How many ways can the train be made up?

The value of x when z is equal to 75 is [tex]$3\sqrt{75}$[/tex]

To calculate the value of $x$ when $z$ is equal to $75$, first rewrite the given proportionality as equations.

When x is directly proportional to [tex]$y^3$[/tex], the equation is given by:

[tex]$x = ky^3$[/tex]

where k is the constant of proportionality.

Similarly, when y is inversely proportional to [tex]$\sqrt{z}$[/tex], the equation is given by:

[tex]$y = \frac{m}{\sqrt{z}}$[/tex]

where m is the constant of proportionality.

Substituting the second equation into the first equation gives:

[tex]$x = k\left(\frac{m}{\sqrt{z}}\right)^3$[/tex]

Since the value of x is 3 when z is 12, the equation can be written as:

[tex]$3 = k\left(\frac{m}{\sqrt{12}}\right)^3$[/tex]

Rearranging gives:

[tex]$k = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}$[/tex]

Substituting this value of k into the original equation gives:

[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{m}{\sqrt{z}}\right)^3$[/tex]

Substituting z as 75 gives:

[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{m}{\sqrt{75}}\right)^3$[/tex]

Simplifying gives:

[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{\sqrt{12}}{\sqrt{75}}\right)^3m^3$$x = \frac{3m^3}{\left(\frac{m}{\sqrt{75}}\right)^3}$$x = \frac{3m^3\sqrt{75}}{m^3}$$x = 3\sqrt{75}$[/tex]

Therefore, the value of x  when z is equal to 75 is [tex]$3\sqrt{75}$[/tex].

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I’ve added my work attached :)
n = 250

The equation becomes true if we put brackets in the following way:

7x(5 - 2 + 3) = 42

Here we have the expression:

7x5 - 2 + 3 = 42

And we want to find where we need to put brackets in such a way that the equation becomes true.

If we solve the equation as it is, we will get:

7x5 - 2 + 3 = 42

35 - 2 + 3 = 42

36 = 42

Now, let's return to the equation:

7x5 - 2 + 3 = 42

If we put one pair of brackets that includes from the 5 to the 3, we will get:

7x(5 - 2 + 3) = 42

7x(4) = 42

42 = 42

So the equation becomes true.

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This is a symbol in mathematics that represents "to the power of" or "exponent".

It is used to indicate that a number or expression is being multiplied by itself a certain number of times. For example, if the expression 2aˆ3 is written, it means that 2 is being multiplied by itself 3 times, or 2x2x2. In other words, 2aˆ3 = 2x2x2 = 8.

The number to the right of the aˆ symbol is called the "exponent". The number or expression to the left of the aˆ symbol is called the "base". When a number is raised to the power of one, it is equal to itself. Any number to the power of zero is equal to one. The exponent can be a positive, negative, or fractional number.

Exponents are used to simplifying calculations and can be used to represent large numbers in a more concise form.

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Answer:

453

Step-by-step explanation:

To perform long division of 11,778 by 26, we follow these steps:

452

_____

26 ) 11,778

-104

------

157

156

----

21

Therefore, 11,778 divided by 26 is equal to 452 with a remainder of 21.

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Answer:

Sales = 20

Step-by-step explanation:

Simply make the equation "1300 = 65s" to solve the problem

1300 = 65s

Divide both sides by 65.

1300/65 = 65s/65

Divide 1300 by 65 to get 20.

20=s

Swap sides so that all variable terms are on the left-hand side.

s=20

Answer:

Step-by-step explanation:

Converting 0.632 to a fraction, Step-by-Step

Step 1:

The first step to converting 0.632 to a fraction is to re-write 0.632 in the form p/q where p and q are both positive integers. To start with, 0.632 can be written as simply 0.632/1 to technically be written as a fraction.

Step 2:

Next, we will count the number of fractional digits after the decimal point in 0.632, which in this case is 3. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 0.632/1 each by 10 to the power of that many digits. For instance, for 0.45, there are 2 fractional digits so we would multiply by 100; or for 0.324, since there are 3 fractional digits, we would multiply by 1000. So, in this case, we will multiply the numerator and denominator of 0.632/1 each by 1000:

\frac{0.632 × 1000}{1 × 1000} = \frac{632}{1000}

1×1000

0.632×1000

​

=

1000

632

​

Step 3:

Now the last step is to simplify the fraction (if possible) by finding similar factors and cancelling them out, which leads to the following answer:

\frac{632}{1000} = \frac{79}{125}

1000

632

​

=

125

79

​

In each of the cases, the series ∑an is convergent. This means that the limit of the sequence of partial sums of the series is finite.

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Joshua will need 7 additional customers.

The parameters that will help us to determine the number of customers is give as follows:

Joshua's goal is to sell more than 20 items at a farmers' market. So far, he has sold 6 items. Each customer buys 2 items.

Since Joshua's goal is to sell more than 20 items at a farmers' market and he has sold 6 items. and If each of his customers buys 2 items, the number of additional customers needed will be:

= (20 - 6) / 2

This is given as  14 / 2

The the number of customers needed = 7

In conclusion He will  need 7 additional customers.

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The constant of proportionality is 9 and equation of the proportion.

is y= 10x.

If the ratio of one variable to the other is constant, then there is a proportional relationship between the two variables. If x and y are in a proportional relationship, then the ratio of y to x is the constant of proportionality.

Given:

As, we know using the Constant of Proportionality

y = kx

or,  k = y/x  where k is Constant of Proportionality.

Then, from the table we have

k = 90/9

k= 10

Thus, y = kx

or, y= 10x

Hence, the equation of the proportion is y= 10x.

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Answer: 4k^7

Step-by-step explanation:

We can determine sin an in the above triangle using the available information without applying the Pythagorean theorem since the length of BC is required because it is the side opposite A.

We are told that we must calculate sin(a) without utilizing the Pythagorean theorem.

Now, we can see from the abbreviation SOHCAHTOA that if we wish to determine Sin a, it will be; sin a = opposite/adjacent

We must now locate a side opposing the angle A or the hypotenuse.

As a result, since the triangle is ABC, the required side is BC because it is the side opposite to A.

Finally, the length of BC is required because it is the side opposite A.

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The complete question should be like:

What additional information would be necessary to determine sin(A) without using the Pythagorean theorem? Explain.

Therefore , the solution of the given problem of expression comes out to be 794.0481.

combinations of numbers, symbols, and operations (such + and) that show how much something is worth. Examples: • 2 + 3 is the formula.

• 3 x/2 variable  is another formula.There is no equals sign in the expression. A mathematical expression is a sentence made up of variables, numbers, or both. There is never an equal symbol in an expression. These expressions are examples. An equation is a mathematical statement proving the equality of two expressions.

Here,

Given : 5 + [tex](5.3)^{4}[/tex]

=> 5 + (5.3)*(5.3)*(5.3)*(5.3)

=> 789.0481 + 5

=> 794.0481

Therefore , the solution of the given problem of expression comes out to be 794.0481.

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When an algorithm necessitates extensive sharing of instantaneous results, parallelism slows it down. Because there are multiple independent parallel processes and the right number of threads, parallelism will speed up an algorithm.

The ones with data dependencies are the most challenging. It will be exceedingly challenging, for instance, if you are dealing with a vector and the input for the computation at point n depends on the output at position n-1.

When this occurs, you must comprehend what the original algorithm is doing and take an alternative approach. For the aforementioned case, it might be a difficulty with digital signal processing including a feedback-containing digital filter. These are challenging to parallelize, but that is not the sole solution. Instead, you might use the filter and signal's fast Fourier transforms, multiply them, and then perform the inverse transform. All of these operations can be partially parallelized.

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Therefore , the solution of the given problem of standard deviation comes out to be 67.15=σx .

It tells about how  dispersed the data is is indicated by the standard deviation. It expresses the deviation of each observed variable from the mean. Any distribution will have roughly 95% of its values within two standard deviations of the mean.

Here,

We know population SD= Σ(xi-mu)2/n where mu is the population mean and n is the number of observation.

Here

we have n=7 and mu can be taken as x- =310.142

Standard deviation = SD=Σ(xi-mu)2/n

=>(Σxi2/n)-x-2

=>(704883/7)-(310.14)2=67.15=σx

Therefore , the solution of the given problem of standard deviation comes out to be 67.15=σx .

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22/154=11/77=1/7

1/7 is the lowest form

The equation of the ellipse with foci (0,14) and co-vertices at (±4,0) is [tex]x^2/16+y^2/36[/tex].

An ellipse is a geometric shape that is defined as the set of points such that the sum of the distances between the points and two fixed points (foci) is constant. It is a type of conic section and is defined by the equation:

[tex](x^2/a^2) + (y^2/b^2) = 1[/tex]

Where a and b are the semi-major and semi-minor axes, respectively. An ellipse can also be defined as the shape that results from the intersection of a plane and a cone at an angle that is not perpendicular to the base of the cone.

[tex]c=14, b=4, a²=b²+c²== > a=2√9\\x^2/b^2 + y^2/a^2\\x^2/16+y^2/36[/tex]

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The  polynomial Y⁴+ 4y²+ 5 does not have zeroes.

Polynomials are an essential component of the "language" of mathematics and algebra. They are used to express numbers as a result of mathematical operations in nearly every field of mathematics. Polynomials can also be used as "building blocks" in other kinds of mathematical expressions, such as rational expressions.

Polynomials can be used to represent a wide range of everyday mathematical processes. A polynomial can be formed by adding the costs of items on a grocery bill. A polynomial can be used to calculate the distance travelled by a vehicle or object. Polynomials can be used to calculate the perimeter, area, and volume of geometric figures. These are just a few of the many uses for polynomials.

We know that,   (a +b)² = a² + b² + 2ab

Here given that,

⇒ y⁴ + 4y² + 5 = 0

⇒ y⁴ + 4y² + 4 + 1 = 0

⇒ (y² + 2)² + 1 = 0

Because the first term is a square, the expression (y² + 2)² + 1  will never be zero for any value of y.

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a = [tex]6\sqrt{5}[/tex] is the right angled triangle's third side when the right angle triangle's opposite sides are 18 and 12, respectively.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

given

by pythagoras theorem

c2 = a2 + b2

18*18 = a2 + 12*12

324  - 144 = a2

a2 = 180

a = [tex]6\sqrt{5}[/tex]

a = [tex]6\sqrt{5}[/tex] is the right angled triangle's third side when the right angle triangle's opposite sides are 18 and 12, respectively.

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Answer:

Step-by-step explanation:

put (0, 125) in a*b^x, we get a = 125, then put (3,8) in 125*b^x, we get 125*b^3=8

b^3=8/125

b=2/5

then the answer is 125*(2/5)^x

Plotting a graph step by step is mentioned below.

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.

Using rectangular bars with heights or lengths proportionate to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

There are a few steps to follow when plotting a graph:

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Using Pythagoras theorem to solve the right angle triangle, the height of the building is 14.87 feet

Pythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as an equation:

x² = y² + z²

where x is the hypothenuse and y, z are the legs of the right angle triangle.

To determine the height of the building in which the ladder will reach, we have to use Pythagoras theorem for that.

x² = y² + z²

15² = 2² + z²

z² = 15² - 2²

z² = 221

z = √221

z = 14.87 feet

The height is 14.87 feet

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Here acccording to the question,We are examining the conditions under which the sampling distributions of the sample proportions given.

Sampling distribution is a statistic that determines the probability of an event based on data from a small group within a large population. Its primary purpose is to establish representative results of small samples of a comparatively larger population. Since the population is too large to analyze, you can select a smaller group and repeatedly sample or analyze them. The gathered data, or statistic, is used to calculate the likely occurrence, or probability, of an event.

We are examining the conditions under which the sampling distributions of the sample proportions appear uniform, roughly normal, skewed to the left or skewed to the right.

When np10 and n(1p)10, where n is the sample size and p is the sample of proportions, are true, we know that the sampling proportions of the sample distributions will have a normal shape.

Aforementioned that our sample size is 300 people and that p = 0.45, we can use the given data to calculate

Successes anticipated: np= 300(0.45) = 135 10

Failures predicted: n(1p)=300 (10.45)=165 10

Since both of these statements are accurate, sample distribution sampling proportions will have a normal shape.

Because we anticipate each sample to have at least 10 successes and 10 failures, we have a normal sampling distribution.

As a result, the sample distribution has a roughly normal shape.

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Answer:

The total cost of the science class trip to the zoo is $1200

Step-by-step explanation:

The cost of the science class trip to the zoo is $1200, and the cost of Mr. Sexton's class trip to the state park is $1000.

Therefore , the solution of the given problem of equation comes out to be  each diagonal measures 8.4 units in length..

An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra contains the fundamental concepts of mathematics.

Here,

Given: 16x + 2 = 36x - 6

8 = 20x

x = 8/20,

simplifying to 2/5, or 0.4

You would set the two equations equal to one another and find x because a rectangle's diagonals are congruent.

Re-enter the value of x into a single of the equations.

=>16(0.4) + 2

=>6.4 + 2

=>8.4

To make sure, confirm with the other diagonal.

=>36(0.4) - 6

=>14.4 - 6

=>8.4

Each diagonal measures 8.4 units in length..

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The complete question is "To find the diagonal  x value by the given equation  16x + 2 = 36x - 6 "

If pesos had it would be so pesos have 169.25 dollars left 200-30.75=169.25

The answer of the equation "2x^2 -  4x - 6 =  0" is -1 and 3.

The equation is solved using factorization:

2x^2 -  4x - 6 =  0        , given equation

2x^2 -  6x + 2x - 6 =  0     , factorizing

2x(x - 3) + 2 ( x - 3 ) = 0    , taking 2x common from the first two terms and 2 common from the last two terms

(2x + 2) (x - 3) = 0

now solving further

( 2x + 2 ) = 0   &   ( x - 3 ) =0

2x = (0 - 2)    ,          x  = (0 +  3)

2x = (-2)        ,         x = 3

x = (-2/2)

x = -1

Thus, the equation gives the solution as x = -1 and x = 3.

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Answer:16,777,216

Step-by-step explanation:

The interest rate is 2.5 %.

Simple interest is the form of interest used for short term loans, such as one receives at pawnshops or from loan sharks. It is governed by the formula:

I = Prt

where I is the amount of interest, P is the principal (amount of money borrowed), r is the interest rate (per year), and t is the time (expressed in years).

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

I = $25, P = $500, r = ?, t = 2 years

∴ I = Prt

∴ r = I / Pt

∴ r = 25 / ( 500 * 2)

∴ r = 25 / 1000

∴ r = 0.025

∴ r = 0.025 * 100 %

∴ r = 2.5 %

Therefore, the interest rate is 2.5 %.

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