Which is the smallest number?13,0.13,1.03,1.3

The distance from London to Swindon is 81 miles.

We have,

Jenny drives from London to Swindon at an average speed of 54 miles per hour.

Time = 1 1/2 hour = 3/2 hour

Using Speed = distance / Time

Distance = speed x time

Distance = 54 x 3/2

Distance = 27 x 3

Distance = 81 miles

Thus, the distance is 81 miles.

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1.  The area of the scale drawing is  1800 cm².

2. We can multiply the dimensions of the drawing by the scale factor of 5.

3. The area of the actual board is 45000 cm².

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

We know, The area of a rectangle is (length×width).

1. Therefore, The area of the scale drawing is (50×36) cm².

= 1800 cm².

2. Given, The scale factor is in the ratio of 5 : 1.

Therefore, The actual length is 50×5 cm = 250 cm and the width is 180 cm.

3. The area of the actual board is 250×180 = 45000 cm².

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This is a pond in the shape of a prism. It is completely full of water. Colin has to wait for the pond to completely empty is 2hrs and 30minutes.

We have a pond which is completely filled with the water.

Area of the side face ( trapezium shaped)

= 1/2 x (1.4 + 0.6) x 2

= 2 m²

Volume = area x height (here width)

V = 2x1 = 2 m³

The level goes down by 20cm in the first 30 mins

Volume of water that will be taken down =

=0.2 x 1 x 2

=0.4 m³ ( upper water will form cuboid face)

Now,

⇒0.4 m³ water is taken out in 30 minutes

⇒1 m³ water is taken out in 30/0.4 minutes

⇒2 m³ water is taken out in 30/0.4 x 2 minutes

⇒30x2/0.4

⇒150 minutes.

So the pond will be completely empty in 150 min that is 2hrs30mins.

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the inequality model given by eva is wrong, the correct answer is 5/3(y-1) = x.

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

The given inequality is y =3/5x +1

Now subtract 1 from both sides y-1 = 3/5x

further taking 5/3 in both side we should have

5/3(y-1) = x

Hence, the inequality model given by eva is wrong, the correct answer is 5/3(y-1) = x.

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The height of the box in feet is 6 feet.

The surface area of a rectangular prism is the overall region or area that is covered by all of its faces. A three-dimensional shape is a rectangular prism. It has six faces, each of which is rectangular in shape. Consequently, a rectangular prism's two bases must likewise be rectangles.

The surface area of the rectangular prism is given by the formula:

A = 2(wl + hl + hw)

Substitute the value of A = 148, l = 4 and w = 5:

148 = 2((5)(4) + (4)h + (5)h)

148 = 40 + 8h + 10h

148 = 40 + 18h

108 = 18h

h = 6

Hence, the height of the box in feet is 6 feet.

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The dimensions of the square are √2n by √2n

Let's call the number of 1-blocks required to form a square "n".

The dimensions of the square can be represented as x^2 + x * (2 * n / x)

This is so because:

Since the square is a perfect square, both sides of the equation must be equal:

x^2 = x * (2 * n / x)

Solving for x:

x^2 = 2n

Take the square root of both sides

x = √2n

So the dimensions of the square are √2n by √2n

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The loan will be (ln(Time) - ln(136,000) + ln(1,180)) / ln(1 + 6.5 / 12) repaid.

What is interest ?

Interest is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum, at a particular rate.

Time = Loan Amount * (1 + Interest Rate / 12)^(12 * Number of Payments) / Monthly Payment

Given the loan amount ($136,000), interest rate (6.5%), and monthly payment ($1,180), we can plug these values into the formula:

Time = 136,000 * (1 + 6.5 / 12)^(12 * Number of Payments) / 1,180

To find the number of payments, we need to take the natural logarithm of both sides:

ln(Time) = ln(136,000 * (1 + 6.5 / 12)^(12 * Number of Payments) / 1,180)

ln(Time) = ln(136,000) + ln((1 + 6.5 / 12)^(12 * Number ofPayments)) - ln(1,180)

ln(Time) = ln(136,000) + 12 * Number of Payments * ln(1 + 6.5 / 12) - ln(1,180)

Next, we can isolate the number of payments on one side:

12 * Number ofPayments * ln(1 + 6.5 / 12) = ln(Time) - ln(136,000) + ln(1,180)

The loan will be (ln(Time) - ln(136,000) + ln(1,180)) / ln(1 + 6.5 / 12) repaid.

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c = log_10(25) is the value of c that makes y(1) = 5.

What is differential ?

A differential is a gear train with three drive shafts that has the property that the rotational speed of one shaft is the average of the speeds of the others, or a fixed multiple of that average.

y'(x) = c * x^(c-1) * x^(-2) + (-2) * x^c * x^(-2) = (c - 2) * x^(c-3)

Now, we can substitute y(x) and y'(x) into the differential equation:

xy' + 2y = 3x

x * (c - 2) * x^(c-3) + 2 * x^c * x^(-2) = 3x

(c - 2) * x^(c) + 2 * x^c * x^(-2) = 3x

(c - 2) * x^c + 2 * x^(-2) = 3x

This confirms that y(x) = x^c * x^(-2) is indeed a solution of the differential equation xy' + 2y = 3x.

To find the value of c so that y(1) = 5, we need to substitute x = 1 and y = 5 into the solution y(x) = x^c * x^(-2):

y(1) = 1^c * 1^(-2) = 5

1^c = 5 * 1^2 = 25

c = log_1(25)

c = log_10(25) / log_10(1) = log_10(25)

So, c = log_10(25) is the value of c that makes y(1) = 5.

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The variance of X is (C) 35/12.

The formula for variance of a discrete random variable X is:

Var(X) = E[(X - E[X])^2] = E[X^2] - (E[X])^2

where E[X] represents the expected value of X.

To calculate the variance, we first need to find the expected value of X, which is:

E[X] = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5

Next, we find the expected value of X^2:

E[X^2] = (1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2) / 6 = 91/6

Now we can substitute the values into the variance formula:

Var(X) = E[X^2] - (E[X])^2 = 91/6 - (3.5)^2 = 91/6 - 12.25 = 35/12.

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The equations that correspond to this situation, that is, the equations that have the value of c as 2 and -3 are: y = - 4/3x + 2 y = 2x -3. Hence, option B is the correct answer.

The point where a graph intersects the y-axis is known as the y intercept. Any point on the y-axis has an x-coordinate of 0, is known as y intercept. Therefore, a x-coordinate of y intercept is 0.

The equation of the line is given by the following formula:

y = mx + c

where, c is the y-intercept of the line.

From the graph we can observe that the y-intercept of the red line is +2 and the y-intercept of the blue line is -3.

Hence, the equations that correspond to this situation, that is, the equations that have the value of c as 2 and -3 are:

y = - 4/3x + 2

y = 2x -3

Hence, option B is the correct answer.

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Answer:

The equation H(x) = (-4x-5)(-x+5) can be simplified to H(x) = 4x^2 + 25.

The lesser value for x is -5, and the greater value for x is 5.

In mathematical terms, if X is the sum of successes in n different Bernoulli trials, and p is the likelihood of success in each trial, then X may be represented as a normal distribution with mean increasing as n rises.

μ = np

variance σ^2 = np(1-p)

The binomial distribution is a discrete probability distribution that produces just two outcomes in an experiment: success or failure. In a binomial distribution, the chance of success must remain constant during the trials under consideration. For example, because there are only two possible outcomes when tossing a coin, the chance of flipping a coin is 1/2 or 0.5 for each experiment we do.

Here,

When the sample size (n) is high, the distribution of the total of successes (k) in n separate Bernoulli trials approaches a normal distribution, according to the normal approximation for the binomial distribution.

In mathematical terms, if X is the total of successes in n separate Bernoulli trials, with p being the chance of success in each trial, then X may be represented by a normal distribution with mean as n increases.

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The value of the current 'I' for the given relation of current , impedance, and voltage  I = E/ Z is equal to I = ( 4.5 + 5.4i ) / ( 6 + 4i ).

Here R=6, and XL=4

Impedance Z = R+ XL i

⇒ Z = 6 + 4i  __(1)

Where

E = 7(cos 50 degrees +i sin 50 degrees)

Simplify the above expression to get the value of voltage E.

⇒ E = 7 ( 0.6428 + i 0.7660 )

⇒ E = 4.4996 + i( 5.362 )

⇒ E = 4. 5 + 5.4i ____(2)

Now alternating current  ,

I = E / Z

Substitute the value of E and Z from (1) and (2) we get,

⇒ I = ( 4.5 + 5.4i ) / ( 6 + 4i )

Therefore, the value of the current I is equal to ( 4.5 + 5.4i ) / ( 6 + 4i ).

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The rate of change of radius is 2.832 mm per second, when the radius is 6 mm.

A height of cone = 15 mm

An initial radius of cone = 16 mm

The volume of the inverted cone is decreasing at a rate of 534 cubic mm per second, with the height being held constant.

The formula of Volume of cone;

V = 1/3 πr^2h

where, r =  radius of the cone and h = height of the cone

To determine the rate of change of the radius we differentiate the volume with respect to t.

dV/dt = 2/3 πrdr/dt h

Now putting the values

534 = 2/3 × 22/7 × 6 × dr/dt × 15

534 = 3,960/21 × dr/dt

Multiply by 21 on both side, we get

3960 dr/dt = 11,214

Divide by 3960 on both side, we get

dr/dt = 2.832

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The probability to win the world series by cubs as per given probability of each game with no ties is equal to 29% ( in percent nearest whole number).

Total number of games played by the teams 'n' = 7

Number of games required to win the world series 'x' = 4

Probability of winning a game by cubs 'p' ( success) = 0.60

1 - p = 1 - 0.60

       = 0.40

Probability of winning the world series by Cubs

= ⁿCₓ pˣ ( 1 - p )ⁿ⁻ˣ

= ⁷C₄ ( 0.60 )⁴ ( 0.40 )⁷⁻⁴

= ( 7! / (4!) ( 7 -4 )! )  ( 0.60 )⁴ ( 0.40 )³

= ( 7 × 5 ) ( 0.0082944 )

= 0.29034

= 29% ( in percent )(nearest whole number)

Therefore, the probability of winning the world series by cubs is equal to 29%.

The above question is incomplete , the complete question is:

In the World Series, the team that wins 4 games out of seven is the champion. Suppose that the Cubs are playing the red Sox (and the world is about to end), and the Cubs have a probability of 3/5 of winning a game over the Sox and there is no ties. What is the probability that the Cubs will win the world series ? Express your answer as a percent rounded to the nearest whole percent.

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The quotient of 10 and a number b is the number you get when you divide 10 by b.

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The amount of the next 50 blogs that are expected to be of pop culture is given as follows:

20 blogs.

The first step in obtaining the expected amount is obtaining the proportion out of the blogs that are of pop culture, dividing the number of blogs that are of pop culture by the total number of blogs.

Considering the data in the table, the proportion is obtained as follows:

p = 26/(20 + 26 + 7 + 12)

p = 0.4.

Then, considering the proportion of 0.4, out of the next 50 blogs, the expected amount of pop culture blogs is given as follows:

0.4 x 50 = 20 blogs.

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The equation of the exponential model is f(x) = 3 * 0.2^x

The opposite of an exponential function is a logarithmic function. A log function and an exponential function both use the same base. An exponent is a logarithm. f(x) = bx is how the exponential function is expressed. The formula for the logarithmic function is f(x) = log base b of x.

Given a data set:

x                                        f(x)

−2                                      71

−1                                       13

 0                                       3

 1                                      0.6

 2                                     0.1

An exponential model is represented as:

f(x) = ab^x

When x= 0 and f(x) = 3;

We have:

ab^0 = 3

This gives

a = 3

When x= 1 and f(x) = 0.6

We have:

ab^1 = 0.6

This gives

ab = 0.6

Substitute 3 for a

3b = 0.6

Divide both sides by 3

b = 0.2

Substitute b = 0.2 and a =3 in f(x) = ab^x

f(x) = 3 * 0.2^x

Hence, the equation of the exponential model is f(x) = 3 * 0.2^x

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The function f(x) = e^(3x) - e^x is increasing on the interval (-∞, +∞).

On the range (-∞, +∞), the function f(x) = e^(3x) - e^x increases. This is because the exponential function e^x is increasing for all x, so the difference of two increasing functions is also increasing.

A mathematical function called an exponential function is applied in numerous instances in the real world. It is mostly used to calculate investments, model populations, and do other tasks like determining exponential growth or decay. In an exponential growth model, the quantity increases initially extremely slowly and subsequently quickly. As time goes on, the rate of change quickens.

Correct Question :

On what interval is the function f (x) = e^(3x)−e^x increasing?

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The factorization case for each polynomial is listed below:

In this problem we find six cases of polynomials, whose factorization case must be found. Now we proceed to show and indicate what kind of factorization case is used for each polynomial:

Case 1: z² + z - 90 (Sum and product)

z² + z - 90

z² - (- 10 + 9) · z + (- 10) · 9

(z + 10) · (z - 9)

Case 2: x² - 4 · x + 6 · x - 24 (Grouping)

x² - 4 · x + 6 · x - 24

x · (x - 4) + 6 · (x - 4)

(x + 6) · (x - 4)

Case 3: 16 · x² + 24 · x · y + 9 · y² (Perfect square trinomial)

16 · x² + 24 · x · y + 9 · y²

(4 · x + 3 · y)²

Case 4: 49 · x² - 100 · y² (Difference of two squares)

49 · x² - 100 · y²

(7 · x - 10 · y) · (7 · x + 10 · y)

Case 5: 121 · m² + 64 (None)

Case 6: 8 · x³ · y² + 4 · z³ (GCF)

8 · x³ · y² + 4 · z³

4 · (2 · x³ · y² + z³)

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To display the distribution of grades (A, B, C, D, F) in a course, it would be correct to use histogram

a) We note that the given histogram contains a

very large number of bars and that most bars are quite low while also very narrow.

The display is then not appropriate, as the histogram should contain less bars to make the shape in the distribution more obvious.

(b) The distribution of grades is skewed to the left as the highest bars in the histogram are to the right in the graph.

The grades appear to be centered roughly at 170, while the graders vary from about 75 to 190.

Moreover, there appear to be a few outliers in the distribution, as there are gaps between the bars of the histogram.

since Histogram contains too many bars and  Left-skewed histogram can be considered to display.

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Answer:

  A.  44.5w + 106.37 = 239.87; w = 3

Step-by-step explanation:

You want an equation and solution for finding the number of weeks (w) required to earn enough for a $239.87 gaming chair if you have saved $106.37 and earn $44.50 per week.

The total amount saved will be the sum of the amount already saved ($106.37) and the amount of earnings. We want that total to be $239.87.

Earnings are $44.50 per week. After w weeks, they total 44.50w. Then the amount saved will be ...

  earnings + already saved = total savings

  44.50w + 106.37 = 239.87

We can find the value of w by subtracting 106.37 from this equation:

  44.50w = 133.50

  w = 3 . . . . . . . . . . . . . . . divide by 44.50

The equation and solution are ...

  44.5w +106.37 = 239.87; w = 3 . . . . . . . matches choice A

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The area of the shaded part is 50(2-π)

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

The area of the shaded part = area of a square - area of a semi circle

area of square = l× l = 10 × 10 = 10²

=100 squared units

the area of the semi circle = πr²/2

= π ×10²/2

= 50π

Therefore the area of the shaded part in term of π is 100-50π

= 50( 2-π) units

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The simplified expression is (- 5√2 - 5√3 - √6 - 3).

Given is the expression as -

(5 + √3) / (√2 - √3)

The given expression is -

(5 + √3) / (√2 - √3)

We can write -

{(5 + √3) x (√2 + √3)} / {(√2 - √3) x (√2 + √3)}

{5(√2 + √3) + √3(√2 + √3)} / (√2² - √3²)

(5√2 + 5√3 + √6 + 3) / (- 1)

- (5√2 + 5√3 + √6 + 3)

- 5√2 - 5√3 - √6 - 3

Therefore, the simplified expression is (- 5√2 - 5√3 - √6 - 3).

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The vertical asymptote is x = 1 or 7

There is no horizontal asymptote

An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance. In other words, Asymptote is a line that a curve approaches as it moves towards infinity.

To find vertical asymptote we set the denominator to 0 and we find the value of x

:. x² - 8x +7 = 0

x² -7x-x+7 = 0

(x²-7)(-x+7) = 0

x( x-7) -1(x-7) = 0

(x-1)(x-7) = 0

x-1 = 0 or x-7 = 0

therefore x = 1 or 7

to find the horizontal asymptote:

Since the degree of the numerator is higher than the denominator, there is no horizontal asymptote

to find the slant asymptote, we divide the numerator by the denominator.

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The missing factor is 9.

Option A is the correct answer.

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,

The factors of 360 are 10 and 36.

360 = 10 x 36

The factors of 10 are 2 and 5.

10 = 2 x 5

The factors of 36 are 4 and 9.

36 = 4 x 9

The factors of 4 are 2 and 2.

The factors of 9 are 3 and 3.

Thus,

9 is the missing factor.

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The error interval needed is [15.375, 15.385)

Given that:

A number 'x' rounded to 2 decimal places = 15.38

According to the rules of the rounding of number, we surely know that

x must be in [ 15.375, 15.385) since if x is outside of this interval, then rounding to two places of decimal won't lead to 15.38.

Since x can't be 15.385 itself since that rounds up to 15.39

Or:

[tex]15.375 \leq x\leq 15.385[/tex]

Thus we have :

Error Interval = [15.375 , 15.385)

The substitution that should best be used in solving the recurrence T(n) = 5T(4n/3) + 2 is "n = (4/3)^k".

The idea behind choosing a substitution for a recurrence relation is to simplify the relation and make it easier to solve. In this case, we want to simplify T(4n/3) to something involving T(n). By setting n = (4/3)^k, we can rewrite T(4n/3) as T((4/3)^(k+1)).

This substitution allows us to express T(4n/3) in terms of T(n) and simplify the relation.

T(n) = 5T(4n/3) + 2

becomes

T(n) = 5T((4/3)^(k+1)) + 2

We can then use this substitution to solve the relation using, for example, the Master Theorem.

In conclusion, the substitution "n = (4/3)^k" is the best option because it simplifies the relation and makes it easier to solve.

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