if 8 litres of petrol cover's 60km , how many litres of petrol will a car need to cover 50km​

From line 11, we have derived A, which contradicts the assumption in line 3 (-(BA - D)). Therefore, our assumption for contradiction must be false.

To prove (BC) by contradiction, we assume the negation of the statement and aim to reach a contradiction. Here's the step-by-step proof  -

From line 11, we have derived A, which contradicts the assumption in line 3 (-(BA - D)). Therefore, our assumption for contradiction must be false.

Thus, we can conclude that (BC) holds based on the given premises.

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The value of the infinite series as n tends to 0 is: 0

Infinite series is defined as the sum of infinitely many numbers related in a given way and listed in a given order. Infinite series are important in mathematics and in such disciplines as physics, chemistry, biology, and engineering.

From the infinite series, we want to find the value of the series as n tends to 0.

We are given the series as:

x/2ˣ

At x = 0, we have:

0/2⁰ = 0/1 = 0

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Answer:

£164.50

Step-by-step explanation:

If the discount is 6%, then the discounted price is 94% of the original price.

95% of £175 = 0.94 × £175 = £164.50

The measure of the side r is 13.29 in

To determine the value of the side of the triangle:

We need to take note of the six trigonometric identities. These identities are;

From the information shown in the diagram, we have that;

side q is the opposite side of angle Q

r is the hypotenuse side

s is the adjacent side

Using the sine identity, we have;

sin 37 = 8/r

cross multiply the values, we have;

r = 13. 29 in

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Stratified random sampling was the technique employed by Homer to choose his sample.

Given case;

Homer Simpson is fascinated with the proportion of the different sprinkled colors on lard lad doughnuts. Homer buys three of each type of donut they produce and counts the sprinkles on them to perform his research.

The method did homer use to select his sample is stratified random sampling. Because each variety is a stratum.

From there 3 3 samples are collected.

Stratified random sampling:

A crucial aspect of the sampling strategy known as stratified random sampling is the stratification of a population into smaller subgroups known as strata. During stratified random sampling, the strata are created based on the shared traits or features of the participants, such as level of education or income. Numerous uses and advantages of stratified random sampling include examining life expectancy and population demography.

The terms proportionate random sampling and quota random sampling are also used to describe stratified random sampling.

The method did homer use to select his sample is stratified random sampling.

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The height of Jeremy is 159 cm.

To find the height of Jeremy:

So,

Then, Jeremy = 135 + 24 = 159 cm.

Therefore, the height of Jeremy is 159 cm.

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When \(\theta\) terminates in quadrant III, both \(\cos\theta\) and \(\sin\theta\) are negative, and

\(\sin^2\theta+\cos^2\theta=1\implies\cos\theta=-\sqrt{1-\sin^2\theta}=-\dfrac{12}{13}\)

When \(\varphi\) terminates in quadrant II, \(\cos\varphi\) is negative and \(\sin\varphi\) is positive, so

\(1+\tan^2\varphi=\sec^2\varphi\implies\sec\varphi=-\dfrac{17}{15}\)

which gives

\(\cos\varphi=\dfrac1{-\frac{17}{15}}=-\dfrac{15}{17}\)

\(\tan\varphi=\dfrac{\sin\varphi}{\cos\varphi}=-\dfrac8{15}\implies\sin\varphi=\dfrac8{17}\)

Now,

\(\sin(\theta+\varphi)=\sin\theta\cos\varphi+\cos\theta\sin\varphi=-\dfrac{21}{221}\)

A square rotated about its center by 360º maps onto itself at 4  different angles of rotation. You can reflect a square onto itself across 4  different lines of reflection.

It is important to note that a square has 4 angles of rotation and 4 lines of symmetry.

The 4 angles of rotation implies that you can tend to  rotate it  4 times so as to have it line up with its main  image before hitting 360°.

The 4 lines of symmetry which are:

Therefore the first and second blank is both 4.

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Answer:

-73

Step-by-step explanation:

substitue the -8 in for x. then multiply -8 by 7 you get -56. then subtract 17.

Answer:

5

Step-by-step explanation:

slopes of the parallel lines are always same this line has slope five

because equation in y intercept form is y=mx+b

where m is the slope.

so the slope of the new line will be five

Answer:

175 i think please mark brainliest

Step-by-step explanation:

The matrix of the relation r={(1,2),(2,3),(3,4),(4,5)} on the set x={1, 2, 3, 4, 5}; ordering of x:1,2,3,4,5 is as follows.

\($$\begin{pmatrix} 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{pmatrix}$$\)

A relation is a set of ordered pairs.

The matrix of a relation is constructed by using its ordered pairs with their respective values as its entries, and its rows and columns by its domain and range, respectively.

So, the relation r is given as{(1,2),(2,3),(3,4),(4,5)}

The elements in the rows of the matrix correspond to the elements of x, while the elements in the columns of the matrix correspond to the elements of x as well, in that order.

So, the matrix of r on x can be written as:

\($$\begin{pmatrix} 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{pmatrix}$$\)

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Answer: the grouping of the factors is changed, but the product is the same

Answer:

The answer is 9y + 18

Step-by-step explanation:

Multiply using the distributive property.

Hoped this helped!

The units for da/dx are pounds per foot squared.

The units for da/dx would be pounds per foot squared. This is because da/dx represents the rate of change of the function a(x), which has units of pounds per foot, with respect to x, which has units of feet. When we take the derivative of a(x), we essential do division of the change in a(x) by the change in x.  

The change in a(x) has units of pounds, and the change in x has units of feet. Therefore, the units for da/dx are pounds per foot squared.

To further explain this, imagine that a(x) represents the weight of a beam that is x feet long. The units for a(x) would be pounds per foot, as it gives us the weight of the beam per unit of length. The derivative of a(x), or da/dx, would give us the rate at which the weight of the beam changes as we increase its length by one foot.

This rate of change would be in units of pounds per foot squared, as we are dividing the change in weight (pounds) by the change in length (feet squared).

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The radius of the pool is 9.01 m.

Given,

In the question:

A circular pool is surrounded by a brick walkway 3 m wide.

The area of the walk- way is 198 m^2.

To find the Radius of the pool.

Now, According to the question:

"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".

Let R = Radius of the pool

Area of the circle bounded by the outside edge of the walkway is:

\(\pi\)(R +3)^2

Area of the pool is:

\(\pi R^2\)

Now, Our equation is:;

\(\pi\)(R +3)^2 - \(\pi R^2\) = 198

\(\pi\)((R+3)^2 - \(R^2\)) = 198

Open the inner bracket :

\(\pi\)(\(R^2+6R+9-R^2\)) = 198

\(\pi\)(6R +9) = 198

6R+9 = 198/\(\pi\)

6R = 198/\(\pi\) - 9

R = (198/\(\pi\) - 9)/6

R = (198/(3.14) - 9)/6

R = (63.057 - 9)/6

R = 54.057/6

R = 9.01 meters

Hence, The radius of the pool is 9.01 m.

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The measure of an angle that is coterminal with a 135° angle is 495°.

Coterminal angles are angles that share the same initial and terminal sides, meaning that they differ by a multiple of 360°.

Therefore, to find an angle that is coterminal with 135°, we need to add or subtract multiples of 360° until we get an angle within the given range.

Here, we have the following options:135° + 360° = 495° (this is the smallest positive angle that is coterminal with 135°)135° - 360° = -225° (this is a negative angle that is coterminal with 135°)Since we are given a list of positive angles as answer choices, the correct answer is 495°.

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For a symmetric distribution, the left whisker extends from the median to the minimum value in the dataset.

The left whisker represents the lower values or the lower tail of the distribution. It is also referred to as the "lower whisker" or the "whisker on the left side". The length of the left whisker may vary depending on the spread or range of the data.

In a box plot or box-and-whisker plot, the left whisker represents the lower values or the lower tail of the distribution. It indicates the range of values that lie below the median. The length of the left whisker is determined by the spread or range of the data.

If the data has a smaller range and is more tightly clustered around the median, the left whisker will be shorter. This indicates that the lower values in the dataset are relatively close to the median. On the other hand, if the data has a larger range and is more spread out, the left whisker will be longer. This suggests that the lower values in the dataset are more dispersed or spread out from the median.

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The percentage change in the index for the period from T to T+1 is 42.85%

Sum of the price of the shares of period T

= 60 + 20 + 18

= 98

Number of shares = 3

For the T period of time = Sum of the price of the shares of period T / Number of shares

Substitute the values in the equation

For the T period of time = 98 / 3

= 32.67

Sum of the price of the shares of period T+1

= 80 + 35 + 25

= 140

Number of shares = 3

For the T+1 period of time = Sum of the price of the shares of period T+1 / Number of shares

Substitute the values in the equation

For the T+1 period of time =  140/ 3

= 46.67

The percentage change = [(46.67 - 32.67) / 32.67] × 100

= (14/32.67)×100

= 42.85 %

Therefore, the percentage change is 42.85%

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The given question is incomplete, the complete question is

You are given the following information regarding prices for a sample of stocks. construct a price-weighted index for these three stocks, and compute the percentage change in the index for the period from t to t 1. do not round intermediate calculations. round your answer to two decimal places.

The dimensions of a norman window of maximum area if the total perimeter is 14 feet are 2 ft and 4 ft respectively.

Given:

a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window

we are asked to  find the dimensions of a norman window of maximum area if the total perimeter is 14 feet.

the area of the semicircle is given by:

A = πr²/2

The area of the rectangle is just the product of its length and width.

Letting A be the area of the window and adding the two ares, we have:

A = xy + π(y/2)²/2

= xy + π(y²/4)/2

= xy+πy²/8

we know the circumference = πd

the circumference of a semicircle is half of that. The perimeter of a rectangle is the sum of twice the length and twice the width. However, one of the sides is replaced by the semicircle, so we remove it from the equation.

Hence, we have the following equation for the perimeter.

14 = 2x+y+πy/2

let us isolate x from this equation

14 = 2x+y+πy/2

14-y-π/2 = 2x

x = 7-y/2-πy/4

substituting x to the equation for the area, w have:

A = xy + πy²/8

= (7 - y/2 - πy/4)y + πy²/8

= 7y - y²/2 - πy²/4 + πy²/8

= 7y - y²/2 - 2πy²/8 + πy²/8

= 7y - y²/2 - πy²/8

differentiating A with respect to x.

A = 7y - y²/2 - πy²/8

A' = 7 - y - πy/4

⇒ 7 - y - πy/4 = 0

⇒ 28 - 4y - πy=0

⇒ 28 = 4y+πy

⇒ 28=(4+π)y

⇒ y = 28/4+π ≈ 4 ft

perimeter:

14 = 2x+y+πy/2

14 = 2x + 28/4+π + π(28/4+π)/2

14(8+2π)=2x(8+2π)+28(2)+28π

112+28π = 16x+4πx+56+28π

112-56=16x+4πx

56=(16+4π)x

x=56/16+4π

= 14/4+π

x=14/4+π≈ 2 ft.

Hence the dimension are 2 ft and 4 ft.

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Answer: 65.4

V = pi r^2 h/3

V = pi (2.5^2) (10/3)

V = pi (6.25) (3.33)

V = 65.4

Answer:

\(v = \pi {r}^{2} \frac{h}{3} = {2.5}^{2} \times 3.14 \times \frac{10}{3} = 65.416\)

Answer:

¼ of the students

Step-by-step explanation:

½×20 = 10

½ × 10 = 5

\( \frac{5}{20} = \frac{1}{4} \)

<3

Answer:

\( \frac{1}{4} \)

Step-by-step explanation:

Refer the attachment for explanation

The features correspond to the following functions:

g(x) - maximum value of 1, y-intercept at (0, -3), x-intercepts at (-3, 0) and (-1, 0)

b(x) - minimum value of -4, y-intercept at (0, -3), x-intercepts at (-3, 0) and (1, 0)

Matching the given features to the corresponding quadratic functions:

Function g(x) = x² - 4x - 3:

- Maximum value of 1

- y-intercept at (0, -3)

- x-intercepts at (-3, 0) and (-1, 0)

Function b(x) = x² + 6x - 5:

- Minimum value of -4

- y-intercept at (0, -3)

- x-intercepts at (-3, 0) and (1, 0)

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Answer:

20:12

Step-by-step explanation:

\(5:3 = \frac{5}{3} \\ 20:12 = \frac{20}{12} = \frac{5}{3} \\ = 5:3\)

Answer:

20:12

Step-by-step explanation:

20divided by 4is 5

12 divided by 4 is 3

Answer:

25

Step-by-step explanation:

f(x)= 3x-5

Let x= 10

f(10)= 3*10-5

     = 30-5

     = 25

Answer:

39.4

Explanation:

Given the expression

9.85 × s

We are to find the equivalent value if s = 4

Substitute;

9.85 × s

= 9.85 × 4

= 9.85 × 2 * 2

= 19.7*2

= 39.4

Hence the value of the expression when s = 4 is 39.4

The correct choice is within your skills and abilities.

Once you get to determine things you are capable of and things you are not capable of, you will be able to concentrate on your strengths more. This will in turn produce big results as compared to if you opted to concentrate on your weaknesses.

It will also result in no or less time wasted in doing what you are less capable of.

Its almost close to impossible to be able to do everything. Each person is gifted in a certain area or skill or capability. We are all different and that's okay.

Its so important to concentrate in the areas you are more comfortable with. This will help you much with improving your skills and abilities.

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Answer:

Step-by-step explanation:

a you just had to say a

Answer:

3

Step-by-step explanation:

A simple way to solve this is by substituting, we start with trying 1 for x, 2+6=8, and 1+9=10. Because the two values are different, that means 1 is the incorrect value. We can try 2, 4+6=10, and 2+9=11, once again inequivalent. We finally try 3, and 6+6=12 and 3+9=12 meaning x must be 3