In what kind of an event does a choice made for one decision affect the choices available for
the other decisions?

The transformation of f(x) to g(x) would be 6 units upwards

To transform f(x) to g(x), the equation is; g(x) = f(x) + 6

We are told that f of x passes through 1, 3 and 3, 13, and g of x passes through negative 1, 3 and 1, 13.

f(x) passes through (1,3) and (3, 13).

Thus;

slope is; m =  (13 - 3) / (3 - 1) = 10/2 = 5

y-intercept is; b = y - mx

Thus;

b = 3 - 5*1 = -2

Equation of the line is;

f(x) = 5x - 2

g of x passes through negative 1, 3 and 1, 13. Thus, the slope is;

m = (13 - 3) / (1 + 1) = 10/2 = 5

y-intercept is; b = y - mx

Thus;

b = -1 - (5)(-1)

b = 4

Equation of the line is; g(x) = 5x + 4

part A: The transformation of f(x) to g(x) would be 6 units upwards

part B: k = 6

part C: To transform f(x) to g(x), the equation is;

g(x) = f(x) + k

g(x) = f(x) + 6

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By direct evaluation, we will see that the limit is equal to 29.

Here we want to find the limit of the given expression when x tends to 5.

[tex]\lim_{x \to \ 5} x^2 + 4[/tex]

We can directly evaluate the expression in x = 5 and see if we get a real value different than zero.

By direct evaluation, we get:

[tex]\lim_{x \to \ 5} x^2 + 4 = 5^2+ 4 = 29[/tex]

Notice that the limit does give a whole number, then in this way, we conclude that the limit of the given expression when x tends to 5 is equal to 29.

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Answer:

square 29

Step-by-step explanation:

Answer:

4 : 25

Step-by-step explanation:

given 2 similar figures with linear ratio a : b , then

ratio of areas = a² : b²

here the linear ratio = 2 : 5 , then

area ratio = 2² : 5² = 4 : 25

The amount of water that will serve the entire container exists 3/10 gallons.

An expression exists a sentence with a minimum of two numbers or

variables and at least one math function.

Given: 1 over 5 gallons of water serve 2 over 3 of the container.

(1/5) gallon / (2/3) container = x gallons / 1 container

cross-multiplying the above equation, we get

1/5 = (2/3)x

multiply both sides by the reciprocal of 2/3 = 3/2

(3/2) (1/5) = x = 3/10 gallons serve the total container

Each 1/10 of a gallon serve 1/3 of the container

So 3(1/10) gallons serve 3(1/3)bins

3/10 gallons serve a whole container.

The amount of water that will serve the entire bin container exists 3/10 gallons.

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Answer:

[tex]r =\bf 8 \space\ cm[/tex]

Step-by-step explanation:

The formula for volume of a cylinder is as follows:

[tex]\boxed{Volume = \pi r^2 h}[/tex]

where:

• r = radius (? cm)

• h = height (7 cm).

Substituting the values into the formula:
[tex]448 \pi = \pi \times r^2 \times 7[/tex]

Now solve for [tex]r[/tex]:

⇒ [tex]r^2 = \frac{448 \pi }{\pi \times 7}[/tex]

⇒ [tex]r = \sqrt{64}[/tex]

⇒ [tex]r =\bf 8 \space\ cm[/tex]

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

Given:

[tex]\longrightarrow\sf{V= \pi r^2 h}[/tex]

[tex]\longrightarrow\sf{448 \pi= \pi r^2 \cdot 7}[/tex]

[tex]\longrightarrow\sf{448=

7r^2}[/tex]

[tex]\longrightarrow\sf{r^2= \dfrac{448}{7} }[/tex]

[tex]\longrightarrow\sf{r^2=64}[/tex]

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

[tex]\longrightarrow\sf{r= 8cm}[/tex]

Answer:

..........................................

Answer:

6.15555555556

Step-by-step explanation:

the 5 is infinite in 6.15 such as 6.155555555 it does not stop 

Answer:

11/24 ths each

Step-by-step explanation:

Add the portions left...then divide by the five of them

3/4 + 5/8 + 11/12  = ?      must find common denominator (24) and convert

(18 + 15+22) / 24 = 55/24  now divide by 5 (which is the same as mult by 1/5)

55/24 * 1/5 = 55/120     now simplify to 11/24

Answer:

Option (1)

Step-by-step explanation:

We need a recursive formula.

The common ratio is 2.

So, the answer is option 1.

Answer:

There are two solutions:  
x = 0, y = -3  Point (0, -3)
x = 3, y = -6  Point (3, 6)

The solutions are at the intersections of the two individual graphs corresponding to each of the two equations (see attached figure)

Step-by-step explanation:

Use a graphing calculator or tool to plot each equation. The point of intersection of the two is the solution to the system of equations. See attached image

Algebraically

The first equation must be equal to the second equation for a unique value of y and x

[tex]y = x^2 - 3 = 3x -3\\x^2 - 3 = 3x - 3[/tex]

Subtract 3x - 3 from both sides giving

[tex]x^2 - 3 - (3x -3) = 0\\x^2 -3 -3x + 3 = 0\\x^2 - 3x = 0\\[/tex]

Factoring out x we get
[tex]x(x-3) = 0[/tex]

This means that x = 0 and also
x -3 = 0, or x = 3

Substituting for x = 0 in y = 3x-3 gives
y = 3.0 - 3 = -3
So x= 0, y = -3 is one solution (0,-3)

Substituting for x = 3 in the same equation gives
y = 3(3) - 3 = 6
So x = 3, y = 6 is another solution (3, 6)

Answer: А=480.

Step-by-step explanation:

Inverse variation is the relationship that occurs between two quantities in which one decreases as the other increases.

The types of variation which exists are;

For instance;

The relationship between John's speed and distance is inversely proportional. If John's speed is 5km/h, his distance is 6km. Find John's distance when his speed increases to 6km/h.

s = k / d

where,

k = constant of proportionality

s = k / d

5 = k/6

30 = k

s = k / d

6 = 30/d

6d = 30

d = 30/6

d = 5 km

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[tex]\sum^{\infty}_{n=1} (a/b)^n=5 \\ \\ =\frac{a/b}{1-\frac{a}{b}}=5 \\ \\ \frac{a}{b-a} =5 \\ \\ \frac{a}{b}=\frac{5}{6}[/tex]

So, we need to find

[tex]\sum^{\infty}_{n=1} n(5/6)^n

[/tex]

Let this sum be S.

Then,

[tex]S=(5/6)+2(5/6)^2 +3(5/6)^3+\cdots \\ \\ \frac{5}{6}S=(5/6)^2 + 2(5/6)^3+\cdots \\ \\ \implies \frac{1}{6}S=(5/6)+(5/6)^2+(5/6)^3+\cdots=5 \\ \\ \implies S=\boxed{30}[/tex]

Answer:

5/12a + 1/3b

Step-by-step explanation:

2/3a + 1/6b + (-1/6a) + 3/18b + (-1/12a)

[2/3a + (-1/6a) + (-1/12a)] + [3/18b + 1/6b]

5/12a + 1/3b

The probability that a student chose football given that they like watching sports is: c. 0.27.

Using this formula

P[Like (Football)/Like (Sport)]

Where:

P=Probability

Like (Football)=0.23

Like (Sport)=0.23+0.18+0.26+0.17=0.84

Let plug in the formula

P[Like (Football)/Like (Sport)]=0.23/0.84

P[Like (Football)/Like (Sport)]=0.27

Therefore the probability that a student chose football given that they like watching sports is: c. 0.27.

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Answer:

C.

Step-by-step explanation:

The line is parallel to y axis

We know that if a line is parallel to y axis

So there is no slope

Here it has constant x value as -2

So the equation is

Option A

Answer:

x = -2

Step-by-step explanation:

The line is crossing the x-axis at -2, The graph is attached

Since it is identical to the graph given in the problem, x=-2 is the correct answer

The given equation, x.cosec²x = cot x - d/dx x.cot x, is proved using the product rule of differentials.

In the question, we are asked to show that x.cosec²x = cot x - d/dx x.cot x.

To prove, we go by the right-hand side of the equation:

cot x - d/dx x.cot x.

We solve the differential d/dx using the product rule, according to which, d/dx uv = u. d/dx(v) + v. d/dx(u), where u and v are functions of x.

cot x - {x. d/dx(cot x) + cot x. d/dx(x)}

= cot x - {x. (-cosec²x) + cot x} {Since, d/dx(cot x) = -cosec²x, and d/dx(x) = 1}

= cot x + x. cosec²x - cot x

= x. cosec²x

= The left-hand side of the equation.

Thus, the given equation, x.cosec²x = cot x - d/dx x.cot x, is proved using the product rule of differentials.

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Answer:

$279.25

Step-by-step explanation:

Multiply 6.50x43

[tex]w = 279.50 + (0.5 \times 6.50) \times (43 - 40)[/tex]

Multiply 0.5x6.50

[tex]w = 279.50 + 3.250 \times (43 - 40)[/tex]

Add 43-40

[tex]w = 279.50 + 3.250 \times 3[/tex]

Multiply 3.250x3

[tex]w = 279.50+ 9.750[/tex]

Solution

The image on the left represents a function. The image on the right does not as a function cannot have multiple variables for a single X quantity.

Answer: A

Step-by-step explanation:

[tex](-5,3)\\(-3, 1)\\(-1,-1)\\(1, -1)\\(3, 1)\\(5, 3)[/tex]

The answer is 114.5%.

Let the original population be denoted by x.

Now, let's go through the percentage increase per year.

Year 1

Year 2

Year 3

Year 4

Overall increase : 214.5% - 100% = 114.5%

Hence, the overall percentage increase in these 4 years is 114.5%.

If the data is symmetrical, then the mean is the best measure of central tendency to use, and the standard deviation is the best spread to use.

If the data is asymmetrical, the median is the best measure of central tendency to use, and the inter-quarterly range is the best spread to use.

A histogram for symmetrical data will give a symmetrical shape, and the mean, median and mode will all be the same value. Therefore, the best measure of the central tendency to use is the mean. The standard deviation shows how far away the values in a given data set are from the mean, and since the mean is used as the measure of central tendency in this case, the standard deviation should be used as the spread.

A histogram for a an asymmetric data set will give an asymmetric shape, and the mean is not always equal to the median. Therefore, the best measure of central tendency to use is the median. The inter-quarterly range shows the range of the middle 50% of a certain data, which is considered from the median value. Since the median is used as the measure of central tendency in this case, it is wise to use the inter-quarterly range as the measure of spread.

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Answer:

see explanation

Step-by-step explanation:

(a)

let the two consecutive odd integers ne n and n + 2 , then

n + 2(n + 2) = 85

n + 2n + 4 = 85

3n + 4 = 85 ( subtract 4 from both sides )

3n = 81 ( divide both sides by 3 )

n = 27

n + 2 = 27 + 2 = 29

the 2 consecutive odd integers are 27 and 29

--------------------------------------------------------------------

(b)

let the first integer be n , then 2nd integer is 3n and 3rd is 3n + 5 , so

n + 3n + 3n + 5 = 40

7n + 5 = 40 ( subtract 5 from both sides )

7n = 35 ( divide both sides by 7 )

n = 5

3n = 3 × 5 = 15

3n + 5 = 15 + 5 = 20

the 3 integers are 5, 15, 20

Answer:

a7=4/3 or a7=-4/3

Step-by-step explanation:

using the geometric sequences formula

an=ar^n-1

a2=ar

a4=ar³

when a2=324 and a4=36

324=ar...........(1)

36=ar³............(2)

from equation (1) a=324/r substitute in equation (2)

we have :

36=324/r *r³

36=324r²

r²=36/324

r²=1/9

r=±1/3

substitute when r=±1/3 in (1)

324=a(±1/3)

a=±972

so the 7th term is

when r=±1/3

we have

a7=ar^6

a7=±972(±1/3)^6

a7=972/729

a7=4/3 or a7=-4/3

By 15% percent does the population of weeds decrease each day given that the function representing the number of weeds is W(d)=1650(0.85)^d. This can be obtained by using the function representing the exponential decay.

Number of weeds is represented by the function,

W(d)=1650(0.85)^d

⇒ W(d)=1650(1 - 0.15)^d

Here, d = number of days since application

Function representing the exponential decay is,

⇒ A(r) = A(1 - r)^t

where,

A = Initial value

r = Percentage decay

t = duration

By comparing the given function and function representing the exponential decay,

r = 0.15 ≈ 15/100

Or r = 15%    

Therefore, population of weeds will decrease 15% each day.

Hence by 15% percent does the population of weeds decrease each day given that the function representing the number of weeds is W(d)=1650(0.85)^d.

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Answer:  [tex]h(\text{x}) = -4\text{x}^2 - 6\text{x} + 6[/tex]

Work Shown:

[tex]h(\text{x}) = f(\text{x}) - g(\text{x})\\\\h(\text{x}) = ( 8\text{x}^2 - 2\text{x} + 3) - ( 12\text{x}^2 + 4\text{x} - 3 )\\\\h(\text{x}) = 8\text{x}^2 - 2\text{x} + 3 - 12\text{x}^2 - 4\text{x} + 3 \\\\h(\text{x}) = (8\text{x}^2-12\text{x}^2) + (- 2\text{x} - 4\text{x}) + (3 + 3) \\\\h(\text{x}) = -4\text{x}^2 - 6\text{x} + 6 \\\\[/tex]

Answer:

You can count how many boxes that are not shaded to find how many eggs were not used, but that's to find out the fraction

Step-by-step explanation:

Count the boxes total in the grid. then count the number of boxes were not shaded. the number of total boxes is your denominator, and the number of boxes thar aren't shaded is your numerator.

I think...

Answer:

110 degrees

Step-by-step explanation:

to find the angle x, we need to use the formula to find the 50 degree angle:

(y - x) / 2 = 50

y is 210

(210 - x) /2 = 50

210-x = 100

x = 110 degrees