The shortest route from London to Bristol is 120 miles.
A lorry is expected to take 2 hours to travel this route.
The lorry actually travels by a different route which increases the distance by 20%, but it still arrives in 2 hours.
By how many more mph than the expected speed does the lorry travel?

The value of [tex]f^{-1}(49)[/tex] is 4

The given function is:

[tex]f(x)=(x+3)^2[/tex]

Let f(x) be represented by y

[tex]y=(x+3)^2[/tex]

Make x the subject of the formula

[tex]\sqrt{y} =x+3[/tex]

Subtract 3 from both sides

[tex]x=\sqrt{y} -3[/tex]

Replace x by [tex]f^{-1}(x)[/tex] and let y be replaced by x

[tex]f^{-1}(x)=\sqrt{x} -3[/tex]

Substitute x = 49 into the inverse function

[tex]f^{-1}(x)=\sqrt{49} -3\\\\f^{-1}(x)=7-3\\\\f^{-1}(x)=4[/tex]

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The value of Mario's car after 5 years is $8,249.

Deprecation is when the value of an asset declines with the passage of time as a result of wear and tear.

V = 15,999 − 1,550t

V = 15,999 − 1,550(5)

V = 15,999 - 7,750

V =$8,249

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The ratio of the lemon water is 10:1

From the information, we have that;

The ratio of water to strawberry juice  is 2 : 1

That of strawberry juice to lemon juice is 5: 1

The, we have that of water to lemon juice to be 10: 1 when compared

Hence,  the ratio of the lemon water is 10: 1

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The cross products of the proportion are equal.

According to the question, Sonny's equation can be written as follows.

16/x = 48/15

Now, the variable x is replaced by the constant 5. So the equation can now be written as follows.

16/5 = 48/15

When two fractions are equal to one another as shown above, the constants are cross multiplied with one another in order to form an equation.

16*15= 48*5

The values of both the products are equal which is 240.

Therefore, because the cross products of the proportion are equal.

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The correct order to express cos3x in terms of cosx is; As shown in steps 1 to 9 below.

The steps to simplify the trigonometric identities cos 3x in terms of cos x are as follows;

Step 1; cos x = cos(2x + x)

Step 2; cos(2x) cosx - sin(2x) sinx

Step 3; 1 - 2sin^2x(cosx) -(2sinxcosx)sinx

Step 4; cosx - 2sin²x cosx - 2sin²x cosx

Step 5; cosx - 4sin²x cosx

Step 6; cosx( 1 - 4sin²x)

Step 7; cosx{1 - 4(1 - cos²x)}

Step 8; cosx{-3 + 4cos²x}

Step 9; 4cos³x - 3cosx

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Answer :

( 6 y^4 + 3 y^2 -7) - (12 y^4 - y^2 + 5)

Step-by-step explanation:

(6 y^4+ 3 y^2-7) - (12 y^4 - y^2 + 5 )

=6 y^4 +3 y ^2 - 7 - 12 y^4 + y^2 - 5

=6 y ^4 - 12 y ^4 +3 y ^2 + y ^2 - 7 -5

= -6 y ^4 + 4 y ^2- 12

Hope this helps!

Answer: b

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Answer:

Arithmetic

Step-by-step explanation:

Arithmetic Sequence is a sequence that has common difference - a common difference is same difference in a sequence. If we take next term to subtract the previous term and you keep getting same difference or value then that's a common difference. It can be mathematically expressed as an equation of:

[tex]\displaystyle{d=a_{n+1}-a_n}[/tex]

Now, I'll show why the sequence is arithmetic - take the sequence to subtract for common difference:

Notice how we keep getting -16 after subtracting previous term with next term. Hence this sequence is arithmetic sequence for sure!

Geometric Sequence is a sequence with common ratio - a common ratio is similar to common difference except ratio is all about division. Since common difference is expressed as subtraction of next term and previous term then common ratio is division of next term and previous term which can be mathematically expressed as:

[tex]\displaystyle{r = \dfrac{a_{n+1}}{a_n}}[/tex]

However this sequence is not geometric sequence because if you divide next term with previous term then you'll keep getting difference result and common ratio means having same ratio or constant ratio for entire sequence.

Now see why this sequence cannot be geometric sequence:

Notice that none of values are equal and thus, this sequence doesn't have common ratio which leads to not being geometric sequence.

Answer:

Domain: All real numbers (infinite) Range: [tex]y \leq -4[/tex]

Step-by-step explanation:

For the domain, the x-axis will continue to be used for the parabola, because the parabola can go on forever and can use an x- value on the x-axis. For the range, the largest number the parabola will go up to is -4. Therefore, if that is the highest point/ where the vertex is, the highest point on the y-axis is -4, resulting in the answer y can be equal to or less than -4 (y [tex]\leq[/tex] -4), since the parabola will continue to go down with the reflection over the x-axis.

Answer:

x ^ (1/3)

Step-by-step explanation:

solution:

the answer is in the picture I have sent.

I hope this will help you

Answer:

No it isn't

As the variable "x" has root in it which means it isn't a whole number and for a expression to be a polynomial the variable must be whole no.

Hope it helps you!

Answer:

yes

Step-by-step explanation:

A polynomial is an algebraic expression of two or more terms

[tex]x^{2} +4\sqrt{x}[/tex]  It is an algebraic expression of two terms, It is more common to label it binomial, but it is also a polynomial.

Hope this helps

The required equation based on the information given is y =0.433x + 24.493

It should be noted that one can simply copy and paste the data set into excel sheet

Then, use intercept and the slope formula to find slope and intercept. We will have

slope = SLOPE(y values, x values)

= 0.433

intercept = INTERCEPT(y values, x values)

= 24.493

Therefore, the required equation is y =0.433x + 24.493

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Answer:

I don't understand what the question is what do you need to find?

Answer:

$0.45.

Step-by-step explanation:

Total amount of money held by all 5 children

= 5 * 0.50 = $2.50.

After 0.25 is lost the total = $2.25.

So the new average = 2.25 / 5

= $0.45.

The average rate of change in weight is 3/8.

According to the statement

Weight of baby during birth = 3 kg

Weight of baby after 8 months = 6 kg

Average rate of change of in weight is calculated by

Average rate = Increased weight - Real weight / Time period

Average rate = 6-3 / 8

Average rate = 3/8

So, the average rate of change in weight is 3/8.

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Answer:

x=4 and y=−9

Step-by-step explanation:

Problem:

Solve 7x+4y=−8;−8x−5y=13

Steps:

I will solve your system by substitution.

(You can also solve this system by elimination.)'

7x+4y=−8;−8x−5y=13

Step: Solve 7x+4y=−8 for x:

7x+4y+−4y=−8+−4y(Add -4y to both sides)

7x=−4y−8

7x/7 =  -4y-8/7 (Divide both sides by 7)

x=-4/7y + -8/7

Step: Substitute -4/7y + -8/7 for x in −8x−5y=13:

−8x−5y=13

-8(-4/7y + -8/7) −5y=13

-3/7y + 64/7 =13(Simplify both sides of the equation)

-3/7y + 64/7 + -64/7 = 13 + -64/7 (Add (-64)/7 to both sides)

-3/7y = 27/7

-3/7y/-3/7 = 27/7/-3/7 (Divide both sides by (-3)/7)

y=−9

Step: Substitute −9 for y in x= -4/7y + -8/7:

x = -4/7y + -8/7

x = -4/7 (-9) + -8/7

x=4(Simplify both sides of the equation)

Answer:

x=4 and y=−9

Answer:

  (a)  (x, y) = (3, 2)

Step-by-step explanation:

The correct answer to the given system of equations can be found by trying the offered choices.

The equations are ...

The first equation tells you the sum of the x and y values is 5. Here's what we get for a sum from the different answer choices:

  A: 3 +2 = 5 . . . . a viable choice

  B: 4 +4 = 8 . . . . doesn't work

  C: 6 +1 = 7 . . . . doesn't work

  D: 3 +5 = 8 . . . . doesn't work

__

Checking (x, y) = (3, 2) in the other equation, we have ...

  7(3) +3(2) = 21 +6 = 27 . . . . as required

The solution is x = 3; y = 2.

__

Additional comment

Often, the easiest way to find the answer to a multiple-choice question is to see which answer works to solve the problem. It can sometimes be easier to check the answer than to develop it in the first place.

Substitution can work for this problem to find the correct y-value. (The answer choices differ by y-values, so knowing y tells the answer.)

  7(5 -y) +3y = 27 . . . . substitute x=5-y

  35 -4y = 27 . . . . . . simplify

  8 = 4y . . . . . . . . . add 4y-27

  2 = y . . . . . . . . . divide by 2. Matches the first answer choice.

If the distribution of heads and tails of a fair coin is very regular in a large number of flips, then flipping a fair coin is: D. random.

A fair coin can be defined as an idealized type of coin that has an equal probability of revealing both heads and tails when randomly flipped or tossed by anybody.

This ultimately implies that, the outcome of flipping a fair coin is generally going to produce only one of two results and these include the following:

In this context, we can infer and logically conclude that if the distribution of heads and tails of a fair coin is very regular in a large number of flips, then flipping a fair coin is considered as being random.

In conclusion, it is important to note that a fair coin is considered as being random when the distribution of heads and tails of a fair coin is very regular in a large number of flips.

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Answer:

Exact form: 19 multiply 4200^28 + 1972^31 / 19

Decimal form: 3.55481422 multiply 10^101

By applying the law of cosine, the length of side BM is equal to 7.05 cm..

A polygon can be defined as a two-dimensional geometric shape that comprises straight line segments and a finite number of sides. Also, some examples of a polygon include the following:

Note: The number of sides (n) of a pentagon is 5.

In Geometry, the interior angle of both a regular and irregular polygon is given by this formula:

Interior angle = 180 × (n - 2)/n

Interior angle = 180 × (5 - 2)/5

Interior angle = 180 × 3/2

Interior angle = 108°.

For the central angle, we have:

Central angle, O = 360/5

Central angle, O = 72°.

By applying the theorem of intersecting secants, angle OCB will be given by this formula:

<OCB = ½ × (180 - 72)

<OCB = ½ × 108

<OCB = 54°.

In order to determine the length of side BM, we would apply the law of cosine:

cos(θ) = Adj/Hyp

cos54 = BM/12

BM = 12 × cos54

BM = 12 × 0.5878

Side BM = 7.05 cm.

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Answer:

as x is approaching positive infinity, y approaches positive infinity

as x is approaching negative infinity, y is approaching negative infinity

There are 0 intersections between the railroad and the highway and there are 2 intersections between the railroad and the turnpike

From the graph, we have the following points on the railroad

(x, y) = (3, 3) and (0, 5)

The slope is calculated as:

m = (y2 - y1)/(x2 - x1)

This gives

m = (5 -3)/(0 - 3)

Evaluate

m = -2/3

The equation is then calculated as:

y = mx + b

This gives

y = -2/3x + b

Substitute (0, 5)

5 = -2/3 * 0 + b

This gives

b = 5

Substitute b = 5 in y = -2/3x + b

y = -2/3x + 5

Multiply through by 3

3y = -2x + 15

Rewrite as:

2x + 3y = 15

The equation of the highway's path is

2x+3y=21

So, we have:

2x+3y=21

2x + 3y = 15

Subtract the equations

2x - 2x + 3y - 3y = 21 - 15

Evaluate

0 = 6

The above equation is false because 0 and 6 are not equal.

This means that the system of equations have no solution

Hence, there are 0 intersections between the railroad and the highway.

Here, we have

y = x^2 and 2x + 3y = 15

Substitute y = x^2 in 2x + 3y = 15

2x + 3x^2 = 15

Rewrite as:

3x^2 + 2x - 15 = 0

Calculate the discriminant using

d =b^2 - 4ac

This gives

d = 2^2 - 4 * 3 * -15

Evaluate

d = 184

The discriminant d is greater than 0.

This means that the equation has 2 real solutions

Hence, there are 2 intersections between the railroad and the turnpike

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Using the probability concept, the correct option of the probability of a day in May being cloudy in Sacramento is:

A. 0.43, because 13 of the 30 days were cloudy.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For Sacramento, 30 days were considering, of which 13 days were cloudy, hence the probability of a day in May being cloudy in Sacramento is given as follows:

p = 13/30 = 0.43.

Hence the correct option is:

A. 0.43, because 13 of the 30 days were cloudy.

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The pound was stronger in 2008 against the dollar than in 2017.

The Pound to greenback rate reached a high of $2.649 on the sixth Mar 1972. That remains the most powerful the Pound has been towards USD because it freely floated in 1971.

One might count on that the strongest economies might have the most powerful international currencies; but, that is not always the case. It turns out that lengthy-term movements in forex costs are extra essential than alternate quotes, that's why the British pound is worth extra than the U.S. dollar.

What topics is how the price of that forex adjustments over the years relative to different currencies. Historically, for over 20 years one U.S. dollar has been really worth less than one British pound. As of July 31, 2020, the greenback is sitting around 1.32 to at least one pound. 2  this is down from 1.68 in may additionally 2014 and 1. forty in March 2018.

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The p-value from the hypothesis test is 0.142 i.e., greater than the given significance level of 0.05. So, the null hypothesis is not rejected. The z-score for the given sample is 1.471.

The decision rule based on p-value states,

Since it is given that the valve would produce a mean pressure of 5.4 pounds/square inch. I.e., μ = 5.4 p/si

So, Defining the hypothesis:

Null hypothesis H0: μ = 5.4

Alternative hypothesis Ha: μ ≠ 5.4

It is given that,

The valve was tested on 24 engines. I.e., Sample size n = 24

The sample mean X = 5.7

Standard deviation σ = 1.0 and

The significance level = 0.05

Since the population distribution is approximately normal,

the test statistic is calculated as follows:

z = (X - μ)/(σ/[tex]\sqrt{n}[/tex])

On substituting the value,

z = (5.7 - 5.4)/(1.0/[tex]\sqrt{24}[/tex])

  = (0.3)/0.204

  = 1.471

Fron this z-score, the p-value is calculated as 0.142.

Since, the value of p > 0.05 (significance level), the null hypothesis is not rejected.

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The dimensions of the given cylinder are that its height is 12cm, while its base radius is 4cm, which implies its diameter is 8 cm.

Thus, the first option, The height is 12 cm, and the diameter of the base is 8 cm, is the right choice.

The volume of a cylinder is calculated using the formula, V = πr²h, where V is its volume, r is its radius, and h is its height.

The expression used by Aiden to calculate the volume of a cylinder is π(16)(12), or, π(4²)(12).

Comparing this expression with the general formula of the volume of a cylinder, V = πr²h, where V is its volume, r is its radius, and h is its height, we can say that the radius can be 4 units and the height can be 12 units.

Assuming the units to be cm, we can say that:

The dimensions of the given cylinder are that its height is 12cm, while its base radius is 4cm, which implies its diameter is 8 cm.

Thus, the first option, The height is 12 cm, and the diameter of the base is 8 cm, is the right choice.

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The complete question is:

Aiden evaluated the expression π(16)(12) to find the volume of a cylinder. What could be the dimensions of the cylinder?

The height is 12 cm, and the diameter of the base is 8 cm.

The height is 12 cm, and the area of the base is 16 cm².

The height is 16 cm, and the diameter of the base is 6 cm.

The height is 16 cm, and the area of the base is 12 cm².

Answer:

Step-by-step explanation:

Answer:

Refer to the attached image!!

Hope it helps!