Order these numbers from LEAST to GREATEST.

Answer:

3.6 miles in 90 mins

Step-by-step explanation:

REMEMBER PROPORTIONS

SO IN THIS CASE THIS IS HOW YOU WRITE IT:

\(\frac{2 miles = 50 mins}{x=90 mins}\)

So this means in 50 minutes he covered 2 miles and in 90 minutes she covered x miles.

To find x cross multiply :

2 miles * 90 = 180 and x * 50 = 50x

That means 180 = 50x

Divide both sides by 50:

\(\frac{180}{50}\)=\(\frac{50x }{50}\)

3.6 = x

180 divided by 50 is 3.6 and 50x divided by 50 is x.

THUS HE TRAVELLED 3.6 MILES IN 90 MINUTES.

HOPE IT REALLY HELPED

HAVE A GOOD NIGHT/DAY

Therefore , the solution of the given problem of equation comes out to be 0.24(d−c) is the required equation.

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given :

$d dollar purchase price

Selling price = $c

25% commission rate

The difference between the selling price and the purchasing price is the profit.

=Buy price - Selling price =d - C

The commission is the result of the profit and the commission rate.

=> Profit = Commission rate * Profit

=> 24% * (d- c)

=>0.24×(d−c)

=> 0.24(d−c)

​

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The polynomial function is therefore a quadratic function with the formula (3x - 10)²/25 + 10.

Unlike the graph that depicts the stock market, the functions for roller coasters need to be smooth curves. The polynomial function\(f(x)= -0.000833^{(x3 + 12x2 -580x -1200)\) can be used to depict a simple rollercoaster.

According to the information provided, the original function was as follows: vertical stretch by a factor of 2 horizontal compression by a factor of 1/0.3 = 10/3 horizontal shift right by one unit.

Starting with a common function like f(x) = x², we can perform the following transformations:

Replace x with 3x/10 for the horizontal compression factor, and with 3x/10 for the horizontal shift to the right. Replace x with 3x/10 - 1 for the vertical stretch factor. Vertically move up 10 units by replacing y with 2y: y = 2y + 10.

When you combine everything, you get:

2 f(0.3x - 1) + 10

= 2 (2(3x/10 - 1)² + 10)

= (3x - 10)²/25 + 10

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To calculate the arc length of a circle, you need to use the formula: arc length = (central angle in radians) x (radius)

where the central angle is measured in radians and the radius is the distance from the center of the circle to the edge. To use this formula, first convert the central angle from degrees to radians by multiplying it by π/180. Then, multiply the result by the radius to find the arc length. For example, if you have a circle with a radius of 5 units and a central angle of 45 degrees, you can calculate the arc length as follows: Convert the central angle to radians: 45 x π/180 = 0.7854 radians. Multiply the central angle in radians by the radius: 0.7854 x 5 = 3.927 unit. Therefore, the arc length of a circle with a radius of 5 units and a central angle of 45 degrees is 3.927 units.

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The cost of Juan's South American stamps issued before the '70s is $10.

To determine the cost of Juan's South American stamps issued before the '70s, we need to consider the prices for stamps from Brazil and Peru, which are both South American countries. According to the information provided, stamps from Brazil and Peru cost 6 cents each.

Since the specific quantity of stamps is not given, we assume that Juan has an equal number of stamps from Brazil and Peru. Therefore, the cost of his South American stamps from these countries can be calculated as follows:

Cost of stamps from Brazil = 6 cents each

Cost of stamps from Peru = 6 cents each

Total cost of South American stamps = (Cost of stamps from Brazil + Cost of stamps from Peru) × Quantity

As the quantity is unknown, we cannot calculate the exact cost. However, the given answer options provide the closest approximation.

Looking at the answer options, the only option that falls within the range of the given prices is $10. Therefore, the cost of Juan's South American stamps issued before the '70s is $10.

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After the translation the coordinates of L' are (-3, 0) for the new triangle of U’M’L’.

The coordinates of triangle are-

U (-3, -4), M(-1, -1) , and L(-2, -5).

The triangle is translated 5 units up and 1 unit left to its original place.

Thus, for the 5 units up translation 5 units will get added to the y-coordinates.

New y-coordinate of L' is -5 + 5 = 0.

For 1 unit left , 1 units will get reduced from the original x-coordinate.

New x-coordinate = -2 - 1 = -3

Thus, the new coordinates L' becomes (-3, 0).

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The conditioning number of a matrix A is defined as the product of the norm of A and the norm of the inverse of A, divided by the norm of the identity matrix:

K(A) = ||A|| * ||A^(-1)|| / ||I||

If the conditioning number is high, it indicates that the matrix is ill-conditioned and small changes in the input can lead to large changes in the output.

In this case, we are given that K(A) = 5, and that:

A = [a 0 0; 0 1 0; 0 0 2]

To find the value of a, we need to calculate the norms of A and A^(-1). Since A is a diagonal matrix, its inverse is also a diagonal matrix with the reciprocals of the diagonal entries:

A^(-1) = [1/a 0 0; 0 1 0; 0 0 1/2]

Using the formula for K(A), we have:

K(A) = ||A|| * ||A^(-1)|| / ||I||

= ||A|| * ||A^(-1)||

Since the identity matrix has norm 1, we can drop the denominator. The norms of A and A^(-1) are given by the maximum absolute value of their singular values:

||A|| = max{|a|, 1, 2} = 2

||A^(-1)|| = max{|1/a|, 1, 1/2}

If a is positive, then the maximum is 1/a, so ||A^(-1)|| = 1/a. If a is negative, then the maximum is either 1 or 1/2, depending on the sign of 1/a. Therefore, we need to consider two cases:

Case 1: a > 0

In this case, we have:

||A^(-1)|| = 1/a

K(A) = ||A|| * ||A^(-1)|| = 2/a

Since K(A) = 5, we can solve for a:

2/a = 5

a = 2/5 = 0.4

Therefore, if a > 0, then the value of a that corresponds to K(A) = 5 is a = 0.4.

Case 2: a < 0

In this case, we have:

||A^(-1)|| = max{1, 1/2} = 1

K(A) = ||A|| * ||A^(-1)|| = 2

Since K(A) = 5, we can conclude that this case is not possible, and a must be positive.

Therefore, the value of a that corresponds to K(A) = 5 is a = 0.4, to three decimal places.

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Total savings after 7 weeks : $140

Total savings after w weeks : $(70 + 10w)

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a phrase : Taub is saving up to buy a new bicycle. She already has $70 and can save an additional $10 per week using money from her after school job.

Taub will have a total of -

70 + 7 x 10 = $140

The expression that represents the amount of money Taub would have saved in [w] weeks is -

y = 70 + 10w

Therefore -

Total savings after 7 weeks : $140

Total savings after w weeks : $(70 + 10w)

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If the utilization of an M/M/1 model is 0.6, the c of time there is at least one person in the system is 100%.

In an M/M/1 model, the utilization represents the ratio of the arrival rate (λ) to the service rate (μ). If the utilization is less than 1, it means that the arrival rate is lower than the service rate, and the system is not fully utilized. However, even with a utilization of 0.6, there will still be instances where there is at least one person in the system. This is because the arrival rate is not zero, indicating that customers are still arriving, albeit at a lower rate compared to the service rate. Therefore, the percentage of time with at least one person in the system would be 100%. If you are told that the utilization rate for an M/M/1 model is 0.8 and the average number of people in the system is 4, it is impossible to determine the average number of people in the queue without further information. The average number of people in the queue depends on factors such as the arrival rate and service rate, which are not provided in this scenario. The utilization rate alone and the average number of people in the system do not provide sufficient information to calculate the average number of people in the queue accurately. Therefore, it is impossible to determine the average number of people in the queue based solely on the given information.

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Based on the previous test scores, the conclusion is that you cannot enter the competition

The given parameters are

Previous test score = 91, 84, 76, 85

Worth of each test = 100

Goal = At least 440

Add up the previous test scores

So, we have:

Previous test score = 91 + 84+76+ 85

Evaluate the sum

So, we have

Previous test score = 336

Let the possible test score in the last test be x

So, we have the following equation

x + Previous test score = Goal

This gives

x + 336 = At least 440

Express as inequality

x + 336 >= 440

Evaluate the like terms

x >= 104

The highest score of a test is 100.

This means that you cannot score 104 in the last test

Hence, the conclusion is that you cannot enter the competition

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Answer:

32cm^3

Step-by-step explanation:

(4/3)*3*(2)^3=32

Answer:

Step-by-step explanation:

(a + b)(a - b) = a² - b²

\((7 + 4\sqrt{3}) (7 - 4\sqrt{3}) = 7^{2}-(4\sqrt{3} )^{2}\\\\ = 49 - 4^{2}*(\sqrt{3})^{2}\\\\= 49 - 16 * 3\\\\= 49 - 48\\\\= 1\)

\(\boxed{1}\) ✅

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\((7 + 4 \sqrt{3} ) \: (7 - 4 \sqrt{3} ) \\ \\ = 7 \: (7 - 4 \sqrt{3} ) + 4 \sqrt{3} (7 - 4 \sqrt{3} ) \\ \\ = 49 - 28 \sqrt{3} + 28 \sqrt{3} - 48 \: (since \: \sqrt{3} \times \sqrt{3} = 3)\\ \\ = 49 - 48 \\ \\ = 1\)

You can also use the identity:

( a + b ) ( a - b ) = \( {a}^{2} - {b}^{2}\)

\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}\)

When the bananas cost 3 IBS for $1.10, the cost for six Bananas is $2.20.

From the information, bananas cost 3 IBS for $1.10, In this his case, the first thing to do is to calculate the price for each. This will be:

= $1.10 / 3

= $0.367

Therefore the cost for six bananas will be:

= Cost for each banana × Number of banana

= $0.367 × 6

= $2.20

The cost is $2.20.

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The value of the integral ∫x²dV using cylindrical coordinates is 512π / 3 .

In this case, the solid is positioned between the cylinder x² + y² = 4 and will be evaluated by using the cone z²= 16x² + 16y² .

Cylindric coordinates will be used to calculate this integral  \(\int\limits_e {x^2} \, dx\).

The distance from the origin to the point (x, y, 0) and the angle the point (x, y, 0) makes with the x-axis, respectively, are provided by the formulas.

x = r cos θ

y= r sin θ

With these coordinates, we shall characterize the solid E.

The boundary is then x² + y² = r²

The boundary also becomes r² = 4 or ( 0 ≤ θ ≤ r² )

Again z = 16r²

The original integral must now be translated into terms of these new coordinates. It is necessary to multiply the function by the Jacobian of the change in coordinates in order to ensure that the result remains the same. The value for the cylindric coordinates is r. Then

\(\int_ex^2 dx = \int\limits^{2\pi}_0\int\limits^2_0\int\limits^{16r^2}_0 r(r^2cos^2\theta)dzdrd\theta\)

\(=\int _0^{2\pi }\int _0^216r^5\cos ^2\theta drd\theta\)

\(=\int _0^{2\pi }\frac{512}{3}\cos ^2\theta d\theta\)

= 512/3 π

Hence the volume of the solid that is enclosed by the integral is given by 512/3 π .

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Step-by-step explanation:

15x - 31 = 9x + 11

6x =42

x = 7

15(7) - 31 = 9(7) + 11

74 = 74

74 × 2 = 148

180-148=32

The possible lengths( in whole elevation) for the third side is

9 elevation< x< 45 elevation, i.e in between 9 and 45 elevation.

 For the below question, we've a rule from the properties of triangle, the sum of the length of any two  sides of the triangle must be lesser than the length of the third side.

Hence

She has two sides of length 18 elevation and 27 elevation

Let the third side = x

Hence

a) 18 27> x

45> x

b) 18 x> 27

x> 27- 18

x> 9

thus, the possible lengths( in whole elevation) for the third side is

elevation< x< 45 elevation

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Using complementary angles, it is found that the solution to the trigonometric equation is of x = 20.

Complementary angles are two angles whose measures add to 90º.

If two angles a and b are complementary, we have that the sine of one is the cosine of other, that is:

\(\sin{a} = \cos{b}\)

In this problem, the equation is:

\(\sin{(2x)} = \cos{(x + 30)}\)

Hence, they are complementary, which means that:

\(2x + x + 30 = 90\)

\(3x = 60\)

\(x = \frac{60}{3}\)

\(x = 20\)

The solution to the trigonometric equation is of x = 20.

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Answer:

C. 2 years

Step-by-step explanation:

Okay if you make $40,000 per year and are setting 20% aside each year you put $8,000 in your emergency fund (multiply 40k by 0.2 to get 20% of it). 8k times 2 is 16k (your goal), so it takes 2 years to reach that.

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Given:

\(0.5(4x-8)+11=0.25(12x+20)-5\)

To find:

The value of x.

Solution:

We have,

\(0.5(4x-8)+11=0.25(12x+20)-5\)

Using distributive property, we get

\(0.5(4x)+0.5(-8)+11=0.25(12x)+0.25(20)-5\)

\(2x-4+11=3x+5-5\)

\(2x+7=3x\)

Subtract 2x from both sides.

\(7=3x-2x\)

\(7=x\)

Therefore, the value of x is 7.

Whave established that the series l~=l an - z converges uniformly for Re(z) ≤ c

What is uniformly?

The keyword "uniformly" refers to the concept of uniform convergence. In the context of the given question, it is stated that the series l~=l an - z converges uniformly for Re(z) ≤ c. Uniform convergence means that the convergence of the series is independent of the value of z within a certain range (Re(z) ≤ c in this case).

To show that the series l~=l an - z converges uniformly for Re(z) ≤ c, where an is a bounded sequence of complex numbers and we choose the principal branch of n - z, we need to demonstrate that for any ε > 0, there exists an N such that for all n > N and for all z with Re(z) ≤ c, the inequality |l~=l an - z| < ε holds.

Given that an is a bounded sequence, there exists an M > 0 such that |an| ≤ M for all n.

Let's consider the series l~=l an - z. We can write it as:

l~=l an - l z.

Now, since |an| ≤ M for all n, we have:

|an - z| ≤ |an| + |z| ≤ M + c.

By choosing N such that M + c < ε, we can ensure that for all n > N and for all z with Re(z) ≤ c, the inequality |an - z| < ε holds.

Now, using the triangle inequality, we have:

|l~=l an - z| ≤ |an - z|.

Since we have shown that |an - z| < ε for n > N and Re(z) ≤ c, it follows that |l~=l an - z| < ε for n > N and Re(z) ≤ c.

Therefore, we have established that the series l~=l an - z converges uniformly for Re(z) ≤ c.

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Given the following quadratic functions

[] y^2 + 12y - 36

[] x^2 + 121

[] x^2 - 6x + 9

[] y^2 - 64

[] 9x^2 - 121

[] 4y^2 + 20y + 25

We need to categorize them as perfect square trinomial, difference of squares, or neither

For the quadratic function y^2 + 12y - 36, 9x^2 - 121, 4y^2 + 20y + 25, and x^2 + 121, they are neither since there are no factors

For the function x^2 - 6x + 9

x^2 - 6x + 9

x^2 - 3x - 3+ 9

x(x-3)-3(x -3)

(x-3)(x-3)

(x-3)^2

This is  a perfect Square Trinomial

For the function y^2 - 64

y^2 - 8^2

(y-8)*(y+8)

This is a difference of squares.

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\(Hey\) \(there!\)

The best and most correct answer among the choices provided is D, because if you did that it would completely cancel out the \(y\)'s and leave you with \(x\).

Hope it helps and have a great day!

The statement which shows whether this graph shows a proportional relationship is: B. Yes, it is proportional because it is a line that intersects with the origin.

A graph can be defined as a type of chart that's commonly used for the graphical representation of data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In Mathematics, the graph of any proportional relationship is typically characterized by a straight line with the points passing through the origin (0, 0) because as the values on the x-coordinate decreases or increases, the values on the y-coordinate decreases or increases simultaneously.

In this context, we can reasonably infer and logically deduce that this graph shows a proportional relationship.

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Answer:

b<11=board is shorter then

b>11=more then 11 books

b<12=fewer then 12

b>12=taller then 12

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we have a 18 -gon

Its a regular polygon with 18 congruent sides and 18 congruent angles

step 1

Find the measure of each interior angle

we know that

the sum of the interior angles in any regular polygon is equal to

where

n is the number of sides

so

for n=18

substitute

Divide by the number of sides n

the measure of each interior angle is 160 degrees

Step 2

Find the measure of each exteriior angle

Remember that the sum of the interior angle and the exterior angle is equal to 180 degrees

therefore

the measure of each exterior angle is equal to 20 degrees

The measure of the angle opposite the longest side is approximately 56.32 degrees.The measure of the angle opposite the longest side of a triangle can be found using the Law of Cosines.

In this case, the sides of the triangle are given as 13 ft, 15 ft, and 11 ft. To find the measure of the angle opposite the longest side, we can apply the Law of Cosines to calculate the cosine of that angle. Then, we can use the inverse cosine function to find the actual measure of the angle.

Using the Law of Cosines, the formula is given as:

\(c^2 = a^2 + b^2 - 2ab * cos(C)\)

Where c is the longest side, a and b are the other two sides, and C is the angle opposite side c.

Substituting the given values, we have:

\(13^2 = 15^2 + 11^2 - 2 * 15 * 11 * cos(C)\)

169 = 225 + 121 - 330 * cos(C)

-177 = -330 * cos(C)

cos(C) = -177 / -330

cos(C) ≈ 0.5364

Using the inverse cosine function, we find:

C ≈ arccos(0.5364) ≈ 56.32 degrees

Therefore, the measure of the angle opposite the longest side is approximately 56.32 degrees.

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2x³ + XY is a binomial with a degree of 3

An algebraic expression containing only two terms is called a binomial. This is a binomial polynomial. It is also called the sum or difference of two or more monomials. This is the simplest form of a polynomial. A binomial is a polynomial with only terms. For example, x 2 is a binomial where x and 2 are two separate terms. Also, the coefficient of x is 1, the exponent of x is 1, and 2 is a constant here. Therefore, an A-binomial is a two-term algebraic expression that contains a variable, a coefficient, an exponent, and a constant.

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