A map has a scale of 1 cm to 12 km.

On a map, the distance between Cardiff and London is 20 cm.

What is the real distance, in km, between Cardiff and London?

Answer:  9.22

Step-by-step explanation:

distance in x direction:  ║-4║ + 2 = 6

distance in y direction:  5 + ║-2║ = 7

Use pythagorean theorem to find hypotenuse of triangle with legs of 6 and 7:

[tex]d^{2} = 6^{2} + 7^{2} = 85\\d = \sqrt{85} = 9.2195 = 9.22[/tex]

Answer:

Step-by-step explanation:

The square of 7 is:

[tex](7)^2=49[/tex]

The difference x and square of 7 is:

[tex]x-49[/tex]

Two times the difference of x and square of 7 is:

[tex]2(x-49)[/tex]

Answer: 10.7142857kg in each bag

Step-by-step explanation: If you divide 75 by 7 you would get 10.7142857. There fore there is about 10.7142857kg of chocolate in each bag.

Answer:

4pm

10:37 + 4:45 hours +38 min makes arrival time 4pm

Answer:

undefined

Step-by-step explanation:

division by zero is undefined

Division Property of zero

For any nonzero real number a

The quotient of "a" and 0 is undefined. That is a/0 is undefined

The conversion of 36 liters to quartz using unit fractions is 144 quarts.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split

It is important to note that 1 liter = 4 quarts. Therefore the quarts can be expressed as:

= 1/4l

Therefore the conversion of 36 liters to quarts will be:

= 36 ÷ 1/4

= 36 × 4

= 144' quartz

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Answer: the estimated mean score is 78

Step-by-step explanation: I took the quick check

Answer:

No. A non-uniform probability is where each outcome does not have the same chance of happening; this is not true of a fair 6-sided die, of which each side has an equal 1/6 probability of being rolled.

[tex]\Large\boxed{\sf uniform\ probability}[/tex]

A unique integer value appears on each side. Rolling the die and getting any particular number has a 1/6 chance of happening. There are six outcomes, each uniformly distributed while rolling the dice. Each has an equal probability of occurring.

The equation the given statement is y=ax.

What is equation?

  The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. Equations come in two varieties: identities and conditional . All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.

Here the weight of the steel beam is proportional to length.

let y be weight and x be length of it. Then

=> y ∝ x

=> y=ax

where a is the constant

we can find it if we have two sets of values of y and x.

Therefore the equation the given is y=ax.

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Answer:

(A) 30 pages

Step-by-step explanation:

Let x = total number of pages in the book.

She read half the book in Monday. She read x/2.

She read 90 pages on Tuesday. By now she read a total of x/2 + 90.

She has 1/8 left to go. That means she read 7/8 of the book.

7/8 x = x/2 + 90

Multiply both sides by 8.

8 × 7/8 x = 8 × x/2 + 8 × 90

7x = 4x + 720

3x = 720

x = 240

The book is 240 pages long.

She has 1/8 to go.

1/8 × 240 = 30

Answer: (A) 30 pages

Given:

The current of a river is 2 miles per hour. A boat travels to a point 8 miles upstream and back in 3 hours.

Required:

What is the speed of the boat in still water?

Explanation:

A boat has to travel 8 miles against the current and 8 miles with the current.

Ustream(against the current) the boat's speed is:

speed in still water - current OR x - 2.

Downstream( with the current) the speed is:

speed in still water + current speed OR x + 2.

We know the distance

OR

The total time is 3 hours

The time upstream + The time downstream = 3 hours

A) The slope is 3/2

B) The line in point-slope form: y = (3/2)*(x - 2) + 10

C) The line in slope-intercept form: y = (3/2)*x  + 7

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

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

Here the line goes through (2, 10) and (-2, 4), then the slope is:

a = (10 - 4)/(2 + 2) = 6/4 = 3/2

b) The line in point-slope form for a point (h, k) is:

y = a*(x - h) + k

So here we get:

y = (3/2)*(x - 2) + 10

c) Expanding the above equation we will get:

y = (3/2)*x - (3/2)*2 + 10

y = (3/2)*x  + 7

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Answer:

D

Step-by-step explanation:

4 - 8 × 2 ← perform multiplication before doing subtraction

= 4 - 16

= - 12

Answer:

x8659-3358468854---6666x

Answer:

[tex]\frac{\sqrt{3} }{2}[/tex] sinx - [tex]\frac{1}{2}[/tex] cosx

Step-by-step explanation:

using the sum identity for cosine

cos(a + b) = cosacosb - sinasinb

then

cos(x + [tex]\frac{4\pi }{3}[/tex] )

= cosxcos([tex]\frac{4\pi }{3}[/tex]) - sinxsin([tex]\frac{4\pi }{3}[/tex] )

[ [tex]\frac{4\pi }{3}[/tex] is an angle in the third quadrant where sin and cosine < 0 ]

[ the related acute angle to [tex]\frac{4\pi }{3}[/tex] = [tex]\frac{4\pi }{3}[/tex] - π = [tex]\frac{\pi }{3}[/tex] ]

= cosx × - cos([tex]\frac{\pi }{3}[/tex] ) - sinx × - sin([tex]\frac{\pi }{3}[/tex] )

= cosx × - [tex]\frac{1}{2}[/tex] - sinx × - [tex]\frac{\sqrt{3} }{2}[/tex]

= - [tex]\frac{1}{2}[/tex] cosx + [tex]\frac{\sqrt{3} }{2}[/tex] sinx

= [tex]\frac{\sqrt{3} }{2}[/tex] sinx - [tex]\frac{1}{2}[/tex] cosx

The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units

If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0

Then the distance of a point from the line is given by the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

Given: the point (5,12) and the line y = 5x + 12. The line can be written as

5x-y+12 = 0. Thus:

x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)

d = 25/√26 = 4.90 units

Therefore, the distance between the point and the line is 4.90 units. Option D is the answer

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By using the formula for slope of a line, it can be calculated that

For 12'' candle

Two points are (1, 10) and (4, 2)

Slope = [tex]-\frac{8}{3}[/tex]

For 8'' candle

Two points are  (3, 4) and (6, 0)

Slope = [tex]-\frac{4}{3}[/tex]

What is slope of a line?

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta\\[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

Here,

For 12'' candle

Two points are (1, 10) and (4, 2)

Slope =

[tex]\frac{2-10}{4-1}\\-\frac{8}{3}[/tex]

For 8'' candle

Two points are  (3, 4) and (6, 0)

Slope =

[tex]\frac{0-4}{6 - 3}\\-\frac{4}{3}[/tex]

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Answer:

x = 148.76

Step-by-step explanation:

tan (37) = 81/x

x = 81/(tan (37)) = measure of "x" from after the height is 81

tan (63) = 81/x

x = 81/(tan (63)) = measurement of "x" from before the height is 81

81/(tan (63)) + 81/(tan (37)) = x

x = 148.76

well, the height of the building is 119 feet, as we can see right there on the picture.  Now, there are 7 floors from the ground up, so the ratio is simply

[tex]\cfrac{\stackrel{overall~height}{119}}{\underset{floors}{7}}\implies \cfrac{17}{1}\implies \stackrel{unit~rate}{17}\hspace{5em}\cfrac{17~feet}{1~floor}\qquad \begin{array}{llll} \textit{each floor is}\\ \textit{17 feet high} \end{array}[/tex]

The equation for resistor 2, R₂ is (d) R₂ = R₁Rt/(R₁ - Rt)

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

Rt = R₁R₂/(R₁ + R₂)

The question implies that we make R₂ the subject of the formula

So, we have

Rt = R₁R₂/(R₁ + R₂)

Cross multiply the equations

(R₁ + R₂)Rt = R₁R₂

Open the brackets

So, the equation becomes

R₁Rt + R₂Rt = R₁R₂

Collect the like terms

R₁R₂ - R₂Rt = R₁Rt

Factor out R₂

R₂(R₁ - Rt) = R₁Rt

Make R₂ the subject

R₂ = R₁Rt/(R₁ - Rt)

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Answer:

2, R₂ is (d) R₂ = R₁Rt/(R₁ - Rt)

Step-by-step explanation:

The Mean measure should be used to summarize the data in all three problems.

What is the mean?

In mathematics, particularly statistics, there are several types of means. Each mean is used to summarize a specific group of data, often in order to better understand the overall value of a data set.

Generally,

For ratio and interval type of data, we use mean as the central tendency

For the ordinal type of data, we use the median as the central tendency

and For the nominal type of data mode is prefered.

Interval data:- In this type of data point lies in some interval on a scale.

Like temperature in degrees Fahrenheit, it has some range of value on the measurement scale of temperature.

Ratio Data:- It is similar to interval type of data but absolute zero is treated as the point of origin.No negative value

Example:- temperature in kelvin (0 is the origin)

Ordinal data:- It is of categorical type of data that is in the natural order and the distance between the two data is not known.

Example:- How you describe your last purchasing experiences,

1) Very Pleasant 2) Somewhat Pleasant 3) Neutral 4) Somewhat Unpleasant 5) Very Unpleasant.

Nominal data:- In this data is leveled or named without any quantitative value.

Example:- Colour of hair, gender, country, etc.

a)

In part (a) the data is ratio type.

Hence, the Mean is the best central tendency of measurement.

b)

In (b) part also ratio type of data.

Hence, the Mean is the best central tendency of measurement.

C)

In this part, data is of the Interval data.

Hence, the Mean is the best central tendency of measurement.

Therefore, the Mean measure should be used to summarize the data in all three problems.

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Maximum of 16 months, will take Jim to save $947.

Total Cost of Computer = $947

Amount that Jim can save monthly = $60

Let time taken by Jim to save amount which is equal to cost of computer = x months

So, the equation for the above statement can be written as: 60x = 947

Dividing both sides by, 60

[tex]\frac{60x}{60} =\frac{947}{60}[/tex]

[tex]x=\frac{947}{60} =15.78[/tex]

⇒Number of months=16

Maximum of 16 months, will take Jim to save $ 957.

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Answer:

52 problems

Explanation:

8.13 hours

8.13 hours × 60 minutes = x minutes

487.8 minutes

487.8 minutes ÷ 9.3 minutes = 52.4516129 problems

Answer:

D

Step-by-step explanation:

y-7 = -1/2 (x-(-2)

y-7 = -1/2 (x+2)

y -7 = -1/2 x - 1

y = -1/2 x -1 +7

y = -1/2 x + 6

The solution of the differentiated equation is dy/dx = -6x⁵

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

x = ⁶√t

y = 8 - t

To start with:

We need to make the variable t the subject of the formula in the equation x = ⁶√t

Make t the subject

So, we have

t = x⁶

Substitute t = x⁶ in the equation y = 8 - t

y = 8 - x⁶

The rule of first principle of differentiation is represented as

If y = axⁿ, then dy/dx = naxⁿ⁻¹

Using the above as a guide, we have

y = 8 - x⁶

dy/dx = 0 * 8x⁰⁻¹ - 6 * x⁶⁻¹

Evaluate the difference

So, we have

dy/dx = 0 * 8x⁻¹ - 6 * x⁵

Evaluate the products

So, we have

dy/dx = 0 - 6x⁵

Evaluate the sum

So, we have

dy/dx = -6x⁵

Hence, the equation result is dy/dx = -6x⁵

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1/2048 is  the probability of getting 11 heads in 11 tosses.

Probability of getting heads in one toss = 1/2

Probability of getting heads in 11 tosses = [tex](1/2)^{11[/tex]= 1/2048 (a one in 2048 chance of occurrence)

It should, therefore, NOT be surprising in a sample space of 950 (which is more than double 2048), that 11 heads can be obtained in a row.

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1/2048 is  the probability of getting 11 heads in 11 tosses.

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The total cost to run Val’s AC costs for a summer month of 30 days will be $67.5.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Quantity of electricity used in kilowatts is;

1000 watts = 1 kilowatts

2,500 watts = 2.5 kilowatts

Given that Number of hours Val runs AC per day = 5 hours

Number of days = 30 days

Cost of electricity = $0.18 kilowatts per hour

The Cost of Val’s AC to run for a summer month of 30 days can be calculated as;

= Quantity of electricity used × Number of hours Val runs AC per day × Number of days × Cost of electricity

= 2.5 × 5 × 30 × 0.18

= $67.5

The total cost to run Val’s AC costs for a summer month of 30 days will be $67.5.

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a) The slope is infinity.

b) We can't write the linear equation in the slope-intercept form because the slope is infinity, in this case, the line is written as x = 2.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

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

Here we have two points (2, 1) and (2, 0), then the slope is:

slope = (1 - 0)/(2 - 2) = 1/0 → ∞

So the slope is infinity, as the case for all vertical lines.

b) Why we can't write the linear equation in the traditional form?

This happens because the slope is infinity, the vertical linear equations are written as:

x = a

In this case, we can see that the line is at x = 2, so that is our linear equation.

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Answer:

[tex]54[/tex]

Step-by-step explanation:

Formula for average A of two numbers m and n is:

[tex]A=\frac{m+n}{2}[/tex]

Substitute the value m=36 and n=72

[tex]A=\frac{36+72}{2}[/tex]

This is equivalent to:

[tex]A=\frac{108}{2}[/tex]

The average is:

[tex]A=54[/tex]

first off, let's convert all those mixed fractions to improper fractions and then subtract.

[tex]\stackrel{mixed}{11\frac{4}{5}}\implies \cfrac{11\cdot 5+4}{5}\implies \stackrel{improper}{\cfrac{59}{5}} ~\hfill \stackrel{mixed}{1\frac{1}{6}}\implies \cfrac{1\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{7}{6}} \\\\\\ \stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{Sarah}{\cfrac{59}{5}}\hspace{5em}\stackrel{Greg}{Sarah - \cfrac{7}{6}} \hspace{5em}\stackrel{Jane}{Greg - \cfrac{4}{3}} \\\\\\ \stackrel{\textit{\LARGE Jane} }{\cfrac{59}{5}~ - ~\cfrac{7}{6}~ - ~\cfrac{4}{3}}\implies \cfrac{(6)59~~ - ~~(5)7~~ - ~~(10)4}{\underset{\textit{using this LCD}}{30}}\implies \cfrac{279}{30}\implies \cfrac{93}{10}\implies {\Large \begin{array}{llll} 9\frac{3}{10} \end{array}}[/tex]