(x) = ∑ xᵢp(xᵢ)

∑ xᵢp(xᵢ) = 1(0.3870) + 2(0.038062) + 3(0.0968) + 4(0.06913) + 5(0.0968) + 6(0.04846) + 7(0.01252) + 8(0.1935)

∑ xᵢp(xᵢ) = 3.43672

Mean = 3.43672

b) Variance = E(x²) - [E(x)]²

E(x²) = ∑ x²ᵢp(xᵢ)

∑ x²ᵢp(xᵢ) = 1²(0.3870) + 2²(0.038062) + 3²(0.0968) + 4²(0.06913) + 5²(0.0968) + 6²(0.04846) + 7²(0.01252) + 8²(0.1935)

∑ x²ᵢp(xᵢ) = 19.6488

∴ Variance = 19.6488 - (3.43672)² = 7.837755

Hence , Mean and Variance of the given table are 3.43672 and 7.837755 respectively.

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Answer:

9/

Step-by-step explanation:

As we have to multiply the fraction so we will multiply numerator with numerator and denominator with denominator we get 45/70. As we know both 45 and 70 are divisible by 5 and the simplest form answer we get will be 9/ 14

Answer:

slope = - [tex]\frac{1}{4}[/tex] , y- intercept = - 8

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

4y = - x - 32 ( divide through by 4 )

y = - [tex]\frac{1}{4}[/tex] x - 8 ← in slope- intercept form

with slope m = - [tex]\frac{1}{4}[/tex] and y- intercept c = - 8

The value of x will be;

⇒ x = 50

Parallel lines are those lines that are equidistance from each other and never intersect each other.

Given that;

Two parallel lines cut by a transversal.

Now,

Since, Two parallel lines cut by a transversal.

Hence, By definition of co-interior angle, we get;

The sum of co-interior angle in supplementary.

Hence, We get;

⇒ (2x + 10)° + (2x - 30)° = 180°

⇒ 4x - 20 = 180

⇒ 4x = 180 + 20

⇒ 4x = 200

⇒ x = 200/4

⇒ x = 50

Thus, The value of x = 50

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Answer:

Option A will be the cheaper plan for any daily mileage over 80 miles.

Step-by-step explanation:

The rate of vertical change is -0.4 m/s and the rate of horizontal change is -0.7 m/s.

       dy/dt = dy/dx * dx/dt

        y = 12 - √(12² - x²)

       dy/dx = x/(√(12² - x²))

       dy/dt = x/(√(12² - x²)) * (-0.7 m/s)

       dy/dt = 2√(35)/√(140) * (-0.7 m/s) = -0.4 m/s

       dx/dt = -0.7 m/s

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On solving the provided question we can say that - the linear equation of .25x + 3y = 1 +3 = 4

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation  two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

here, x= 4 and = 1

.25x + 3y

= 1 +3

= 4

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Answer:

The square root of -10 is already in the simplest radical form. Therefore, the answer is:

√10

-10 in simplest radical form is written as -√10.

Answer:

65 Adults and 106 children

Step-by-step explanation

a= adults

c= children

2.5a+1.5(171-a) =321.5

a=65

now we have the number of adults we minus that by the amount of people (171) to give us for the number of children and we get 106.

Answer:

She sold 8 bracelets

Step-by-step explanation:

I knew the number of bracelets would have to be an even number otherwise the total cost would have a decimal. Then I just went down the list doing 3.5*16 + 6*2, etc. until I got the answer (she sold 10 necklaces btw)

The system of equations that models the situation and can be used to get the prices is:

4*t + 7*b = $10

t + b = $4

We know that the variables that we will be using are:

First, we know that Owen spent $10 on 4 pieces of toast and 7 pieces of bacon, so we can write the equation:

4*t + 7*b = $10

And James spent $4 on 1 piece of each, then the other equation is:

t + b = $4

Then the system of equations that models this situation is the one we can make with these two equations:

4*t + 7*b = $10

t + b = $4

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The probability of getting 2 red marbles will be 0.298.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

In this case, there is a bag filled with 5 blue and 6 red marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced.

The probability of getting 2 reds will be;

= 6/11 × 6/11

= 0.298

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Statement correctly compares the values of the digit 4 in the numbers 3,245 and 8,407 are number 4 is in 10th place, and number 4 is in the 100th place respectively.

What are numbers?

A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that uses digits or symbols to represent them.

In mathematics, the first ten numbers are referred to as the fundamental numbers. These fundamental numbers are listed beginning at 0 and ending at 9. Basic numbers include 0 through 9 are 0, 1, 2, 3, 4, 5, 6, 7, and 8.

The given numbers are 3245 and 8407.

We have to find the place of 4 in the given numbers.

Consider, the number 3245.

In this number 4 is in 10th place.

Consider, the second number 8407.

In this number 4 is in the 100th place.

Hence, statement correctly compares the values of the digit 4 in the numbers 3,245 and 8,407 are number 4 is in 10th place, and number 4 is in the 100th place respectively.

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The factor of x3 5x2 2x 24 is (x - 4)(x + 2)(x + 6), which can be expanded as x3 + 2x2 - 4x2 + 6x - 8x - 24.

1. Factor out the greatest common factor (GCF) from the coefficients of the terms.

x3 5x2 2x 24

2. Factor out the GCF from each term:

x3 = x•x•x

5x2 = 5•x•x

2x = 2•x

24 = 24

3. Our factors are now:

x•x•x 5•x•x 2•x 24

4. Group the terms with common factors:

(x•x•x) (5•x•x) (2•x) (24)

5. Factor out the common factor from each group:

x•x (x•5) (2•x) (24)

6. Our factors are now:

x (x•5) (2•x) (24)

7. Factor out the common factor from each group:

x (x•5) (2•x) (24)

8. Our factors are now:

x (x + 2)(x + 6) (24)

9. Our final answer is:

(x - 4)(x + 2)(x + 6)

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The population in 123 years will be 5600000.

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. in this case, it is vital to note that they have at least two terms which have to be related by through an operator.

In this case, the city doubles its size every 41 years. If the population is currently 700,000. After 123 years, it'll have doubled 3 times.

The population will be:

= 700000 × 2³

= 5600000

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Answer: 5600000

Step-by-step explanation: I got it right on my ixl

Answer: 103.96

Step-by-step explanation:

Answer: 161

Step-by-step explanation: 23 + 3 times 46 (since the first 4 numbers are already there) is 161

All properties that apply to the differential equation dy/dx+sin²(x)y = cos²(x)y are following

(A) homogeneous

(B) ODE

(D) first order

(G) linear

(I) separable

Ordinary Differential equation: A differential equation consisting an unknown function and its derivatives with respect to a single independent variable.

Partial Differential equation: A differential equation consisting an unknown function and its partial derivatives with respect to a two or more independent variables.

First order Linear differential equation: The standard form of first order Linear differential equation is dy/dx + p(x)y = q(x)

and if q(x)=0, then this linear differential equation is homogeneous.

Separable Differential equation: A differential equation, y′ = f(x,y)

is said to be in separable form if the function f(x,y) can be written as

fx,y) = g(x)h(y). Now, we have an equation

dy/dx+sin²(x)y=cos²(x)y --(1)

As we see differential equation (1) contains derivative with respect to a single independent variable, x only, therefore this is an Ordinary differential equation. Also, the order of the differential equation (1) is one, i.e. first order differential equation. Now the given differential equation can be written as

dy/dx + ysin² x - ycos²x = 0

=> dy/dx − y(sin²x−cos²x) = 0

This is the standard form of first order Linear differential equation with q(x) = 0 . Therefore, there is not a candidate for integrating factors. The right side function is zero, therefore the the differential equation is homogeneous and dy/dx = y(sin²x−cos²x) = f(x,y)

= g(y) h(x) , so, it is a separable one . Hence, we check all properties for equation (1) .

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The submarine's final positions expressions are

Generally, An expression is a finite combination of symbols that is well-formed according to principles that rely on the context in which it is used. In mathematics, an expression is also known as a mathematical expression.

3F + 4A = -5 units

Working:

3 floats * -1 unit/float + 4 anchors * -1 unit/anchor

= -3 units + -4 units

= -7 units

3F - 4A = -5 units

Working:

3 floats * -1 unit/float - 4 anchors * 1 unit/anchor = -3 units - 4 units

= -7 units

F + 2A = -5 units

Working:

1 float * -1 unit/float + 2 anchors * -1 unit/anchor

= -1 units + -2 units

= -3 units

5F - A = -5 units

Working: 5 floats * -1 unit/float - 1 anchors * 1 unit/anchor

= -5 units - 1 unit = -6 units

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Multiply the central angle by the radius squared, and divide by 2: Sector Area = r² × α / 2.

To the nearest 10 square feet, what is the area of the 130° part covered by the sprinkler?

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Based on the graph which shows the relationship between pounds and euros, the value of a is €0 and the value of b is €1.45.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

In order to have a proportional relationship and equivalent ratios, the relationship between pounds (£) and euros (€) must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 1.45/1

Constant of proportionality (k) = 1.45.

When x = 0, the value of a is given by:

y = a = 1.45x

a = 1.45(0)

a = €0.

When x = 1, the value of b is given by:

y = a = 1.45x

b = 1.45(1)

b = €1.45.

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All the possible values of each expression is given as an inequality as;

1 < a/b < 5

We are given the inequalities of the domain and range as;

2 < a < 5

1 < b < 2

Thus, we can say that the maximum value of a/b will be the division of  the maximum value of a by the minimum value of b to give;

(a/b)max = 5/1

(a/b)max = 5

Similarly, minimum value of a/b will be the division of  the minimum value of a divide by the maximum value of b to give;

(a/b)min = 2/2

(a/b)min = 1

Thus, all possible values would be expressed as;

1 < a/b < 5

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The number of numbers that are greater than 4000 which can be formed using the digit 2,3,4,5,6 without repetition is 192.

We are having digits 2,3,4,5 and 6. Numbers greater than 4000 are to be formed using these digits without repetition.

The number can have 4 digits but greater than 4000 or can have 5 digits.

The total number of 4 digits number greater than 4000 is => 3*4P3 = 3*24 = 72.

Total number of 5 digits numbers = 5P5=5!=120

So, the Total number of required numbers =120+72=192

Hence, The number of numbers that are greater than 4000 which can be formed using the digit 2,3,4,5,6 without repetition is 192.

Complete question: Find the number of numbers that are greater than 4000 which can be formed using the digit 2,3,4,5,6 without repetition.

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According to the combination method, the number of formation using the digit 4 is 192

The term combination in math is called as the mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

While we looking into the four-digit has 4 digits and the first digit is the thousands place. Then the digits 2 and 3 are less than 4, here we know that they can't take the thousands place. Here we also know that the digit 4, 5, and 6 can take this place.

Here we have the remaining 4 numbers and the remaining three digits can be taken by any of them to form a number greater than 4000.

Then the number of ways is calculated as

=> 3×4×3×2 = 72

Then the number of 5 digit numbers greater than 4000.

Here we have to observe that all five-digit numbers are greater than 4000. And here we have 5 digits and hence the number of five-digit numbers is written as

=> 5×4×3×2×1 = 120

Then the total number of ways is calculated as

=> 72 + 120 = 192

Therefore the number of numbers that are greater than 4000 which can be formed using the digits 2, 3, 4, 5, 6 without repetition is 192.

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Using the provided equation of the ellipse as [tex]\frac {x^2}{49} + \frac {y^2}{64} = 1[/tex]  and comparing with the general form, The answer is (0,+- 3.87)

An ellipse is a geometric shape that is defined as the set of all points such that the sum of the distances from two fixed points (called the foci) is constant. It is a closed curve that is similar to a circle, but with a different shape. An ellipse can be defined by its semi-major and semi-minor axes, and its center. It is often used in mathematics and physics to describe the orbits of planets, moons, and other celestial bodies. The semi-major axis is the distance from the center of the ellipse to the longest point on the ellipse, and the semi-minor axis is the distance from the center of the ellipse to the shortest point on the ellipse.

The standard equation of an ellipse can be written as:

(x - h)^2/a^2 + (y - k)^2/b^2 = 1

where (h, k) is the center of the ellipse, and a and b are the semi-major and semi-minor axes, respectively. The semi-major axis is the distance from the center of the ellipse to the longest point on the ellipse, and the semi-minor axis is the distance from the center of the ellipse to the shortest point on the ellipse. The foci (plural of focus) of an ellipse are two points located inside the ellipse that are used to define its shape.

equation provided,

[tex]\frac {x^2}{49} + \frac {y^2}{64} = 1[/tex]

[tex]64x^2+49y^2-3136 = 0[/tex] is the general form.

foci = (0,+- 3.87)

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Answer:

foci (0 +- sqrt 15)

Step-by-step explanation:

This standard form is given. We are given [tex]a^{2}[/tex] = 64 and [tex]b^{2}[/tex] = 49. We need to figure out [tex]c^{2} =a^{2} -b^{2}[/tex]. Substitute 64 for a, and 49 for b.

[tex]c^{2} =64-49[/tex]

[tex]c^{2} =15[/tex]

Take the square root of both sides to get [tex]\sqrt{c^{2} } =\sqrt{15}[/tex].

[tex]c=\sqrt{15}[/tex]

This is a horizontal ellipse, so the x-values will be 0 for each focal point.

The foci are (0, ±[tex]\sqrt{15}[/tex])

The approximate length of the radius, r is 4.51 cm. SO the option 1 is correct.

In the given question we have to find the approximate length of the radius, r.

As given, circle O has a circumference of approximately 28.3 cm.

The calculation of the circle's boundary is referred as the perimeter or circumference of the circle. Although the circumference of the circle determines the space it occupies.

The circumference of a circle is its length when it's actually opened and represented as a single direction. Units like cm or unit m are typically used to measure it.

As we know that the formula of circumference of circle = 2πr

As circumference of circle = 28.3 cm

So 2πr = 28.3 cm

Divide by 2π on both side, we get

r = 14.15/π

π = 3.14

So r = 14.15/3.14

r = 4.51 cm

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The complete question is:

Circle O has a circumference of approximately 28.3 cm.

What is the approximate length of the radius, r?

a. 4.5 cm

b. 9.0 cm

c. 14.2 cm

d. 28.3 cm

The approximate length of the radius, r, is 4.5 cm.

The formula for calculating the radius, r, of a circle is r = C/2π, where C is the circumference of the circle. In order to calculate the approximate length of the radius, we must first calculate the circumference.

Let's assume that the circumference of the circle is 28.3 cm. To calculate the circumference, we can use the formula C = 2πr. We know the circumference and want to solve for the radius, so we can rearrange the formula to solve for r: r = C/2π.

Plugging in our values, we can calculate the approximate length of the radius: r = 28.3 cm/2π = 4.5 cm. Therefore, the approximate length of the radius, r, is 4.5 cm.

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Answer:

474.119 kilometers

Step-by-step explanation:

The class traveled 474.119 kilometers in total. You can find this by adding the distance traveled by train (471.459 km) to the distance traveled by bus (2.66 km).

471.459 + 2.66 = 474.119

Answer:

it means 3 weeks and time traveled

When a swimming coach needs to choose a team for a relay race then the number of ways they can arrange 444 of the 666 swimmers is 3.53×[tex]10^{1735}[/tex]

There are a total of 444[tex]C_{444}[/tex] (or 6.64 x [tex]10^{847}[/tex]) ways to select 444 swimmers from the pool of 666.

Once the swimmers have been chosen, they need to be arranged in a strategic sequence.

This can be done in 444! (or 5.34 x [tex]10^{906}[/tex]) ways.

Therefore, the total number of unique ways to arrange 444 of the 666 swimmers is

6.64 x [tex]10^{847}[/tex] x 5.34 x [tex]10^{906}[/tex]

3.53 x [tex]10^{1735}[/tex]

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The inverse of the given statement is if x does not equal 4 then 4x - 5 doesn't equal 11. Option C is the correct option.

What is a statement?

A statement in mathematics is a declarative utterance that can only be either true or false. A proposal is another name for a statement. It's important that there be no ambiguity. A sentence can only be true or untrue and not both for it to be a statement.

The given statement is if x equals 4, then 4x - 5  equals 11.

Each of the original statements' inverses is presumptive in the inverse statement.

The inverse statement of the given statement is if x does not equal 4 then 4x - 5 doesn't equal 11.

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