A certain United States flag has a perimeter of 58 feet. The length of the flag is 9 feet longer

than the width. What are the dimensions of the flag?

Assuming segments that appear to be tangent are tangent, sqrt(277) = x has an estimated value of 16.64331698.

The Pythagorean Theorem, often referred as the Mathematics, is the fundamental Euclidean geometry relationship among the three sides of a right triangle. The area of a squares with the equilateral triangles side is the sum of the surfaces of square with the other two sides, according to this rule. The Pythagorean Theorem says that the square that spans a right triangle's hypotenuse opposite the perfect angle equals the sum of the squares that span its sides. It is sometimes written as the generic algebra notation a2 + b2 = c2.

given

14 is tangent to the circle and 9 is a radius, making this a right triangle.

In order to resolve this issue, we can employ the Pythagorean theorem.

a^2 +b^2 =c^2

9^2+14^2 =x^2

81+196 = x^2

277 = x^2

Taking the square root of each side

sqrt(277) = sqrt(x^2)

sqrt(277) =x

Assuming segments that appear to be tangent are tangent, sqrt(277) = x has an estimated value of 16.64331698.

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The number of blueberry muffins the baker makes on Tuesday is given by the equation A = 24 blueberry muffins

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of blueberry muffins the baker makes be A

Now , the equation will be

The total number of muffins the baker makes on Tuesday = 60 muffins

The percentage of blueberry muffins = 40 %

So ,

The number of blueberry muffins the baker makes A = total number of muffins the baker makes on Tuesday x percentage of blueberry muffins

Substituting the values in the equation , we get

The number of blueberry muffins the baker makes A = 60 x ( 40/100 )

On simplifying the equation , we get

The number of blueberry muffins the baker makes A = 60 x 0.4

The number of blueberry muffins the baker makes A = 24 blueberry muffins

Therefore , the value of A is 24

Hence , the number of muffins is 24

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Answer:

The value of x is 12.

i think it is correct.

value of x = 8 as per logarithm laws.

In mathematics, logarithm is an exponent or power for which a particular number is raised to achieve a required number. In other words, logarithm is a mathematical expression that states about how many times a number can be multiplied by the same number to get some required numbers.

The method of expressing any exponential relationship in the inverse form is called log notation.

In this question, we are given a log base 2 or binary logarithm.

given, ㏒₂ x = 3

     as per the logarithm laws ㏒a y = m

                                          y = a∧m

                               we write. ㏒₂ x = 3

                                                  x = 2³

                            hence, x = 8

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The amount that Cheryl left with is $ 1.9 or 1 dollar and 90 cents.

1. READ and reread the problem first

2. DRAW an image to illustrate the information. Ask your self Can I infer anything from this information during this step? What could I doodle? Which model will best convey the information? What inferences may I draw from the illustration?

3. WRITE the drawings as a basis for your conclusions. This can be expressed as a mathematical expression, an equation, or a statement.

Given that

Cheryl bought a sandwich for 5 1/2 dollars and a drink for $2. 60  

Here 5 1/2 = 11/2 = 5.5 dollars

Then the total cost of the sandwich and drink = $ 5.5 + $ 2.60 = $ 8.1  

Given that Cheryl gave $ 10

The amount that Cheryl left with = $ 10 - $ 8.1 = $ 1.9

Here is $ 1.9 = 1 dollar and 90 cents

Therefore,

The amount that Cheryl left with is $ 1.9 or 1 dollar and 90 cents.

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The graphic solution for each system of equations is given as follows:

20. (5/3, 28/3).

21. (0.205, 3.846).

22. (-1/2, -5/2).

23. (-4.615, 7.462).

The graphic solution of a system of equations is given by the point of intersection of all the equation that compose the system.

For this problem, the systems are composed by functions of the first degree, hence they are linear functions.

For each system, the graph is traced, and then the point of intersection is identified on the graph given at the end of the answer.

Each system is traced on a different color, as follows:

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Answer:

D

Step-by-step explanation:

A Gradient is also called a slope of a line, which represents how steep a line is.

Formula of slope: Vertical difference ÷ Horizontal difference

For a slope to be zero, the line must be horizontal.

Based on the question given, we can deduce that D is a horizontal line and therefore the slope is zero.

The length of XY, with the area of the rectangular surface of the prism 720 sq.cm, XX' 20 cm and XY : XZ: YZ = 5:3:4, is 12 cm.

Area of the rectangular surface of the prism = 720 sq. cm

XX' = 20 cm

XY : XZ: YZ = 5:3:4

As we know, area of prism = 3 × area of rectangle

⇒720 = 3 × area of rectangle

⇒area of rectangle = 720/3

⇒XY × XX' = 240

⇒XY × 20 = 240

⇒XY = 240/20

⇒XY = 12 cm

Thus, the length of the XY is 12 cm.

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Answer:

3/4

Step-by-step explanation:

Answer:

2/3 of a day

Step-by-step explanation:

3/4 : 1/2 = 1 : X

X=2/3

The value of the expression [tex]343^{-4/3}[/tex] is 1/2401.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

[tex]343^{-4/3}[/tex]

This can be written as,

1/[tex]343^{4/3}[/tex]

343 = 7³

= 1/[tex]7^{3\times4/3}[/tex]

= 1/[tex]7^4[/tex]

[tex]7^4[/tex] = 7 x 7 x 7 x 7 = 49 x 49 = 2401

= 1/2401

Thus,

The value of the expression is 1/2401.

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The velocity of an ant moving along the x-axis whose position is given by x(t) = 2cos(π/2 t^2) is v(t) = -πtsin(π/2 t^2) and acceleration is a(t) = -π²t²cos(π/2 t^2) - πtsin(π/2 t^2). The ant moves in right direction in the time interval [-1, 0) and changes direction at t = 0.

(a) To find the velocity of the ant at any given time t, we need to take the derivative of the position function x(t) with respect to t. The derivative of x(t) = 2cos(π/2 t^2) is:

v(t) = -πtsin(π/2 t^2)

So the velocity of the ant at time t is given by -2πsin(π/2 t^2)

(b) To find the acceleration at any given time t, we need to take the derivative of the velocity function v(t) with respect to t. The derivative of v(t) = -πtsin(π/2 t^2) is:

a(t) = -π²t²cos(π/2 t^2) - πtsin(π/2 t^2)

So the acceleration of the ant at time t is given by  -π²t²cos(π/2 t^2) - πtsin(π/2 t^2).

(c) To determine the values of t for which the ant is moving to the right, we need to look at the sign of the velocity function v(t) = -πtsin(π/2 t^2). Since the sine function oscillates between -1 and 1, this function will be positive when sin(π/2 t^2) is negative, and negative when sin(π/2 t^2) is positive. Moving rights means positive value of x.

Therefore, the ant is moving to the right when sin(π/2 t^2) < 0. That is

(π/2)t^2 < sin⁻¹(0)

sin⁻¹(0) = nπ, where n = ..., -2, -1, 0, 1, 2, ...

t is in interval [-1, 1] so π/2t^2 is in interval [0, π/2]

sin⁻¹(0) = 0

(π/2)t^2 < 0

Therefore t < 0

That is possible values of t is [-1, 0)

(d) To determine the values of t for which the ant changes direction, we need to look at the sign of the acceleration function a(t) = -π²t²cos(π/2 t^2) - πtsin(π/2 t^2).

When ant change direction a(t) = 0.

-π²t²cos(π/2 t^2) - πtsin(π/2 t^2) = 0

πtcos(π/2 t^2) + sin(π/2 t^2) = 0

sin(π/2 t^2) = -πtcos(π/2 t^2)

tan(π/2 t^2) = -πt

On solving possible values of t in the interval [-1, 1] is 0.

So, the ant changes direction when t = 0.

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Answer:

P=3000$

T=2 years

R=1.6% per annum

Now,

interest=(3000×2×1.6)/100=96$

Amount=P+interest=3096$

Hence,Conan needs to pay back 3096$ and the interest is 96$

Null hypothesis (H0): There’s no effect in the population. Alternative hypothesis (Ha or H1): There’s an effect in the population.

The null and alternative hypotheses are two opposing ideas that researchers use a statistical test to analyze evidence for and against: The null hypothesis (H0) states that there is no influence in the population. Alternative hypothesis (Ha or H1): There is a population effect.

Identify the null and alternative hypotheses.

As well as the sample size, specify.

Choose a suitable statistical test.

Gather information (note that the previous steps should be done prior to collecting data)

Based on the sample data, compute the test statistic.

Examine the null hypothesis, usually indicated by H0.

Always write the alternative hypothesis, which is usually marked by Ha or H1, with less than, greater than, or not equals symbols, i.e., (,>,or).

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The easiest way to find the slope of a line is converting the line equation into the slope-intercept form.

There are 3 forms of line equations:

- slope intercept form, the equation is given by:

 y = mx + b

Where:

m = slope

- point slope form, the equation is given by:

y − y₁ = m (x - x₁)

Where:

m = slope

- standard form: Ax + By = C

The easiest way to find the slope of a line is to convert it into a slope-intercept form.

Example:

Line equation in standard form:

2x + 4y = 6

We will convert it into  slope-intercept form.

4y = -2x + 6

y = (-2/4) x + 6

y =  (-1/2) x + 6

Hence, the slope is  (-1/2)

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The flux of F across S will be [tex]\frac{3\Pi}{2}[/tex]

A vector of magnitude 1 that is at some point perpendicular to a two-dimensional curve is referred to as the unit normal vector. Normally, you search for a function that returns not just one vector but all potential unit normal vectors of a given curve.

A vector that is perpendicular to a surface at a certain location is known as the normal vector, also referred to as the "normal" to a surface. The inward-pointing normal (pointing toward the interior of the surface) and outward-pointing normal are often distinguished when normals are taken into consideration on closed surfaces.

[tex]$Z_x=-2 x: \quad Z_y=-2 y$[/tex]

[tex]$N=\langle 2 x, 2 y, 1\rangle \quad: f=\langle x, y, z\rangle$[/tex]

[tex]f. $N=2 x^2+2 y^2+z=2 x^2+2 y^2+1-x^2-y^2$[/tex]

=1+x^2+y^2

[tex]x^2+y^2=1\\ \Rightarrow \quad x=r \cos \theta\\ \Rightarrow \quad y=r \sin \theta \\ \Rightarrow x^2+y^2=r^2 \\ 0 < r < 1: \quad 0 < \theta < 2 \pi[/tex]

[tex]$R \cdot v=\int_0^{2 \pi} \int_0^1\left(1+r^2\right)(r) dr d \theta$[/tex]

[tex]$=2 \pi \int_0^1 r+r^3 d r$[/tex]

[tex]$2 \pi\left[\frac{r^2}{2}+\frac{r^4}{4}\right]_0^1$[/tex]

[tex]$=(2 \pi)\left(\frac{1}{2}+\frac{1}{4}\right)$[/tex]

[tex]$=\frac{(2 \pi)(3)}{42}=\frac{3 \pi}{2}$[/tex]

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So, 600 full cup would be able to be filled from the cooler. This can be solved using the concept of volume of cylinder.

The three-dimensional form of a cylinder is made up of two parallel circular bases connected by a curving surface. The right cylinder is created when the centers of the circular bases cross each other. The measure of space within a cylinder is measured by its volume. Find it by dividing the base area by the height. V = πr²h is the formula for the volume of a cylinder with base radius "r" and height "h."

Given that,

diameter of cylinder = 30 inch

diameter of cup = 3 inch

height of cylinder = 24 inch

height of cup = 4 inch

Calculate the volume of the cylinder:

Volume = πr²h

putting the values we get:

Volume = (3.14)(30/2)²(24)

Volume = (3.14)(15)²(24)

Volume = (3.14)(225)(24)

Volume = 16959 in³

Calculate the volume of the cup:

Volume = (3.14)(3/2)²(4)

Volume = (3.14)(1.5)²(4)

Volume = (3.14)(2.25)(4)

Result

Volume = 28.26 in³

Divide the volume of the cylinder by the volume of the cup, we get:

Number of full cups =  16959 in³ /  28.26 in³

Number of full cups = 600

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The width and height of the rectangle for which the perimeter of the window will be as small as possible are (3sqrt(2), 2sqrt(2)).

What is the Lagrange multiplier?

The Lagrange multiplier, λ, measures the increase in the objective function (f(x, y) that is obtained through a marginal relaxation in the constraint (an increase in k). For this reason, the Lagrange multiplier is often termed a shadow price.

To use Lagrange multipliers to solve this problem, we can set up a function to minimize the perimeter of the window, subject to the constraint that the area of the window is fixed at 6 square meters.

Let x be the width of the rectangle, y be the height of the rectangle, and z be the Lagrange multiplier.

The function to minimize is the perimeter of the window, which is P = 2x + 2y + (2 * sqrt(x^2 + y^2))

The constraint is the area of the window, which is A = xy + (x * sqrt(x^2 + y^2))/2 = 6

The Lagrange equation is

L(x,y,z) = P + z(A-6) = 2x + 2y + (2 * sqrt(x^2 + y^2)) + z(xy + (x * sqrt(x^2 + y^2))/2 - 6)

To find the critical points, we will take the partial derivatives of L(x,y,z) with respect to x, y, and z, and set them equal to zero:

∂L/∂x = 2 + zy + zx * (x/sqrt(x^2 + y^2)) = 0

∂L/∂y = 2 + zx + zy * (y/sqrt(x^2 + y^2)) = 0

∂L/∂z = xy + (x * sqrt(x^2 + y^2))/2 - 6 = 0

Solving these equations simultaneously will give us the critical points of the function.

We will get two critical points (x,y) = (3sqrt(2), 2sqrt(2)), (0,2sqrt(2))

We should eliminate the point where x=0 as it does not fulfill the condition of the problem ( the width should be greater than 0)

Hence, the width and height of the rectangle for which the perimeter of the window will be as small as possible are (3sqrt(2), 2sqrt(2)).

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Therefore, for x = 45 and y = 20, the quadrilateral is a parallelogram.

In geometry a quadrilateral is a four-sided polygon, having four edges and four corners.

A polygon is a closed polygonal chain made up of a limited number of straight-line segments and is a type of planar figure in geometry. A polygon is an area that is bordered by a bounding circuit, a bounding plane, or both.

We know opposite sides of a parallelogram are equal in length and parallel. Given opposite sides of a parallelogram are:

(4x - 35) and (3x + 10)

(y + 15) and (2y - 5)

Now, setting those opposite sides equal to each other:

4x - 35 = 3x + 10 = >x = 45

y + 15 = 2y - 5 => y = 20

Therefore, x = 45 and y = 20, the quadrilateral is a parallelogram.

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The 3 horizontal line refers the equivalent relation.

The term horizontal line in math defined as a straight line that is mapped from left to right and it is parallel to the X-axis in the plane coordinate system.

Here have to find the meaning of 3 horizontal line.

As per the definition of horizontal line, the three horizontal line also known as triple line defines the equivalent relation of the term.

Here the equivalent that is not the same as 'equals'

Where the double bar is more common and generally implies equality on the other hand the triple bar or equal sign with three lines means congruent or, more generally, an arbitrary equivalence relation.

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Answer: B

Step-by-step explanation:

Area = 4 x 5

         = 20 cm^2

Remember that area of parallelogram is the base x perpendicular height. is The perpendicular height is not 6cm but 5cm. (right angle labelled on diagram)

Answer: 20 cm²

Step-by-step explanation:

area parallelogram = base x height

=> 4 x 5 = 20

The length of OP to the nearest tenth of a foot is 16.9 ft

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

ΔOPQ is right triangle

 Tan (p) = opposite/adjacent = OQ/PQ

Tan (76) =  OQ/4.1

4.010 = OQ/4.1

OQ = 4.010 * 4.1 = 16.441

OP² = OQ² + PQ² = 16.441 ² + 4.1² = 287.116

=> OP = √ 287.116 = 16.944

OP≅ 16.9 ft

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The number of machines to minimize the unit cost is 110 and minimum cost is 10,389 .

What is Quadratic Equation?

Quadratic equation can be defined as the equation which is in the form of ax^2 +bx +x = 0.

where a,b,c are constants.

Given ,

The standard form of a quadratic is given by:

ax^2 + bx + c

So for our function, we can say,

a = 0.1

b = -22

c = 11599

We can find the vertex (x-coordinate where minimum value occurs) by the formula -b/2a

So,

= -(-22) / 2*0.1

=22/0.2

= 110

Plugging this value into original function would give us the minimum (unit cost):

C(x) = 0.1 x ^2 - 22x +11599

C(x) = 0.1(110*110) - 22(110)+11599

C(x) = 110(11-22) + 11,599

C(x) = -11(110) + 11599

C(x) = -1210 + 11599

C(x) = 10,389

Hence , The number of machines to minimize the unit cost is 110 and minimum cost is 10,389 .

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Answer:

a: School W is has the most consistent attendance

b:  School W has the highest average attendance

Step-by-step explanation:

For a:

The most consistent school will be the school whose data has the smallest variance.  *Consistent doesn't mean the best, it's just the least differing among it's own data.  The variance tells us how spread out the data is, so the school with the smallest variance is the most consistent.  

See photo 1 for the calculations of the variances of each school...

For b:

Take the mean for each school.  Whichever has a higher value is the school with the highest average.  

See photo 1 for the calculations if the means for each school.  (the mean is used to calculate variance, so we will do this part first)

In linear equation, Ben is 9 years old currently.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

Ben's mom = 22 years

Ben is 9 years old currently.

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A particle takes 5 × 10^7 sec of time to travel a distance of 9.0 × 10^12 meters at a rate of 1.8 × 10^5 meters.

What is speed?

Speed indicates how quickly something or someone is moving. If one knows how far something has travelled and how long it took to get there, then one can calculate its average speed.

The particle travels at a rate of 1.8 × 10^5 m.

The particle travels a distance of 9.0 × 10^12 m.

Let the time taken for the particle to travel be x.

The formula for calculating the distance traveled by the particle is -

distance = rate × time

time = distance/rate

Plugging in the values in the equation -

x = 9.0 × 10^12/1.8 × 10^5

x = 9.0/1.8 × (10^12-5)

x = 5 × 10^7 sec

Therefore, the time taken by the particle to travel is 5 × 10^7 sec.

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The Equation for the value y is a. y = 21 + 0.25x (where x represents the number of weeks)

b. The value of the stock after 20 weeks would be 21 + (0.25 * 20) = $26.

This equation represents the linear relationship between the value of the stock (y) and the number of weeks (x). The value of the stock is initially $21, and it increases by $0.25 every week. This is represented by the coefficient of x (0.25) in the equation. By plugging in x=20 into the equation, we can find that after 20 weeks, the value of the stock would be $26. This is assuming that the rate of increase remains constant over time.

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Answer:

Step-by-step explanation:

91

As you can see 91 is the largest 2 digit multiple of 13 as the next multiple is 104 which is a 3 digit number.

N is the integer between {3,4,5}.so we can find all possible values of n is 2 and 8.

An integer is a whole number that can be positive, negative or zero. Examples of integers are -5, 1, 5, 8, 97, and 3,043.The integers are generated from the set of counting numbers and the operation.

Subtract the same number from both sides. Multiply both sides by the same positive number. Divide both sides by the same positive number. Multiply both sides by the same negative number and reverse the sign.

Now we solve

3n+4 <19

3n+4-4<19-4

3n<15

n<5

so n is less than and equal to 5 it will be {3, 4, 5].

10n/[tex]n^{2}[/tex]+16  >1

10n> [tex]n^{2}[/tex] +16

0> [tex]n^{2}[/tex]-10n +16

0>[tex]n^{2}[/tex] -8n -2n +16

0> n(n-8)-2(n-8)

0> (n-8) (n-2)

So         n-2<0          n-8<0

             n<2              n<8

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Answer: John is 29 years old and Jane is 36 years old.

Step-by-step explanation:

There are many parts to this problem, so let's start by defining John as x and Jane as y.

We know that the sum of their age 10 years ago was 55, which gives us x+y-10=55. The reason we put -10 is because of 10 years ago. If you think about it in terms of now, 10 years back is 55, so now they would be 65 years old. So we can have either x+y-10=55 or x+y=65. For simplicity, I will use x+y=65.

We also know that John is 7 years younger than Jane, which gives x=y-7.

Luckily, we have x defined for us, so we can directly substitute that into our equation.

[tex](y-7)+y=65[/tex]         [combine like terms]

[tex]2y-7=65[/tex]                [add both sides by 7]

[tex]2y=72[/tex]                      [divide both sides by 2]

[tex]y=36[/tex]

Now we know that y=36, we can plug that into either equations to find x.

[tex]x+36=65[/tex]                [subtract both sides by 36]

[tex]x=29[/tex]

This concludes that John is 29 years old and Jane is 36 years old.