the cruising speed of the bullet train will be in excess of 150 miles per hour. use s to represent the train's cruising speed (in miles per hour).

The 2.5kg of potatoes cost £1.40 so the cost of 4.25 kg of potatoes is £2.38.

A cost is an outlay needed to create, market, or prepare an asset for regular use. In other words, it's the cost incurred to produce a good, buy inventory, sell goods, or prepare equipment for use in a business process.

Given,

2.5 kg of potatoes = £1.401 kg of potatoes

cost = 1.40/2.5

       = £0.56

To find the cost of 4.25 kg of potatoes is: Then,

1 kg = £0.564.25 kg

      = 0.56 x 4.25

      = £2.38

Thus from the above conclusion we can say that the cost is £2.38.

To know more about calculating cost visit here: https://brainly.com/question/11871927

#SPJ1

To solve the inequality 4y>12 we use the multiplication or division property of inequality

a relationship between two expressions or values that are not equal to each other is called 'inequality.

Given that Stuart solves the inequality 4 y greater than 12

We can write this as 4y>12

Then in the next step is y>3

We need to find which step is used in second step.

As Four times of y is greater than 12.

4y>12

When we divide both sides by 4 we get 3

y>3

Hence, multiplication or division property of inequality is used to solve the inequality.

To learn more on Inequality click:

https://brainly.com/question/28823603

#SPJ1

Answer: $79.79

Step-by-step explanation:

First, take 899 divided by 100% = 8.99

Then take 8.99 times 8.875 = $79.79

Answer:

Below

Step-by-step explanation:

8.875 % is .08875 in decimal form:

899 * .08875 = 79.79 dollars

The statement that correctly compares the function of the given graph with the function y = 2x - 5 is; Option C: The function shown on the graph has a greater rate of change and a higher starting point.

The rate of change of function is defined as the change in the value of the function with respect to x value.

Rate of change of function f(x) is;

f'(x) = df(x)/dx

The given function is;  y = 2x - 5

Thus;

Rate of change of function = f'(x) = df(x)/dx = dy/dx = d(2x - 5)/dx = 2

The starting point of the function f is the y-intercept of the function.

The y-intercept of the function is the point where the function touches the y-axis which can be calculated by putting x value is equals to 0.

Thus; y = 2*0 - 5

y= -5

The starting point of function is -5.

Slope = (y intercept)/(x - intercept)

Slope = 4/1 =4

Thus, the rate of change of the graph = slope of the graph= 4

The y-intercept of the graph is equal to the starting point of the graph which is -5

Read more about graph of linear functions at; https://brainly.com/question/4025726

#SPJ1

Answer: The correct answer is b

Step-by-step explanation:

25% off $30 is 22.50 and then when you add 7%ax it turns out to be 24.08

Null Hypothesis that is, the average errors for two processes differ significantly.

Two options being the same is the null hypothesis in inferential statistics. That the observed discrepancy is solely the result of chance is the null hypothesis. Calculating the probability that the null hypothesis is correct using statistical testing is achievable.

Always indicate the "null hypothesis" with an equal sign, and the alternative with a less-than, greater-than, or not equal sign. The researcher is looking for evidence that the two methods/processes produce different average errors since this alternative statement contains the not equal to symbol.

Hence, the correct pair of “null and alternative” hypotheses is given by,

[tex]Null Hypothesis(H0): UA = UB versus\\ H1: UA \neq UB; that is, the average .errors. for .two .processes .differ .significantly.[/tex]

[tex]"H0: UA = UB H1: UA \neq UB"[/tex]

To know more about null hypothesis visit:

https://brainly.com/question/28920252

#SPJ4

The values for a and b in the expression for the area of the rhombus, a·√b, where the area of the regular hexagon that forms the rhombus that has an area of 24·√3, are; a = 8, b = 3

a + b = 8 + 3 = 11

A rhombus is a quadrilateral in which the length of the each of the four sides are the same.

Coprime integers integers are two integers that have 1 as their only common divisor

The area of the hexagons = 24·√3

The formula for the area of regular  hexagon, A = 3·√3×s²/2

Where;

s = The sider length of the regular hexagon

Therefore; 24·√3 = 3·√3×s²/2

The division property indicates that dividing booth sides of the above equation by √3, we get;

24 = 3×s²/2

2 × 24/3 = s²

16 = s²

s² = 16 (symmetric property)

s = ±√(16) = ±4

The possible value for the side length of the regular hexagon is +4

The formula for the area of a rhombus = s²·sin(θ)

Where;

θ = The interior angle of a regular hexagon = 120°

Therefore; A = 4² × sin(120°) = (16 × √3)/2 = 8·√3

Therefore; a·√b = 8·√3

a = 8, b = 3

a + b = 8 + 3 = 11

Learn more on the area of a rhombus here: https://brainly.com/question/12173486

#SPJ1

the sum of yhe age ofa father and his son us 50 years if the ages of the is 10 years. find the age of the father

Solution of 8^x=1000 is x ≈ 3.322 .

Use the

law of logarithms

[tex]log x^{n} = nlogx[/tex]

The word algorithm does not appear in data protection law. But an algorithm often results in an automated decision (or algorithmic decision making). It is code that decides something. There is a law that deals with automated individual decision-making and this is very relevant to algorithms.

An algorithm is a set of rules or a computational procedure that is typically used to solve a specific problem.

Applies to logarithms to any base.

Take the ln ( natural log) of both sides.

log 8^x = log 1000

An algorithm is a procedure used for solving a problem or performing a computation. Algorithms act as an exact list of instructions that conduct specified actions step by step in either hardware- or software-based routines. Algorithms are widely used throughout all areas of IT.

Using the above law

x log 8 = log 1000

dividing both side by log 8

[tex]\frac{xlog8}{log8} = \frac{log1000}{log8}[/tex]

x = ㏒8 (1000)

[tex]log_{a} b = \frac{log_{c}b }{log_{c}a }[/tex]

[tex]x = log_{10} 1000/log_{10} 8[/tex]

x ≈ 3.322  to 3 decimal places

To learn more about Law of Algorithms visit:

brainly.com/question/29316461

#SPJ4

On solving the provided question, we got to know that 91/4 feet is the vertical distance that ball traveled.

What is equation?

An equation in algebra is a formula that proves two other formulas are equivalent. For instance, the equation 3x + 5 = 14 is produced when the two equations 3x + 5 and 14 are combined with an equal sign. Mathematical equations in algebra frequently have one or more variables.

If the balls land in a straight line:

dropped = 13 ft

rebounds 3/4 (13) ft  = 39/4 ft

vertical travel = 13 + 39/4 = 91/4 ft

To know more about equation visit:

https://brainly.com/question/649785

#SPJ4

Answer:

13

Step-by-step explanation:

1. convert percent into decimal

12.5% = 0.125

2. find the product

0.125 * 104 = 13

The number 13 is 12.5 percent of 104.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means.

Let x be 12.5% of 104.

Here, 12.5% of 104 =x

x= 12.5/100 ×104 (The word "of" means multiplication)

x= 0.125×104

x= 13

Therefore, 13 is 12.5 percent of 104.

To learn more about the percentage visit:

brainly.com/question/24159063.

#SPJ2

Answer:

f(-1)= -1

Step-by-step explanation:

put -1 where x is

f(x)=3x+2;f(-1)

f(-1)=3(-1)+2

f(-1)= -3+2

f(-1)= -1

The linear equation to model the scenario -

For the stated question;

Let the side of the equilateral triangle be 'x'.

Then,

Perimeter of the equilateral triangle = x + x + x

Perimeter of the equilateral triangle P = 3x

Now,

One side of rectangle = side of equilateral triangle = x.

Second side of rectangle = 6 + side of equilateral triangle = 6 + x.

Perimeter of the rectangle P = x + x + 6 + x + 6 + x

Perimeter of the rectangle P = 4x + 12

Thus, linear equation to model the scenario -

To know more about the linear equation, here

https://brainly.com/question/2030026

#SPJ1

The percent increase of the trees is 50%

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

Initial = 2 feet

Final = 3 feet

The percent increase can then be calculated using

Percentage increase = (Final length - Initial length)/Initial length * 100%

Substitute the known values in the above equation, so, we have the following representation

Percentage increase = (3 - 2)/2 * 100%

Evaluate

Percentage increase = 50%

Hence, the percentage increase is 50%

Read mroe about percentage increase at

https://brainly.com/question/11360390

#SPJ1

The probability to win the game is 4/7.

Clearly, you can not win with zero dollars:

Pr(W|S0)=0

and you cannot lose with three dollars:

Pr(W|S3)=1

If you start with two dollars, then the probability of winning is:

Pr(W|S2)=Pr(S1|S2)Pr(W|S1)+Pr(S3|S2)Pr(W|S3)=1/3×Pr(W|S1)+2/3

If you start with one dollar, then the probability of winning is:

Pr(W|S1)=Pr(S2|S1)Pr(W|S2)+Pr(S0|S2)Pr(W|S0)=2/3×Pr(W|S2)

So, we have two equations in two unknowns:

Pr(W|S1)=2/3×Pr(W|S2)

Pr(W|S2)=1/3×Pr(W|S1)+2/3

Solving them we get:

Pr(W|S1)=4/7

Pr(W|S2)=6/7

So, your chance of winning when you start with one dollar is 4/7.

Learn more about Probability here:

brainly.com/question/24756209

#SPJ4

The mean yield for the three temperatures are equal.

Temperature is a unit used to express how hot or cold something is. It can be expressed using the Celsius or Fahrenheit scales, among others. Temperature shows which way heat energy will naturally flow, i.e., from a hotter (body with a higher temperature) to a colder (body with a lower temperature) (one at a lower temperature).

Given:

Number of groups [tex]k=3[/tex]

Number of observation in group 50°C, [tex]n_{1} =5[/tex]

Number of observation in group 60°C, [tex]n_{2} =5[/tex]

Number of observation in group 70°C, [tex]n_{3} =5[/tex]

Total number of observation [tex]N=15[/tex]

Null hypothesis [tex]H_{0}[/tex] :

The mean yield for the three temperatures are equal.

Alternative hypothesis [tex]H_{1}[/tex] : The mean yield for the three temperatures are not equal.

Now, Sum of the squares of between groups:

⇒∑  [tex]n_{i} (X_{i} -X)^{2}[/tex]

Here, [tex]X_{i}[/tex] is the mean of the jth group, [tex]X[/tex] is the overall mean and [tex]n_{1}[/tex] is the sample size of the jth group.

[tex]X=\frac{X_{1} +X_{2}+...+X_{i} }{i}[/tex]

[tex]X_{1} =34+24+36+39+32=165\\X_{2} =30=31+34+23+27=145\\X_{3} =23+28+28+30+31=140[/tex]

[tex]X_{i} =\frac{X_{i} }{n_{i} }[/tex]

⇒ [tex]X_{1} =\frac{165}{5} =33[/tex]

⇒ [tex]X_{2} =\frac{145}{5} =29[/tex]

⇒ [tex]X_{3} =\frac{140}{5} =30[/tex]

[tex]=n_{1} (X_{i} -X)^{2}+n_{2} (X_{2} -X)^{2}+n_{3} (X_{3} -X)^{2}[/tex]

SSB= 5 × [tex](33-30)^{2}[/tex]+ 5 × [tex](29-30)^{2}[/tex] + 5 × [tex](28-30)^{2}[/tex]

      = 5 × [tex]3^{2}[/tex] + 5 × [tex]1^{2}[/tex] + 5 × [tex]2^{2}[/tex]

      = 5 × 9 + 5 × 1 + 5 × 4

      = 45 + 5 + 20

      = 70

Now, Sum of difference between each element and grand mean squared (SST)

⇒ [tex](34-30)^{2} +(34-30)^{2}+(36-30)^{2} +...+(31-30)^{2}[/tex]

⇒ 306

Now, SSE = SST - SSB

= 306 - 70 = 236

Therefore,

Source of         Sum of                 Degrees of                   Mean

variation         squares             freedom                    square

Between      [tex]SSB=70[/tex]           [tex]df_{1} =k-1=2[/tex]            [tex]MSB=\frac{SSB}{df_{1} } =\frac{70}{2} =35[/tex]          

groups

Error    [tex]SSE=236[/tex]        [tex]df_{2} =N-k=12[/tex] [tex]MSE= \frac{SSE}{df_{2} } =\frac{236}{2} =19.67[/tex]                                          

Total                [tex]306[/tex]

Given .05 level of significance. i.e, [tex]F(0.05,2,12)=3.8853[/tex] tabulated value.

As [tex]1.7794 < 3.8853[/tex], tabulated value is higher than calculated value.

So, the null hypothesis is accepted.

Hence, the mean yield for the three temperatures is equal.

Learn more about temperatures

https://brainly.com/question/24746268

#SPJ4

On September 16, 2011, U.S. President Barack Obama approved the Leahy-Smith America Invents Act (AIA). The AIA changed U.S. Patent law from a first-to-invent system to a first-to-file one following years of dispute.

The first inventor of the claimed invention may be given a patent, according to long-standing U.S. patent law. The goal of this rule was to provide equal opportunity for small businesses to compete with "the big dogs" in the field of developing technology.

The argument was that these tiny, occasionally one-person operations lacked the legal infrastructure required to prepare and submit patent applications in a timely manner. The costs of establishing inventorship in front of the U.S. Patent and Trademark Office (USPTO) or federal judges may have, regrettably, outweighed the advantages of the first-to-invent system. In order to prove their claims in one forum or another, the creators of competing technologies ultimately had to navigate a maze of rules and standards. These legal actions were expensive for many small businesses.

To read more about US patent law:

https://brainly.com/question/12358486

#SPJ4

On solving the provided question we got to know that, favorable cases for X4 to be the least  is that = 0.25

Probabilities are mathematical justifications of the probability that an event will happen or that a proposition is true. A number between 0 and 1, where 0 often indicates impossibility and 1 normally indicates certainty, denotes the likelihood of an event.

[tex]X1, \\X2, \\X3[/tex]

can be arranged in 3! Ways so, in tottal  6 ways

[tex]Hence, there are 6 cases where X4 is the lowest.[/tex]

Total no. of cases on which [tex]X1, X2, X3, X4[/tex] be  arranged are  4! = 24

Favorable cases for [tex]X4[/tex] to be  the least = [tex]6/24 = 1/4 = 0.25[/tex]

To know more about probability visit:
https://brainly.com/question/11234923

#SPJ4

Answer:

It's the digit 3.

Step-by-step explanation:

Since all digits from 33 to 38 are digits not less than 3, it follows that in the result there will be at least one digit bigger than 3. Since 33 to 38 represent a set with six numbers, we can conclude that the product of those numbers must have at least six digits to the left of the decimal, which is the ones place. Therefore, the digital 3 gets into the ones place.

Answer:

The first expression to represent the new price of an item after the markdown would be:

new price = d * (1 - 0.70)

This expression uses the original price (d) and multiplies it by (1 - 0.70), which is equal to 0.30. This results in the new price being equal to 30% of the original price.

Another way to write this expression would be:

new price = d - (d * 0.70)

This expression also uses the original price (d) and subtracts from it the product of the original price and 0.70. This also results in the new price being equal to 30% of the original price.

Step-by-step explanation:

The Binomial expansion of given expression, (1+x)⁻¹ is 1 − x + x² - x³+ x⁴ + ...

Binomial theorem primarily helps to find the expanded value of the algebraic expression of the form (x + y)ⁿ

Using the Binomial theorem we can expand the series of ( x + y )ⁿ as

( x + y)ⁿ = ∑ ⁿCₖ xⁿ⁻ᵏ yᵏ

k= 0 to n

= xⁿ + (n(n-1)/2!)x⁽ⁿ⁻¹⁾y + (n(n-1)(n-2)/3!)x⁽ⁿ⁻²⁾y² + .......

where n ≥ 0 and (ⁿCₖ ) is known as a binomial coefficient and they should be positive integers.

We have given that (1+x)⁻¹ comparing it with ( x + y )ⁿ we get, y = 1 ; n = -1

Binomial expansion for this is followed the same way as expanding larger power expansion,

So (1+x)⁻¹ = 1 + (-1)x + (-1)(-1–1)/2! x² + (-1)(-1–1)(-1–2)/3! x³+…….

= 1 -x + x²- x³ +….

but this will result in an infinite series and will converge for values belonging to

|x|<1. So, the required binomial series is

1 -x + x² - x³ +….

To learn more about binomial theorem, refer:

https://brainly.com/question/13672615

#SPJ4

 - x =< y is the expression and acceptable syntax.

A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases.

A term may be a number, a variable, a product of two or more variables, or a combination of both. A single phrase or a set of terms can make up an algebraic expression. The two terms in the formula 4x + y, for instance, are 4x and y.

Algebra's associative, commutative, and distributive characteristics are the ones that are most frequently utilized to make algebraic expressions simpler.

The converse of the expression and having proper syntax is

   = x >= y.

   = -x <= y

    =- x =< y

To learn more about expression refer to:

https://brainly.com/question/723406

#SPJ4

The difference between the two confidence intervals is given as follows :

Width of confidence interval is directly proportional to confidence level.

This is because,  width is directly proportional to critical value (z or t), which is directly proportional to confidence level.

Now, width is inversely proportional to square root of sample size.

But if sample size is same for both levels of confidence. Then, sample size would have same effect.

Hence, the appropriate answer here is,

The 95 percent confidence interval will not be as wide as the 99 percent confidence interval.

To learn more about critical value click here:

brainly.com/question/14508634

#SPJ4

Answer: 9:50 AM/PM

Step-by-step explanation: Since the shorthand (hour) is on the 9, the hour is 9:00. The long hand (minutes) is on the 10, so it is 50. So, therefore we have 9:50. We don't know if it's am or pm, so we don't know if it's in the morning or the afternoon.

Answer:

because the absolute value of -5 is positive 5

Answer:

A

Step-by-step explanation:

Point [tex]F[/tex] must remain invariant.

The rectangular prism has a capacity of 707.4 ft3  when it is fully filled with water.

Dimensions: 13.1 ft long, 7.5 ft wide, and 7.2 ft tall.

Thus:

Water volume equals 13.1 × 7.5 × 7.2

Water capacity is 707.4 feet3

Consequently, 707.4 ft3 of water will fit inside the rectangular prism when it is full.

To Learn more About  rectangular prism refer To:

https://brainly.com/question/26265930

#SPJ1

The radius is 1,264 cm

The area of the two circular bases and the area of the curving surface together make up the cylinder's total surface area. The area of the circular top and base, as well as the curved surface area, are included in the overall surface area (CSA).

According to the given information

Let radius = r

Height of shorter rain barrel [tex]h_{1}[/tex] = r

Height of taller rain barrel [tex]h_{2}[/tex] = 2r

We know that

Each Barrel is a cylinder without top

So

Total Surface area for each = 2[tex]\pi[/tex]rh + [tex]\pi[/tex][tex]r^{2}[/tex]

TSA for both Barrels = [tex]2\pi rh_{1} + \pi r^{2}+ 2\pi rh_{2} + \pi r^{2}[/tex]

                                  = [tex]2 \pi r^{2} + 2\pi r^{2} + 4\pi r^{2}[/tex] ( put  [tex]h_{1}[/tex] = r , [tex]h_{2}[/tex] = 2r )

                                  = [tex]8\pi r^{2}[/tex]

r = [tex]\sqrt{\frac{TSA}{8\pi } }[/tex]

Total surface area is 40 ,212 [tex]cm^{2}[/tex]

r = [tex]\sqrt{\frac{40,212}{8\pi } }[/tex]

So

The radius is 1,264 cm

To know more about Surface Area

https://brainly.com/question/29298005

#SPJ1

Answer: cylinder , 20

Step-by-step explanation:

The interval for which particle moves to the right is D. t ≥ 4

Intervals are the range of values of a function.

Given that a particle moves along the x-axis so that a time t≥0 is given by x(t) = (t-1)³(t-5).

To find the inverval, we differentiate x(t) with respect to t since the velocity is the derivative dx/dt.

So, x(t) = (t - 1)³(t - 5).

dx(t)/dt = d(t - 1)³(t - 5)/dt

= (t - 5)d(t - 1)³/dt + (t - 1)³d(t - 5)/dt

= (t - 5) × 3(t - 1)² + (t - 1)³ × 1

= 3(t - 5)(t - 1)² + (t - 1)³

= (t - 1)²[3(t - 5) + (t - 1)]

= (t - 1)²[3t - 15 + t - 1]

= (t - 1)²(4t - 16)

For the particle to be moving to the right, dx/dt ≥ 0.

So, dx/dt ≥ 0

⇒ (t - 1)²(4t - 16) ≥ 0

⇒ (t - 1)² ≥ 0 or 4t - 16 ≥ 0

⇒ (t - 1) ≥ 0 or 4t ≥ 16

⇒ t ≥ 1 or t ≥ 16/4

⇒ t ≥ 1 or t ≥ 4

⇒ t ≥ 4 (since 4 is greater than 1.)

So, the interval for which particle moves to the right is D. t ≥ 4

Learn more about interval particle moves to right here:

https://brainly.com/question/28953055

#SPJ1