Which graph represents the function f(x) =4·3^x​

Answer:

3

Step-by-step explanation:

Range: 19

Interquartile range: 6.5

Variance: 44.86

Standard deviation: 6.70

Given set:

27, 25, 20, 15, 30, 34, 28, 25.

(i) Range is the difference between the largest value and smallest value in a given data.

In the data above, the;

largest value = 34

smallest value = 15

Range = largest - smallest

Range = 34 - 15

Range = 19

(ii) Interquartile range is the difference between the median (Q₁) of the lower half of the given data, and the median (Q₃) of the upper half of the given data. i.e Q₃ - Q₁.

This should be done after ordering the given data in ascending order.

Ordering the above data gives:

15, 20, 25, 25, 27, 28, 30, 34

In the data above;

lower half = 15, 20, 25, 25

upper half = 27, 28, 30, 34

Find median (Q₁)  of the lower half

Since there are even number of data, the median is the average of two middle numbers (20 and 25) i.e.

Q₁ = [tex]\frac{20+25}{2}[/tex] = [tex]\frac{45}{2}[/tex] = 22.5

Find median (Q₃)  of the upper half

Since there are even number of data, the median is the average of two middle numbers (28 and 30) i.e.

Q₃ = [tex]\frac{28+30}{2}[/tex] = [tex]\frac{58}{2}[/tex] = 29

Interquartile range = Q₃ - Q₁

Interquartile range = 29 - 22.5

Interquartile range = 6.5

(iii) Variance is the measure of variability of a given set of data. It is calculated by following these steps:

=> First find the mean of the data by summing the numbers and dividing by the number of numbers. i.e

mean(x) = [15 + 20 + 25 + 25 + 27 + 28 + 30 + 34] / 8

mean(x) = [204] / 8

mean(x) = 25.5

=> Next, get the mean deviation by subtracting the mean from each individual value in the given set of data. i.e

15 - 22.5 = -7.5

20 - 22.5 = -2.5

25 - 22.5 = 2.5

25 - 22.5 = 2.5

27 - 22.5 = 4.5

28 - 22.5 = 5.5

30 - 22.5 = 7.5

34 - 22.5 = 11.5

=> Next, find the square of each of the results obtained above. i.e

(-7.5)² = 56.25

(-2.5)² = 6.25

(2.5)² = 6.25

(2.5)² = 6.25

(4.5)² = 20.25

(5.5)² = 30.25

(7.5)² = 56.25

(11.5)² = 132.25

=> Next, add all the results above together as follows;

56.25 + 6.25 + 6.25 + 6.25 + 20.25 + 30.25 + 56.25 + 132.25 = 314

=> Now, obtain the variance by dividing the result above one less than the number of numbers.

The number of numbers is 8. One less than this gives 7.

Therefore,

Variance = 314 / 7

Variance = 44.86

(iv) Standard deviation is the measure of how the numbers in the given data are spread out. It is calculated as the square root of variance.

Therefore,

Standard deviation = √variance.

Variance has been calculated above.

Standard deviation = √44.86

Standard deviation = 6.70

Answer:

108.75km

Step-by-step explanation:

please find attached the diagram

total displacement can be determined by using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

length of x =

20² + 40²

= 400 + 1600

2000

square root of 2000

= 44.72km

length of y

40² + 50²

1600 + 2500 = 4100

square root of 4100

64.03km

total displacement = 44.72 + 64.03 = 108.75

Answer:

F. (x, y) = (-y, x)

Step-by-step explanation:

270º clockwise transformation:

The 270° clockwise transformation of a point (x,y) is:

(x,y) -> (-y,x)

Thus, as we just apply the rule in this conceptual question, the correct answer is given by:

F. (x, y) = (-y, x)

Answer:

good luck always brings luck the answer is 12

Step-by-step explanation:

Answer:

11 patients were satisfied with neither and 23 patients were satisfied with only the medical treat

Step-by-step explanation:

trust me i'm Asian

Answer:

3. (-48) devide 48 = -1 class 7th Chapter integer

The answer is : -1

Answer:

Its D

Step-by-step explanation:

Its D because each one is multiplied by 16

Answer:

The sum of x and y is a rational number.

Step-by-step explanation:

-5 + -4 = -9

-9 is a rational number

Answer:

[tex]\sqrt[12]{8} ^x[/tex]

Step-by-step explanation:

[tex]3 / \frac{1}{4} = 12[/tex]

Answer:

We will split the trapezoid into right angle triangle and rectangle

Traingle with base 3cm and height 10 - 6 = 4cm

Area of traingle

       = [tex]\frac{1}{2}*base *height = \frac{1}{2} * 3 * 4 = 6cm^{2}[/tex]

Area of rectangle with sides 6cm and 3cm

       =[tex]6 * 3 = 18cm^{2}[/tex]

Therefore, area of the trapezoid

       = [tex]6+18 = 24cm^{2}[/tex]

Area of the semi circle with radius 3/2 = 1.5cm

        = [tex]\frac{1}{2}\pi r^{2} = \frac{1*\pi *1.5*1.5}{2} = 1.125\pi cm^{2}[/tex]

[tex]Total area = 24 + 1.125\pi =27.53cm^{2}[/tex]

Answer:

4

Step-by-step explanation:

To find the common ratio, take the second term and divide by the first term

24/6 = 4

Check by taking the third term and dividing by the second term

96/24 = 4

The common ratio is 4

Answer:

12

Step-by-step explanation:

12 is 75 of 15 %^%^%^%^^^___<<<7<

Answer:

- 13

Step-by-step explanation:

[tex]log \frac{ {a}^{6} {b}^{6} }{ {c}^{7} } \\ \\ = log( {a}^{6} {b}^{6} ) - log {c}^{7} \\ \\ = 6log \: a + 6log \: b - 7log \: c \\ \\ = 6(2) + 6( - 3) - 7(1) \\ \\ = 12 - 18 - 7 \\ \\ \therefore \: log \frac{ {a}^{6} {b}^{6} }{ {c}^{7} } = - 13[/tex]

Answer: 100

Explanation: triangle area is l x h ÷ 2 rectangle area is l x h. 4 x 3 =12÷2 +12÷2 =12 11x4x2= 88 88+ 12=100.

The 3 inside angles of a triangle need to equal 180 degrees.

Add the 3 together to equal 180:

X + 2x + x+ 14 = 180

Combine like terms:

4x + 14 = 180

Subtract 14 from both sides:

4x = 166

Divide both sides by 4

X = 41.5

Answer:

Fraction form: x = 83/2

Decimal form: x = 41.5

Step-by-step explanation:

The 3 angles inside the triangle will always add up to 180 degrees.

So that gives us the equation:

x + 14 + x + 2x = 180

Combine like terms:

4x + 14 = 180

Subtract on both sides:

4x = 166

Divide:

41.5

Answer:

Step-by-step explanation:

let the numbers be x and y,then

x+y=18

x=18-y

also xy=-63

(18-y)y=-63

18y-y²=-63

y²-18y-63=0

y²-21y+3y-63=0

y(y-21)+3(y-21)=0

(y-21)(y+3)=0

y=21,-3

when y=21

x=18-21=-3

when y=-3

x=18-(-3)=18+3=21

so numbers are -3 and 21.

Answer:

36

Step-by-step explanation:

The numbers given represent an arithmetic series with a common difference of -5. The formula to find the nth term of an arithmetic sequence is:

a + (n - 1)d

where a is the first term and d is the common difference. We can substitute our values in:

261 + (46 - 1)(-5)

261 + (45)(-5)

261 + (-225)

36

Answer:

36

Step-by-step explanation:

Have a good day :)

Answer: 6 pounds

Step-by-step explanation:

Answer:

The mini fish would weigh 6 times its original amount hypothetically but if we were talking realistically then you would need more information to figure that out. But even then there's no way of determining the specific weight.

Step-by-step explanation:

Answer:

t = 4 seconds

Step-by-step explanation:

The height of a soccer ball as a function of time is given by :

[tex]h(t)=-16t^2+48t+64[/tex]

We need to find the time when the ball hit the ground i.e. h = 0

Put h = 0 in above equation. So,

[tex]-16t^2+48t+64=0\\\\16(-t^2+3t+4)=0\\\\-t^2+3t+4=0[/tex]

It is a quadratic equation such that,

t = -1 s and t = 4 s

Neglecting -1 s, the ball will hit the ground after 4 seconds.

Answer:

(-∞,0)

Step-by-step explanation:

The graph of ƒ(x) = |x| is below.

The function is decreasing  on (-∞,0) .

A is wrong. The function both decreases and increases on (-∞,∞).

C is wrong. The function is decreasing on (-6,0), but that is only a portion of the interval.

D is wrong. the function is increasing on (o,∞)

Answer:

A. Translate 1 to the right, reflect over the x-axis, then scale vertically by a factor of 1

Step-by-step explanation:

Initially:

We have the function [tex]y = k(x)[/tex]

k(x + 1)

To translate a function k(x) a units to the left, we find k(x + a).

Thus, k(x+1) is the translation of k(x) 1 unit to the left.

-k(x+1)

Multiplying a function by a negative constant is the same as reflecting it over the x-axis, and then scaling it vertically by a factor of the constant.

Thus:

The answer is given by option A:

A. Translate 1 to the right, reflect over the x-axis, then scale vertically by a factor of 1

Answer:

7

Step-by-step explanation:

9 - 2 = 7

7 + 9 = 16

Mark as Brainliest

Answer:

200

Step-by-step explanation:

41 x 5 = 205

20% x 5 = 100%

Answer:

B

Step-by-step explanation:

-x - 1 = x^2 + x

x^2 + 2x + 1 = 0

(x+1)(x+1) = 0

x = -1 (double soution)

y = 1-1 =

y =0

(-1,0) = double solution